Experimental analysis of additive manufacturing parameters on the dynamic response of ABS components

Additive manufacturing has been extensively studied under quasi-static load conditions; however, limited research exists on the dynamic response of these printed components, particularly in relation to the influence of manufacturing parameters. This study addresses this critical knowledge gap by investigating the dynamic behavior of Acrylonitrile Butadiene Styrene (ABS) components fabricated via 3D printing. Specifically, the effects of six key printing parameters on the natural frequency and damping ratio of the specimens were systematically analyzed. Using modal analysis based on impulse excitation tests, conducted in accordance with ASTM E1876-22, the study provides robust experimental evidence and insights into the dynamic characterization of printed components. The natural frequency, with results ranging from 72 to 92 Hz, increases with reduced infill density and fewer perimeter walls, while it decreases with a reduction in top and bottom layers. Conversely, the damping ratio, with results ranging from 2.2% to 6% was found to increase significantly with lower print bed temperatures, reduced infill density, and fewer perimeter walls. Notably, specific combinations of parameters were identified to optimize damping performance under dynamic loading conditions. This research contributes novel experimental data and a deeper understanding of the interplay between 3D printing parameters and dynamic mechanical properties, offering a valuable framework for the design and optimization of AM components for dynamic applications.

Additive Manufacturing (AM) has experienced substantial growth in recent years, driven by its ability to fabricate components with complex geometries at reduced costs, its broad spectrum of processable materials, and its efficient use of resources. These characteristics enable rapid prototyping and a high degree of product customization in industrial production. Among these techniques, material extrusion (ISO-ASTM, 2021), commercially known as Fused Deposition Modeling (FDM), remains the most widely adopted due to its versatility and accessibility.

Fused Deposition Modeling (FDM) stands out for its accessibility, low cost, and compatibility with a wide variety of thermoplastic polymers. This technique involves the extrusion of molten filaments layer by layer. Some of the most commonly used materials in FDM include polylactic acid (PLA), polycarbonate (PC), nylon (PA), polyethylene terephthalate glycol (PETG), and acrylonitrile butadiene styrene (ABS), each offering unique mechanical and thermal properties that make them suitable for diverse applications.

Acrylonitrile Butadiene Styrene (ABS) is a commonly used amorphous thermoplastic in industry, renowned for its impact resistance, hardness, thermal stability, chemical resistance, and overall excellent mechanical properties. These characteristics make ABS a material widely employed in components for aircraft, automobiles, and other vehicles. Currently, injection molding is the preferred method for manufacturing ABS parts, which presents an opportunity for additive manufacturing to produce lighter components without compromising strength. This is particularly critical in aerospace applications, where specific strength (i.e., the strength of a component relative to its density) plays a fundamental role (Singh et al., 2020; Khan and Kumar, 2020; Zhou, 2021; Selvamani et al., 2059; Algarni and Ghazali, 2021).

Although the quasi-static response of PLA components manufactured by FDM has been extensively characterized (Singh et al., 2020; Zhou, 2021; Cuan-Urquizo et al., 2019; Singh et al., 2022; Hsueh et al., 2021), investigations into their dynamic performance have only recently emerged; for instance, Ficzere et al. have found that build orientation and internal infill structures significantly affect the resonant frequencies, although limited in the amount of process parameter combinations and not looking into loss factors or mechanisms (Ficzere and Borbas, 2019); similarly, the work of Oteyaka et al. evaluated the effects of infill pattern and density on the flexural properties and vibration damping, finding that infill density directly relates to vibration attenuation, with specific patterns providing a higher energy dissipation. However, Oteyaka et al. focused solely on PLA specimens under fixed environmental and boundary conditions (Öteyaka et al., 2022).

Another example of recent studies focusing on the dynamic performance of FDM printed specimens is the work developed by Medel et al. whose primary focus was examining the relationship between additive manufacturing parameters, stiffness and material damping capabilities. This work showed that damping and natural frequencies are coupled through the mesostructural porosity and layer bonding quality, although their focus was constrained to a set of geometries and testing configurations and did not address non-destructive defect quantification (Medel et al., 2022). Additionally, the work developed by Arunprasath et al. in PLA and ABS components demonstrated distinct viscoelastic transitions and damping regimes across a range of temperatures and frequencies when undergoing Dynamic Mechanical Analysis (DMA) (Arun et al., 2021).

Similarly, research on ABS specimen behavior has expanded (Khan and Kumar, 2020; Selvamani et al., 2059; Algarni and Ghazali, 2021; Ahmad and Yahya, 2023; Vicente et al., 2020; Samykano et al., 2019), as layer-by-layer deposition inherent to FDM introduces structural anisotropy and internal porosity. These features fundamentally alter the stiffness-to-mass ratio and energy dissipation mechanisms, necessitating a more rigorous evaluation of the dynamic properties of these materials.

Vibrations present a significant challenge for structural elements, as they can induce fatigue, resonance-related damage, loosening of bolted connections, excessive noise, and safety risks, particularly in applications such as aircraft cabins. Mitigating vibrations typically involves enhancing damping properties, either through material modifications or structural adjustments. The ability to analyze and predict the dynamic behavior of such elements is critical for improving performance, reducing noise, and ensuring the reliability of components in vibration-prone environments.

Dynamic analysis of ABS polymer structures fabricated via fused deposition modeling (FDM) offers valuable insights into optimizing additive manufacturing techniques as alternatives to traditional methods. Such analyses are essential for identifying factors that influence the safety and performance of printed components, predicting failure modes, and refining manufacturing processes to achieve desired mechanical and dynamic properties.

Vibration analysis is critical for understanding the behaviour of structures and materials under dynamic loads, ensuring their safety, reliability, and performance. This is particularly important in systems where uncontrolled vibrations can lead to structural failures, reduced lifespan, inefficiencies, or issues such as resonance, fatigue, and noise (Coca-Gonzalez et al., 2022; Brandt, 2023). In this context, recent advances in additive manufacturing have facilitated novel passive attenuation strategies; for instance, embedding 3D-printed mechanical metamaterials into robotic arms has been shown to effectively mitigate end-effector vibrations while preserving static structural integrity (Fayyaz et al., 2026), and tailoring cellular metamaterial morphologies has demonstrated superior damping and dynamic energy dissipation compared to conventional solid designs (Fayyaz et al., 2025). However, these investigations focus primarily on large-scale geometry and simulation models, without isolating how core print parameters change a material’s internal damping. Investigating these manufacturing variables is crucial to creating more accurate design guidelines and stronger, safer components.

Experimental vibration analysis, which complements theoretical models, is essential for mitigating design risks. It can be performed through two primary approaches: measuring responses under normal operating conditions or under controlled excitation forces. The latter, known as Modal Analysis, offers greater precision by characterizing dynamic properties such as natural frequencies, damping ratios, and mode shapes (Rao, 2017; Inman, 2013; Ewins, 1997). As highlighted by Ewins (Ewins, 1997), accurate vibration analysis requires a solid foundation in vibration theory, carefully controlled experimental conditions, and rigorous data interpretation to ensure reliable results.

While previous investigations have primarily focused on isolated parameters in PLA specimens or relied on micro-scale forced dynamic tests, this study addresses these gaps by systematically evaluating the coupled effects of six key FDM processing variables on the dynamic response of engineering-grade ABS. Utilizing a standardized impulse excitation approach under free-free nodal support (ASTM E1876), this work captures full-scale modal parameters and provides predictive optimization models to actively tailor natural frequency and structural damping for targeted dynamic applications.

Specifically, this study investigates the effect of 3D printing parameters on the dynamic response of Acrylonitrile Butadiene Styrene (ABS), with a focus on natural frequency and damping ratio. Grounded in a thorough review of existing literature, six critical process parameters were identified: layer height, number of perimeter walls, infill density, number of top and bottom layers, nozzle temperature, and bed temperature. Given the scarcity of research on the dynamic characterization of 3D-printed components, this work provides valuable experimental insights to close this knowledge gap. The findings reveal that natural frequency is positively correlated with reduced infill density and fewer perimeter walls, but decreases with a reduction in the number of top and bottom layers. Damping behavior, on the other hand, is significantly influenced by lower bed temperatures, reduced infill density, and fewer walls. Notably, the studied parameters collectively explain 94% of the variation in natural frequency, underscoring their critical role in dynamic performance. However, these variables account for only 47% of the variation in damping ratio, highlighting the potential influence of additional, unexplored factors. This research contributes novel insights into the dynamic behavior of 3D-printed ABS components, offering a foundation for future studies and the optimization of additive manufacturing processes for dynamic applications.

To present the study in an organised fashion, the manuscript is structured as follows: Section 2 presents the theory and equations utilised to obtain the calculated data, Section 3 describes the methodology followed to ensure consistency in the results, Section 4 explains the results obtained during the study and discusses possible implications, Section 5 explains the limitations the present study has and Section 6 concludes with the key findings gathered from the study.

Theoretical background

Dynamic analysis is rooted in the study of mechanical vibrations, which are defined as the oscillatory motion of a system around its equilibrium position. In any dynamic system, three primary phenomena are observed: the storage of kinetic energy, associated with system mass or inertia; the storage of potential energy, arising from elasticity; and energy dissipation through damping mechanisms (Rao, 2017; Inman, 2013).

The experimental approach employed in this study is based on the technique described in (Coca-Gonzalez et al., 2022), with modifications for optimization. Specifically, the methodology adheres to the ASTM E1876-22 standard, which outlines procedures for determining dynamic elastic properties—such as Young’s modulus, shear modulus, and Poisson’s ratio—using impulse excitation of vibration (ASTM, 2022). This method involves applying a controlled impact to a sample supported under free-free conditions, recording its vibrations via a transducer (e.g., microphone or accelerometer), and analyzing the fundamental natural frequency to correlate it with the material’s mechanical properties using validated analytical models. The technique is widely recognized for its simplicity, reproducibility, and applicability to anisotropic materials, including those produced through additive manufacturing (Mezzomo and Gomes de Moraes, 2020).

To ensure accurate results, the support conditions follow the guidance of ASTM E1876-22. This setup emulates the first flexural mode of an Euler-Bernoulli beam, with nodes (zero displacement) located at 0.224L, where the support points are placed, considering that L is the sample length; and antinodes (maximum displacement) at the sample’s centre and ends (ASTM, 2022).

The ASTM standard also explains that either the central or the end antinodes can be used as impulse points and that, for direct contact transducers, placement should be only as far from a node as necessary to obtain a reading (ASTM, 2022). These conditions, as illustrated in Figure 1, are critical for accurately capturing the dynamic response of the material. The present work uses the central antinode as the impulse point and, for the contact transducer point, a small distance from the node to the free end of the sample was established using the displacement envelope shown in Figure 1, shown in red.

It is possible to obtain a theoretical frequency (calculated using the known properties) and compare it with the frequency obtained experimentally to evaluate the validity of the results obtained in subsequent experimental tests. The mentioned equation is defined as follows (ASTM, 2022):

Where E is the Young’s Modulus, m is the specimen’s mass, f f is the fundamental natural frequency, L, t and b are the specimen’s length, thickness and width, respectively, and T 1 is a correction factor that accounts for the finite thickness of the bar.

In equation Equation 1, the correction factor T 1 must be calculated. The standard specifies that if the length/thickness ratio L / t of the specimen is greater than or equal to 20, the calculation of T 1 can be done with the Equation 2 (ASTM, 2022):

In the case of the specimens used for the tests, the ratio is 83.3333.

The theoretical frequency can be calculated from this data by rearranging equation Equation 1 to solve for the fundamental frequency f f (Equation 3), such that:

The logarithmic decrement is a fundamental tool for analyzing damped vibratory systems using signals in the time domain. It quantifies the energy loss per cycle in the system’s free response and is particularly useful in experimental setups where the free damped vibration is recorded after a punctual excitation, such as that produced by an impact hammer.

Mathematically, the logarithmic decrement (δ) is defined as the natural logarithm of the ratio between two successive peaks of the time-domain response separated by a full cycle. It is expressed in Equation 4 (Rao, 2017):

where x (t) and x (t + T) are peaks separated by a period T.

If more than one pair of peaks is available, an average can also be calculated from several non-consecutive cycles Equation 5 so that

where x n and x k + N are peaks separated by N period (Rao, 2017).

A method to obtain the optimal number of separation cycles that minimizes the uncertainty in the calculation of the logarithmic decrement was developed by Little & Mann (Little and Mann, 2019). This previous research describes that when damping is known, it is possible to determine the ideal number of separation cycles, defined mathematically. Furthermore, when damping is unknown, the first amplitude can be taken and multiplied by a proportional value, which is defined through a specific Equation 6 (Little and Mann, 2019).

where x N is the amplitude at the N − t h cycle, x 0 is the amplitude in the first cycle and W 0 (2 e 2) is the function evaluated at 2 e 2 in the Lambert´s W function (Little and Mann, 2019).

The damping ratio (ζ) is a dimensionless parameter that quantifies energy dissipation in a vibratory system. Mathematically, it is defined as the ratio between the actual damping coefficient and the critical damping coefficient (Rao, 2017). Additionally, the damping ratio can be estimated using the logarithmic decrement through the following Equation 7:

The damping ratio can also be estimated using the logarithmic decrement or alternative methods, such as the Half-Power Bandwith Method (as illustrated in Figure 2a) or the Nyquist Circle Method (shown in Figure 2b), also known as the Modal Circle Method; the latter is a graphical technique for estimating the damping ratio from the Frequency Response Function (FRF). In this method, the FRF is plotted in the complex plane (real vs. imaginary components), forming a curve that approximates a semicircle around the resonance frequency. The damping ratio is then determined based on the circle’s geometry, either by measuring the radius and characteristic distances or by applying numerical adjustments using modal analysis software (Rao, 2017; Inman, 2013; Dewesoft, 2023).

This approach is particularly advantageous for isolating individual modes in systems with multiple degrees of freedom or in noisy signals where amplitude measurements may be unreliable. The closed curve in the complex plane provides a robust representation against disturbances. As shown in Figure 2b, the method involves separating the real and imaginary components of the FRF, plotting them in the complex plane, and performing a circular fit near the resonance frequency. This process enables the extraction of modal parameters both graphically and analytically, even in scenarios where modes are closely spaced or noise is present.

It is possible to estimate the resonance frequency f r, using Equation 8 (Dewesoft, 2023):

Here, f A and f B correspond to the frequencies at the points preceding and following the resonance, respectively, while θ A and θ B represent the angles between the radius pointing to the resonance frequency and the preceding and following points, respectively. Once f r is determined, the damping ratio ζ r can be calculated using Equation 9 (Dewesoft, 2023):

This procedure demonstrates that it is possible to obtain precise estimates of damping without analyzing the time-domain response, making it a valuable alternative for the experimental study of complex systems. Together with other methods, such as logarithmic decrement or the −3 dB bandwidth method, it allows for comparison and validation of results from different approaches, depending on the domain of analysis used.

This study builds upon the methodology and dimensions proposed in a previous investigation on composite materials (Coca-Gonzalez et al., 2022), optimizing the technique outlined in the ASTM E1876-22 standard (ASTM, 2022), while accounting for the build volume constraints of the available additive manufacturing equipment. Rectangular specimens with dimensions of 250 mm in length, 15 mm in width, and 3 mm in thickness were selected, complying with the aspect ratio and geometry recommendations of the standard. These dimensions enable the effective implementation of the impulse excitation method, ensuring a clear separation of natural frequencies and emphasizing the fundamental frequency. Additionally, the layer thickness was treated as a variable to assess its influence on the dynamic response, while maintaining the overall geometry of the specimens constant.

The experimental framework is adapted from (Coca-Gonzalez et al., 2022), which evaluated the modal frequencies of glass-fiber-reinforced composites using the impact hammer technique. While that study provided a functional baseline for impulse excitation on elastic supports, this work introduces refinements tailored to additive manufacturing materials to ensure compliance with ASTM E1876-22 (ASTM, 2022).

In this study, six fundamental printing parameters (layer height, infill density, number of perimeter walls, number of top and bottom layers, nozzle temperature and bed temperature), shown in Table 1, were selected for investigation. These variables were chosen because they directly govern the internal structure and the thermal history of the part. Specifically, the interaction between printing temperatures and structural settings is hypothesized to be the primary driver of natural frequency shifts and damping capacity in Acrylonitrile Butadiene Styrene (ABS) specimens. By analyzing these parameters, this work aims to provide experimental evidence that addresses the current gap in the dynamic characterization of 3D-printed components.

The Classification column in Table Table 1 shows the alphabetical identifier of each parameter, where the high and low values become uppercase and lowercase, respectively (i.e., For a high value of 0.2 mm layer height, the identifier is “ A ”, and for a low value of 0.08, the identifier is “ a ”). This classification system is used to abbreviate the parameter combinations used in the factorial experiment matrix, as is shown in Figure 5.

For specimen fabrication via extrusion, white ABS filament from the brand HATCHBOX was used. The Bambu Lab X1C printer (Bambu Lab, Shenzhen, China) was selected as the manufacturing system due to its closed-chamber design, high printing speed, dimensional accuracy, and operational reliability, ensuring controlled and repeatable conditions throughout the experimental process. Prior to printing, the filament underwent a drying process at 80 °C for 8 h to minimize moisture content, which could affect print quality. After printing, the specimens were carefully stored in a moisture-free environment to prevent post-processing degradation. The printing equipment and an example of the slicing process for a batch of specimens are shown in Figure 3.

In order to ensure that the impact hammer tests are performed with the highest possible uniformity and in compliance with the guidelines of standard (ASTM, 2022), an experimental platform was designed and manufactured using PLA with a 100% infill density, complemented by supports made of ABS, also printed with a 100% infill density. This configuration ensures high rigidity and mass in the experimental platform, so that if frequencies are induced during the analysis, they are sufficiently high to avoid interfering with the natural frequency of the specimen. Additionally, this platform was placed on a polyurethane sponge to reduce the influence of frequencies transmitted from the table or the floor to the specimen.

To further minimize potential interference, it is recommended to conduct the tests on a granite surface plate, a material that offers high rigidity and low susceptibility to inducing frequencies during the experiment. The main elements of the experimental setup (Fig.Figure 4) are composed of: Krypton 4xACC (Dewesoft d.o.o., Trbovlje, Slovenia): DAQ used to convert signals from the transducers into data for storage.

The Dytran 3133D1T triaxial IEPE accelerometer (Dytran Instruments Inc., Chatsworth, CA, United States) was used to measure the vibrational response of the specimens. This mini-accelerometer was selected due to its low weight (0.8 g), which represents less than 7% of the mass of the measured components, minimizing its influence on the dynamic behavior of the specimens. To ensure consistent and reliable comparisons, all specimens were instrumented using the same accelerometer throughout the experimental process.

PCB Piezotronics 086C03 (PCB Piezotronics Inc., Depew, NY, United States): Impact hammer used to induce vibration.

To ensure the reliability and statistical robustness of the experimental assessment, five components were manufactured for each variant under identical conditions. For each component, five independent measurements were conducted. This approach was chosen to account for potential variability in the manufacturing process and measurement system, thereby enhancing the accuracy and repeatability of the results. By averaging the measurements for each component and analyzing the overall dataset, potential outliers and inconsistencies were identified and minimized. This comprehensive methodology ensures that the experimental findings are both reliable and representative of the performance of each variant.

In accordance with Nyquist-Shannon sampling theory (Brandt, 2023), the sampling rate was set between 500 and 1000 samples per second, ensuring it exceeded twice the frequency of interest and fell within the ideal range of 5–10 times this frequency. Exploratory tests with ABS specimens determined an average fundamental frequency of approximately 80 Hz, guiding the selection of these rates for accurate data acquisition. The Fast Fourier Transform (FFT) was implemented to enable real-time visualization of frequency content, with a spectral resolution of 1024 lines, established as optimal based on preliminary tests.

The system geometry was defined using four key points: the left support, the impact point, the right support, and the accelerometer reading point, configured according to the accelerometer’s coordinate system for precise alignment. Given the low weight of the specimens (approximately 13 g each), an impact force between two and 5 N was applied in the negative Z direction (vertically downward). A 3% impulse window was defined based on the hammer signal’s duration, while the response signal used the full window, ensuring proper time-domain alignment. For 1024 spectral lines, a processing time of 2.05 s was achieved, balancing temporal and spectral resolution effectively.

Three frequency results were obtained: the first, derived from signal processing through the calculation of the logarithmic decrement (referred to as Calculated); the second, from the frequency response function (FRF) obtained in DewesoftX (FRF); and the third, from the Modal Circle analysis also in DewesoftX (Experimental). The percentage error between the frequencies obtained through calculation and those derived from the FRF was analyzed, resulting in an average error of 0.2965%. Similarly, the calculated frequencies were compared with those obtained through the Modal Circle, yielding an average error of 0.1529%. Since the lowest percentage error corresponds to the comparison between the calculated frequencies and those obtained through the Modal Circle, the latter are considered the experimental reference frequencies.

Figure 5 presents the box-and-whisker plots representing the average frequencies for each experimental combination, corresponding to the Calculated, FRF, and Experimental frequencies. The graphs highlight groupings of combinations with similar frequencies (e.g., groups 1–4, 5–8, and 21–24). These patterns suggest that variables such as nozzle temperature and bed temperature have a minor influence on frequency compared to other factors. The observed frequency range (between 72 Hz and 92 Hz) aligns with values reported in previous studies on ABS specimens, albeit under different experimental conditions (Medel et al., 2022; Funke et al., 2023).

An analysis of variance (ANOVA) was performed to determine the magnitude of the effects of the factors and their interactions. Figure 6 presents the Pareto diagram corresponding to the calculated frequency response, where factors and interactions are ranked in descending order of their impact.

The Layer Height (A) has a barely perceptible effect, and the Bed Temperature (F) does not produce a significant effect on the frequency, according to the generated model. Likewise, the interactions with the greatest effect on the frequency are those associated with layer height, infill density, and the number of top and bottom layers. All these variables directly influence the stiffness of the specimens, both individually and in combination.

To verify that the generated model meets the basic statistical assumptions, the software also generates the corresponding residual plots (Figure 7).

Figure 8 illustrates the effects of the experimental variables: the X-axis represents the minimum and maximum values defined in the experimental matrix, while the Y-axis displays the mean of the Calculated Frequency. Variables with steeper slopes have significant effects on the response, whereas variables with nearly horizontal lines have minimal effects. As the Layer Height (A) increases, the expected frequency decreases: A smaller layer height results in a greater number of global layers, which increases the stiffness of the specimen and consequently raises the frequency.

As the Number of Walls (B) increases, the expected frequency decreases: A greater number of perimeter walls reduces the space available for low-density infill, thereby decreasing the stiffness of the specimen and lowering the frequency.

With lower Infill Density (C), the frequency increases: Higher infill density reduces the size of the cells within the specimen, leading to lower stiffness and consequently reducing the frequency.

With fewer Top and Bottom Layers (D), the frequency decreases: A greater number of top and bottom layers reduces the effective amount of low-density infill while increasing the material concentration at the top and bottom of the specimen. This enhances the flexural stiffness of the specimen, thereby increasing the frequency.

With lower Nozzle Temperature (E), the frequency increases: Although ABS generally requires higher printing temperatures, the filament manufacturer recommends nozzle temperatures between 210 °C and 240 °C. At the minimum value of 230 °C, the nozzle temperature remains within the recommended range, which can influence adhesion between layers and individual “threads” within a layer, thereby modifying the overall stiffness of the specimen and affecting the frequency.

With lower Bed Temperature (F), the frequency increases: Similarly to the previous point, the manufacturer recommends bed temperatures between 55 °C and 85 °C. At the minimum value, the bed temperature falls within the recommended range, enhancing adhesion between layers, increasing stiffness, and consequently raising the calculated frequency.

It is important to note that the temperature recommendations mentioned above were provided by the manufacturer after the definition of variables and midway through the specimen fabrication process. While the maximum nozzle and bed temperatures exceed the recommended limits, the manufacturer indicated that the material can be printed at higher temperatures than those suggested.

The response of Experimental Frequency can also be almost entirely explained by the selected experimental variables, although there are other variables (approximately 5%) not considered in this study that complement the model for the response. Additionally, it is important to emphasize the similarity between the R 2 values obtained for the Calculated Frequency (94.84%) and the Experimental Frequency (94.75%), which provide an initial indication of the high correlation between the calculated and experimental data.

Figure 9 illustrates that the variables with the greatest effect on frequency retain a similar order and magnitude; however, Layer Height (A) no longer exhibits a noticeable influence and has been excluded from the diagram, along with Bed Temperature (F). While the interactions with the most significant effect on Experimental Frequency follow a similar ranking to those presented in the Pareto diagram of the Calculated Frequency, this analysis highlights the interactions involving Number of Walls, Infill Density, Number of Top and Bottom Layers, and Bed Temperature as having the most pronounced impact on the response.

In Figure 10, the effects of the experimental variables are shown, corroborating the observations made with the Pareto diagram for the Experimental Frequency. Infill Density (C) has the greatest effect, followed by Number of Walls (B) and Number of Top and Bottom Layers (D). Finally, the variables with the least effects are Nozzle Temperature (E), Layer Height (A), and Bed Temperature (F).

Figure 11 presents the effects from the regression model for Calculated Damping. The nozzle temperature (E) and the number of top and bottom layers (D) show negligible influence on damping. The most significant interactions involve the number of walls, top and bottom layers, and bed temperature, which are interrelated due to the bed temperature’s impact on layer adhesion and internal distortions, amplified by the number of walls and layers.

Figure 12 presents the residual plots, which align closely with the normal distribution trend line. The residuals are evenly dispersed around zero, showing no clear patterns or cycles, indicating independence and non-constant variance. The histogram reflects a symmetric normal distribution, confirming that the residuals satisfy the assumptions of normality, homoscedasticity, and independence. This validates the model’s reliability within the defined range of variables.

Figure 13 shows the effects of the experimental variables: on the X-axis are the minimum and maximum values defined in the experimental matrix, and on the Y-axis is the mean of the Calculated Damping. As Layer Height (A) increases, the average damping slightly increases: with thicker layers, greater damping is generated, leading to faster energy dissipation.

As the Number of Walls (B) increases, the expected damping decreases: with a greater number of walls, the specimen becomes stiffer, reducing its damping.

With a lower Infill Density (C), the damping is higher: a denser infill restricts internal deformations in the specimen, reducing its damping.

With a lower Number of Caps and Bases (D), the damping is higher: with a greater number of caps and bases, the material on the surfaces increases, enhancing stiffness and reducing damping.

With a lower Nozzle Temperature (E), the damping is lower: as mentioned earlier, the nozzle temperature, at its minimum value of 230 °C, is within the range recommended by the manufacturer. This influences the adhesion between layers and between “threads” within the same layer, promoting the formation of continuous interfaces with greater internal friction, resulting in higher damping than at 260 °C.

With a lower Bed Temperature (F), the damping is higher: this is the factor with the greatest effect. A higher bed temperature allows for better specimen shaping, promoting the formation of continuous interfaces with fewer defects, consequently reducing its damping.

A strong correlation was observed between the printing variables and the natural frequency of the specimens. However, the relationship with damping is more complex, as additional factors not included in the experimental design also influence this behavior. The damping values found were in a range of 2.2%–6%, with a Composite Desirability indicating an 82.89% validity for these predictions. In comparison, the average experimental damping is 3.078%, and the average calculated damping is 3.158%

The study also showed that certain combinations of parameters can be used to increase or decrease damping, allowing for tailored dynamic response selection for specific engineering needs. The values, combination, corresponding damping ratio and overall average damping ratio are shown in Table 2:

This table has been added to display the maximized and minimized damping ratio and their corresponding combination.

It should be emphasized that the parameter configurations identified to maximize or minimize structural damping are strictly derived from the experimental domain and screening models of the present study. Given the comparatively lower statistical confidence associated with the damping response and the unmonitored influences of environmental fluctuations, raw material batch variability, and internal microstructural defects, the predicted damping values may differ under independent confirmation testing or alternate manufacturing environments. Consequently, these combinations should be interpreted as candidate configurations and directional screening trends rather than definitive global optima, serving as target baselines for dedicated empirical validation in future investigations.

Limitations

The study provides valuable experimental evidence and novel insights into the influence of 3D printing parameters on the dynamic response of ABS components. By addressing a critical gap in the literature, this work establishes a solid foundation for the optimization of additive manufacturing processes and the design of components for dynamic applications. However, several limitations of the present study should be noted.

Although five replicates were evaluated per parameter combination and both fabrication and testing sequences were fully randomized, environmental factors, such as ambient temperature and relative humidity during filament storage, printing, post-processing, and testing, were not continuously monitored, nor was raw material batch-to-batch variation. These ambient fluctuations may contribute to experimental variance.

Furthermore, internal microstructural defects (e.g., void distribution and inter-layer bonding flaws) were not characterized, representing an additional source of variability in natural frequencies and damping ratios; future work should incorporate non-destructive evaluation techniques, such as ultrasonic testing, X-ray radiography, or micro-computed tomography, to assess these internal features.

Additionally, the scope of this work is restricted to free-free transient dynamic response using a single commercial ABS filament formulation and a specific FDM printer platform, meaning results may vary across alternative material grades or machine architectures.

Finally, estimating the damping ratio via the logarithmic decrement method exhibits inherent sensitivity to signal noise, filtering thresholds, and internal structural discontinuities, which introduces an added layer of measurement uncertainty.

Analyzing and evaluating the effect of various printing parameters on the natural frequency and damping ratio of ABS specimens manufactured through additive manufacturing, as well as the interaction between these parameters and the combinations that allow maximizing or minimizing the damping ratio.

The natural frequency is strongly influenced by the infill density, the number of perimeter walls, and the number of top and bottom layers. A lower infill density and fewer perimeter walls increase the natural frequency, while a reduction in the number of top and bottom layers decreases it. The factorial model explains 93%–95% of the observed variation.

Damping exhibits a more complex and less linear dependence, partially explained by the printing variables. It was identified that a lower bed temperature, as well as a lower infill density and fewer perimeter walls, tend to increase the damping ratio. However, the factorial model explains only 29%–48% of the observed variation, suggesting that additional factors significantly influence energy dissipation.

The interaction between variables also plays a relevant role, indicating that, although each parameter has its own effect, the combination of geometric, structural, and thermal factors can significantly modify the dynamic behavior of the specimens.

There are optimal configurations that may allow maximizing the damping ratio; while further analysis of the specific combinations that increase or decrease the damping is requires, the study’s methodology showed the usefulness of the factorial approach for optimizing parameters in additive manufacturing.

Further research is needed to enrich the limited literature on the fatigue life of printed polymers by extending and validating the findings of this study.