A Parallel Polyurea Method for Enhancing Damping Characteristics of Metal Lattice Structures in Vibration Isolation and Shock Resistance

Abstract

The inherent damping deficiency in metal lattice structures leads to inadequate attenuation of both resonant peaks and shock-induced vibrations, significantly limiting their effectiveness in vibration isolation and shock resistance applications. To address this limitation, we developed a novel parallel polyurea method that utilizes the viscoelastic energy dissipation mechanism of polyurea to substantially improve structural damping performance. The metal lattice–polyurea parallel vibration isolation system was designed with its theoretical model established to characterize damping properties, vibration isolation, and shock-resistant performance. An experimental setup was developed to validate theoretical predictions through controlled semi-sinusoidal shock and swept-frequency tests. Experimental results demonstrate excellent agreement with theoretical predictions. The introduction of the polyurea damping structure significantly enhances the system’s damping performance. Compared to the conventional metal lattice isolator, the proposed metal lattice–polyurea parallel composite structure shows remarkable damping improvements: under shock excitation, it achieves substantial attenuation of peak response amplitude with accelerated decay rate, while under frequency-sweep excitation, it maintains the original resonance frequency but reduces the transmissibility peak significantly.

1. Introduction

Lattice structures have been extensively investigated for vibration isolation, primarily focusing on two mechanisms: bandgap-based isolation [1,2,3] and conventional passive vibration isolation [4,5,6,7]. With the advancement of additive manufacturing, the fabrication of metal lattice structures has become relatively mature. By designing the parameters of metal lattice structures, their stiffness and damping characteristics can be adjusted; therefore, they can be used as traditional vibration isolation and shock resistance components. Metal lattice structures should operate within their linear elastic regime to make them possible for repeated long-term use for traditional vibration isolation and shock resistance applications. The stronger radiation resistance and corrosion resistance of metal lattice structures exhibit their potential for application in extreme environments, such as high radiation and strong radiation conditions, compared to rubber vibration isolators. However, the metal lattice’s low intrinsic damping leads to pronounced resonance peaks and inadequate shock attenuation, ultimately limiting its vibration isolation and shock resistance applications. Therefore, it is imperative to develop a damping enhancement approach that improves the damping performance of metal lattice structures, which should also maintain the capacity of resisting radiation and corrosion.

The addition of viscoelastic layers is an effective method to enhance structural damping [8], mainly including two forms: base/viscoelastic/base platens with confined layer damping [9] and viscoelastic/base platens with free layer damping [10]. Polyurea, a viscoelastic material, exhibits inherent radiation and corrosion resistance [11,12,13]. Extensive research on its ballistic penetration resistance and blast mitigation capabilities further highlights its exceptional energy absorption properties [14,15,16,17,18,19]. These multifunctional characteristics suggest significant potential for using polyurea in vibration isolation systems for large equipment in harsh environments, including radiation exposure, corrosive media, or combined extreme conditions, to enhance system damping performance. Three structural configurations incorporating polyurea layers into the metal panels of lattice sandwich structures were proposed to enhance damping performance. Modal vibration tests were conducted to evaluate the natural frequencies and damping loss factors of the first three modes [20]. Subsequently, the structural optimization design was investigated in further detail [21]. The damping performance of honeycomb structures could be enhanced by filling the pores with viscoelastic materials [22,23,24,25], offering valuable insights for improving the damping of lattice structures. The damping properties of 316L BCC lattice structures incorporating different filler materials were examined [26]. Modal testing results indicate that while the composite structures exhibited an increased damping ratio compared to the unfilled lattice, the maximum attainable ratio remained limited to 0.007. A hybrid approach was proposed [27] to enhance the damping performance of pyramidal lattice structures by simultaneously incorporating both viscoelastic damping layers and filler materials. The damping and stiffness efficiency of the composite structures were evaluated through combined modal and quasi-static compression tests. However, adding a viscoelastic damping layer to the surface of the metal lattice structure cover plate formed a series combination of the metal lattice and the viscoelastic structure, whose load-bearing capacity was limited by the relatively weak viscoelastic damping layer, resulting in insufficient load-bearing capacity. When damping materials are filled internally, it is constrained by the fixed pore structure. The ability to achieve the desired optimal damping characteristics through adjustments to the shape and size of the damping materials is limited. Additionally, the performance of the lattice structure and the damping materials cannot be decoupled, complicating theoretical analysis and hindering the replacement of damping materials after failure. Furthermore, the aforementioned research primarily focused on vibration damping, aiming to enhance damping performance while maintaining a relatively high natural frequency, with the frequency range of interest being below the natural frequency of the lattice structure [28]. However, the vibration isolation performance of the composite structure has not been investigated.

To enhance the damping performance and shock resistance of lattice structures, several studies have been conducted. The damping performance of lattice structures was enhanced by applying a polyurea coating to the surfaces of beams with a negative Poisson’s ratio lattice and the energy absorption characteristics of the composite structure under shock loading were analyzed [14]. However, this damping method makes it difficult to control the coating thickness for optimal damping performance and does not decouple the performance of the lattice structure and the damping material, complicating theoretical analysis. Additionally, its focus is primarily on preventing structural damage. A composite polyurea foam was proposed, which was created by infiltrating polyurea foam into a lattice structure made of polyurea. Stress–strain characteristics, energy absorption, and cushioning efficiency were analyzed by quasi-static and dynamic strain rate experiments [29]. However, the aforementioned studies primarily focused on energy absorption and did not investigate vibration transmission under shock loading.

In summary, existing studies have predominantly examined the vibration damping and energy absorption properties of composite structures while largely neglecting their vibration transmission behavior under vibration and shock loading conditions. Furthermore, the potential for enhancing their vibration isolation and shock resistance capabilities remains unexplored. This study focuses on vibration isolation and shock resistance for large power equipment operating in extreme environments, such as those involving strong radiation and severe corrosion. A parallel polyurea method for enhancing the damping characteristics of metal lattice structures is proposed, which utilizes the metal lattice structure to achieve a large load-bearing capacity and leverages the parallel polyurea’s viscoelastic properties to improve the system’s damping performance. The dynamic properties of polyurea materials are investigated, and a metal lattice–polyurea parallel composite vibration isolation system is designed. A theoretical model of the composite system is established, followed by a theoretical analysis of its damping performance, shock resistance, and vibration isolation effectiveness. The analytical results are subsequently validated through semi-sinusoidal shock and swept-frequency experiments.

The rest of this paper is structured as follows: Section 2 introduces the metal lattice–polyurea parallel composite structure and presents the theoretical modeling of the corresponding composite vibration isolation system. Section 3 outlines the experimental methodology, including dynamic mechanical property tests of polyurea materials and shock and swept-frequency excitation tests of the metal lattice–polyurea parallel composite vibration isolation system. Section 4 is the results and discussion. Section 5 is the conclusion of the paper.

2. Metal Lattice–Polyurea Parallel Composite Structure and Theoretical Modeling

2.1. Metal Lattice–Polyurea Parallel Composite Structure

The metal lattice–polyurea parallel composite structure consists of the metal lattice structure and the separate polyurea damping structure. The metal lattice provides significant load-bearing capacity, while the polyurea damping structure enhances the system’s damping performance. Through the rational design of the polyurea damping structure’s shape and size, along with precise modulation of the composite’s elastic and damping properties, optimal vibration isolation and shock resistance performance can be tailored for specific application requirements.

Polyurea materials exhibit linear elastic behavior during the initial deformation stage, resulting in relatively low damping. Therefore, preloading is essential to enhance their damping performance. Figure 1 illustrates the design of the polyurea damping structure and the metal lattice–polyurea parallel composite structure model. As shown in Figure 1a, the polyurea damping structure consists of two identical polyurea samples (#1 and #2). A pressing plate between the samples is connected to the external load via a guide rod, with an upper plate and a lower plate placed at the opposite end of each sample. The preload can be adjusted by modifying the thickness of the upper and lower plates. The guide rod is rigidly connected to the pressing plate, maintaining the polyurea samples in a state of compressive contact rather than rigid fixation. Consequently, when the vibration is transmitted to the system and the load mass applies downward pressure through the guide rod, polyurea sample (#2) primarily contributes to stiffness and damping; the stiffness and damping produced by polyurea sample (#1) can be ignored due to preload release or weakened contact. Under the opposite load condition, polyurea sample (#1) primarily provides stiffness and damping.

As shown in Figure 1b, the upper ends of the two metal lattice structures are rigidly connected to the load mass, while the lower ends are fixed to the baseplate via support frames. The polyurea damping structures are fixedly connected to the load mass through guide rods. Together, the metal lattice–polyurea parallel composite structure and the load mass form a composite vibration isolation system.

2.2. Theoretical Modeling

A theoretical model for the metal lattice–polyurea parallel composite structure vibration isolation system, based on the system shown in Figure 1b, is established in Figure 2. In the model, the metal lattice structures and polyurea samples are represented by Kelvin models. In Figure 2, m represents the load mass of the system, while k₀ and c₀ are the stiffness and damping coefficient of the metal lattice structure, respectively. k₁, c₁, k₂, and c₂ denote the stiffness and damping coefficients of polyurea samples #1 and #2 under the pre-compression displacement x₀. x₁ and x₂ correspond to the vibration displacements of the base and load mass.

Since the connections between k₁, c₁, k₂, c₂, and the load mass are compression contacts, and the polyurea samples are identical with the same preload, k₁ = k₂ and c₁ = c₂. Therefore, the motion equation of the system is

$$m{\ddot{x}}_2+2k_0\left(x_2-x_1\right)+2c_0\left({\dot{x}}_2-{\dot{x}}_1\right)+4k_1\left(x_2-x_1\right)+4c_1\left({\dot{x}}_2-{\dot{x}}_1\right)=0$$

(1)

where ${\dot{x}}_1$ and ${\dot{x}}_2$ are the vibration velocities of the base and load mass, respectively, and ${\ddot{x}}_2$ is the vibration acceleration of the load mass.

Taking the Laplace transform of Equation (1) and simplifying yields the system’s vibration transmissibility:

$$H(s)={\displaystyle \frac{2\left(c_0+2c_1\right)s+2\left(k_0+2k_1\right)}{m{s}^2+\left(2c_0+4c_1\right)s+2\left(k_0+2k_1\right)}}$$

(2)

The frequency-domain expression for the vibration transmissibility is given by

$$H(\omega )=\left|{\displaystyle \frac{X_1}{X_2}}\right|=\sqrt{{\displaystyle \frac{1+4{\xi }^2\frac{{\omega }^2}{{\omega }_0^2}}{{\left(1-\frac{{\omega }^2}{{\omega }_0^2}\right)}^2+4{\xi }^2\frac{{\omega }^2}{{\omega }_0^2}}}}$$

(3)

where ${\omega }_0$ is the system’s natural frequency, ${\omega }_0=\sqrt{k/m}$, and k is the equivalent stiffness, with $k=2(k_0+2k_1)$. $\xi$ is the system’s damping ratio, with $\xi =c/(2\sqrt{k\mathrm{m}})$, and c is the equivalent damping coefficient, with $c=2(c_0+2c_1)$.

When $\omega ={\omega }_0$, the system resonates and the vibration transmissibility is the maximum. The damping ratio of the system can be calculated as

$$\xi =\sqrt{{\displaystyle \frac{1}{4\left(H_{\max }^2-1\right)}}}$$

(4)

The shock response under half-sine wave excitation can be theoretically determined following the methodology in Ref. [30].

3. Experimental Methodology

3.1. Experiments of Dynamic Mechanical Properties of Polyurea

Polyurea is a viscoelastic material, and incorporating a polyurea damping structure enhances the system’s damping while also increasing stiffness, thereby raising its natural frequency. Therefore, the polyurea sample parameters should be carefully chosen to maximize the damping coefficient while minimizing the additional stiffness.

Although the mechanical properties of polyurea have been extensively studied under different strain rates [31,32,33], to the best of our knowledge, its stiffness and damping performance under dynamic excitation remain unclear. Dynamic cyclic loading experiments are widely used to investigate the dynamic properties of viscoelastic materials [34]. In this study, polyurea samples with varying parameters were prepared, and dynamic cyclic loading tests were conducted to examine their dynamic stiffness and damping properties, thereby facilitating the damping structure design of metal lattice–polyurea composite structures.

3.1.1. Design of Polyurea Samples

The polyurea material used in this study is a single-component polyurea grouting liquid (reinforced JL0007-II). Cylindrical polyurea samples with varying specifications are fabricated, and their parameters are listed in

Table 1. Specifications of the cylindrical polyurea samples.

Diameter D/mm	Thickness t/mm
$\varphi 40$	10	20	40
$\varphi 60$	10	20	40
$\varphi 80$	10	20	40

. The dynamic stiffness and damping coefficients of the polyurea sample are influenced by preload, area and thickness, excitation frequency, and excitation amplitude. Therefore, the effects of these parameters on the dynamic properties of polyurea were analyzed to guide the design of the polyurea damping structure.

3.1.2. Dynamic Experimental Setup

The dynamic mechanical properties of polyurea samples were evaluated using an MTS 370.10 servo-hydraulic test system. As shown in Figure 3, the samples were positioned between the upper and lower platens.

An initial preload (F_p) was applied to the polyurea sample under quasi-static conditions with a controlled strain rate of 0.12 s⁻¹. Subsequently, a low-frequency sinusoidal displacement excitation was applied to the sample. The effects of various parameters, including preload, area, thickness, excitation frequency, and excitation amplitude, on the dynamic stiffness and damping performance of the polyurea sample were investigated.

3.1.3. Identification Methods for Dynamic Stiffness and Damping

Under low-frequency excitation, the resultant force transmitted through the polyurea sample consists of two orthogonal components: the elastic restoring force (F_k) and the damping force (F_c). The typical force–displacement curve of viscoelastic material under dynamic cyclic loading is shown in Figure 4. The equivalent dynamic stiffness (k₁) and loss factor (η₁) are then derived from Equations (5) and (6), respectively.

$$k_1=F_k/X_0=\left|AC\right|/\left|BC\right|$$

(5)

$${\eta }_1=F_c/F_k=\left|DE\right|/\left|AC\right|$$

(6)

where X₀ is the amplitude of the excitation signal.

The damping coefficient c₁ of the polyurea sample can be calculated as

$$c_1=2{\xi }_1\sqrt{k_1{m}_p}={\displaystyle \frac{\left|DE\right|}{\left|AC\right|}}\sqrt{{\displaystyle \frac{\left|AC\right|}{\left|BC\right|}}\cdot m_p}$$

(7)

where ξ₁ is the damping ratio of the polyurea sample, with ξ₁ = η₁/2, and m_p is suspended mass.

3.2. Shock and Swept-Frequency Experiments of Metal Lattice–Polyurea Parallel Composite Structure

3.2.1. Experimental Setup

To evaluate the damping enhancement effect of the parallel polyurea damping structure on the metal lattice vibration isolation system, an experimental setup was designed based on the metal lattice–polyurea parallel composite structural model shown in Figure 1b. Shock and swept-frequency tests were then conducted on the metal lattice–polyurea parallel device using the TBS-800 shaking table (Suzhou Su Shi Testing Group Co., Ltd., Suzhou, China). The experimental setup is shown in Figure 5, where the load mass and baseplate are made of 304 stainless steel, with the load mass m = 56.54 kg.

The two body-centered cube with balls (BCC-B) metal lattice structures, fabricated using selective laser melting (SLM) with Ti-6Al-4V powder, and the polyurea damping structures were symmetrically arranged and rigidly connected between the load mass and baseplates using screws. Figure 6 shows the BCC-B metal lattice structure model and sample. The BCC-B metal lattice structure consists of a 3 × 3 × 3 BCC-B lattice unit cell and two integrated cover plates at the top and bottom. The unit cell has a side length (L) of 15 mm, a beam diameter (d) of 1.5 mm, a ball diameter (b) of 2.5 mm, and a cover plate thickness (t) of 2 mm. The stiffness and damping coefficients under shock and vibration excitations were calculated through shock and swept-frequency experiments, respectively. Polyurea samples were designed based on the research results of their dynamic mechanical properties.

The shock excitation and swept-frequency signals were provided by the shaking table, with the vibration signals detected by acceleration sensors (Model B06A00, Shandong LNS Intelligent Technology Co., Ltd., Dezhou, China) whose factory calibration certificate specified measurement range (±50 g), sensitivity (10.469 mV/(m/s²)), frequency response (±5% within 1 Hz to 8 k Hz), and resolution (0.1 mg rms). The shaking table’s output signal was monitored and controlled by sensor (#1), the shaking table’s output was detected by sensor (#2), and the load response signal was measured by sensor (#3). The output signals from the shaking table and load response signals were acquired using the high-precision data acquisition device INV3018 (China Orient Institute of Noise & Vibration, Beijing, China) and processed with DASP–V11 software.

3.2.2. Experimental Scheme

Firstly, a shock test was conducted on the vibration isolation system comprising two metal lattice structures and the load mass m. The shock signal used was a semi-sinusoidal wave with a duration of 6 ms and a peak value of 1g, expressed as $a=9.8\sin (\pi t/0.006)[\epsilon (t)-\epsilon (t-0.006)]$ m/s², where $\epsilon (t)$ is the unit step function. By analyzing the shock response curve, the stiffness and damping coefficients of the metal lattice structure under shock were determined. Through spectral analysis of the system load’s response signal, the system’s natural frequency was found to be 73.5 Hz. Consequently, the swept-frequency range for the subsequent swept-frequency experiment was set from 20 Hz to 100 Hz, and the linear sweep frequency method was adopted with a sweep rate of 10 Hz/min. To prevent structural damage due to excessive acceleration during resonance, a sinusoidal wave with a peak value of 0.05 g was used as the excitation signal in the swept-frequency test. Finally, the shock resistance and vibration isolation performance of the metal lattice–polyurea parallel composite vibration isolation system were tested through shock and vibration swept-frequency experiments, respectively.

4. Results and Discussion

4.1. Dynamic Mechanical Properties of Polyurea

4.1.1. Effects of Preload

Using 60 mm × 40 mm polyurea samples, with the excitation signal frequency fixed at 0.5 Hz and amplitude fixed at 1 mm, preloads of 100 N, 200 N, and 300 N were applied. The force–displacement curves of the polyurea samples under different preloads are shown in Figure 7a. The dynamic stiffness and damping coefficients of the polyurea samples were calculated, yielding the curves presented in Figure 7b,c.

As shown in Figure 7, as preload increases, the area enclosed by the force–displacement curve increases, indicating a gradual rise in energy dissipation. Correspondingly, the damping coefficient increases approximately linearly with preload. When preload increases from 100 N to 300 N, the damping coefficient rises from 115.98 N·s/m to 283.06 N·s/m. The slope of the curve progressively increases with preload, reflecting a corresponding rise in the dynamic stiffness of the polyurea sample. Similarly, dynamic stiffness increases approximately linearly with preload, rising from 38.48 N/mm to 64.32 N/mm as preload increases from 100 N to 300 N.

4.1.2. Effects of Area

Dynamic experiments are conducted on polyurea samples with dimensions of $\varphi$80 mm × 20 mm, $\varphi$60 mm × 20 mm, and $\varphi$40 mm × 20 mm to investigate the influences of area on the dynamic stiffness and damping coefficient. In these experiments, the preload is set to 100 N, the excitation frequency is set to 0.5 Hz, and the excitation amplitude is set to 0.5 mm. The obtained force–displacement curves of the three polyurea samples are shown in Figure 8a, with the dynamic stiffness and damping coefficients calculated and presented in Figure 8b,c.

From Figure 8, it can be observed that as the area of the polyurea sample increases, the area enclosed by the force–displacement curve gradually enlarges, indicating a corresponding increase in energy dissipation capacity. Consequently, the damping coefficient of the polyurea sample increases. As the area of the polyurea sample increases from 1256 mm² to 5024 mm², the damping coefficient rises from 99.04 N·s/m to 286.65 N·s/m. Furthermore, as the area increases, the slope of the force–displacement curve becomes steeper, suggesting that the dynamic stiffness of the polyurea sample also increases. Specifically, as the area of the polyurea sample increases from 1256 mm² to 5024 mm², its dynamic stiffness increases from 52.64 N/mm to 238.27 N/mm. Although the area of polyurea sample increases four times, the dynamic stiffness increases more than four times while the damping coefficient increases less than three times. Therefore, the changes of dynamic stiffness must be considered when enhancing the damping coefficient using enlarged area.

4.1.3. Effects of Thickness

Figure 9 presents the force–displacement curves, dynamic stiffness, and damping coefficients of three polyurea samples with dimensions of $\varphi$80 mm × 40 mm, $\varphi$80 mm × 20 mm, and $\varphi$80 mm × 10 mm under dynamic excitation, with a preload of 300 N. The excitation frequency is 0.5 Hz, and the amplitude is 0.15 mm.

As shown in Figure 9a, the force–displacement curve of the $\varphi$80 mm × 40 mm polyurea sample is nearly horizontal, indicating relatively low dynamic stiffness. Accordingly, as shown in Figure 9b, the dynamic stiffness of this sample is 73.73 N/mm. The dynamic stiffness of polyurea decreases monotonically with thickness, decreasing from 1084.40 N/mm to 73.73 N/mm as the thickness increases from 10 mm to 40 mm. Simultaneously, the area enclosed by the force–displacement curve diminishes, indicating degraded damping performance. As shown in Figure 9c, the polyurea sample exhibits enhanced energy dissipation capacity with decreasing thickness. Specifically, the damping coefficient declines from 1144.10 N·s/m to 284.00 N·s/m as thickness increases from 10 mm to 40 mm. When the thickness increases from 10 mm to 40 mm, which is four times the original value, the dynamic stiffness decreases to 6.80% of the original, and the damping coefficient decreases to 24.82% of the original. Therefore, based on the analysis of the influence of area, the damping coefficient can be increased by enlarging the area, and at the same time, the thickness can be increased to achieve the goal of reducing the additional dynamic stiffness.

4.1.4. Effects of Excitation Frequency

Figure 10a presents the force–displacement characteristics of a $\varphi$80 mm × 10 mm polyurea sample subjected to a 300 N preload and 0.2 mm excitation amplitude at varying frequencies. The resulting dynamic stiffness and damping properties are plotted in Figure 10b and Figure 10c, respectively.

Figure 10a shows that as the excitation frequency increases, the area enclosed by the force–displacement curve expands, indicating enhanced energy dissipation capacity. Correspondingly, Figure 10c demonstrates a progressive rise in the damping coefficient with frequency, with the rate of increase accelerating. Simultaneously, the slope of the force-displacement curve steepens, reflecting an increase in the dynamic stiffness of the polyurea sample. As depicted in Figure 10b, when the excitation frequency increases from 0.1 Hz to 2 Hz, the dynamic stiffness grows from 1270.19 N/mm to 1732.17 N/mm, yet the rate of stiffness augmentation gradually declines. Consequently, to ensure accurate prediction of damping performance and the vibration isolation system’s shock resistance and isolation effectiveness, polyurea samples should be tested under low-frequency excitation conditions.

4.1.5. Effects of Excitation Amplitude

The effects of varying excitation amplitudes (0.5 mm, 1 mm, and 2 mm) on the dynamic stiffness and damping characteristics of a $\varphi$40 mm × 20 mm polyurea sample under a constant 200 N preload at a 0.5 Hz excitation frequency were investigated. Figure 11 illustrates the force–displacement curves, along with the variations in dynamic stiffness and damping coefficient, under different excitation amplitudes.

Figure 11a demonstrates that the area enclosed by the force–displacement curve for the polyurea samples expands significantly with increasing excitation amplitude, reflecting enhanced energy dissipation capacity. Notably, the slope of the force–displacement curve remains nearly constant, indicating stable dynamic stiffness. Furthermore, although both damping and elastic restoring forces increase with excitation amplitude, the latter exhibits a more pronounced growth rate. As shown in Figure 11b,c, the excitation amplitude has a negligible effect on dynamic stiffness, which remains stable at approximately 81 N/mm, while the damping coefficient decreases from 268.19 N·s/m to 209.67 N·s/m with increasing amplitude. In practical applications where polyurea damping structures are arranged in parallel with metal lattice structures, the deformation of the lattice constrains the vibration displacement of the polyurea. When employed in vibration isolation systems, the metal lattice structure operates within its linear elastic regime, exhibiting relatively minor deformations. Consequently, during dynamic stiffness and damping characterization of polyurea materials, it is recommended to employ low-amplitude excitations.

Previous studies have demonstrated that polyurea materials exhibit superior damping characteristics under dynamic loading. The dynamic stiffness and damping coefficient can be effectively modulated by adjusting the preload, area, and thickness. The systematic analysis of polyurea’s dynamic stiffness and damping properties reveals that decreasing the material thickness can effectively enhance the damping coefficient. Nevertheless, this geometrical modification may induce a marginal elevation in natural frequency, attributable to the concomitant increase in dynamic stiffness. Thus, a balance must be struck between the natural frequency and response peak, depending on specific requirements. In this study, the polyurea specimen was fabricated with the dimension of 80 mm × 40 mm. Under a pre-compression displacement of 6 mm, the estimated dynamic stiffness (k₁) and damping coefficient (c₁) are 80 N/mm and 200 N·s/m, respectively. When the pre-compression displacement increases to 8 mm, k₁ rises to 96 N/mm, accompanied by an increase in c₁ to 300 N·s/m.

4.2. Shock Resistance Performance

A semi-sinusoidal wave signal excitation with a peak of 1 g and a duration of 6 ms was applied to the vibration isolation system consisting of two metal lattice structures and the load mass m. The resonance peak derived from spectral analysis of the system’s response signal was utilized to calculate the dynamic stiffness of the metal lattice structure. The damping coefficient was determined using the free decay oscillation method [35,36]. The calculated dynamic stiffness and damping coefficient of the metal lattice structure were 5.7214 × 10⁶ N/m and 1051.8 N·s/m, respectively.

The shock response curves of the metal lattice structure (LS) and metal lattice–polyurea parallel composite structures under the pre-compression displacements of 6mm and 8mm (CS-6mm and CS-8mm) vibration isolation systems, respectively, were numerically calculated using a semi-sinusoidal wave signal excitation with a peak of 1 g and a duration of 6 ms, as shown in Figure 12a. The shock response curves of the three isolation systems, obtained from the corresponding shock experiments, are shown in Figure 12b.

The acceleration response attenuation rates of the composite structures are both increased, with the CS-8 mm system exhibiting the most rapid attenuation.

Table 2. Theoretical and experimental results of the shock responses.

Type	Theoretical Maximum Response/(m/s2)	Experimental Maximum Response/(m/s2)
LS	13.286	11.659
CS-6 mm	13.200	9.525
CS-8 mm	13.146	9.506

shows the theoretical and experimental results of the shock responses. There is a certain error between the theoretical and the experimental results of the maximum peak value of the shock response of the LS system, which might be caused by the certain errors in calculating the stiffness and damping of the metal lattice structure. However, the error does not affect the analysis of the shock resistance performance of the composite structure after the introduction of the polyurea damping structure. The experimental results show that the maximum peak value of the shock response of CS-6 mm and CS-8 mm systems decrease by 18.3% and 18.5% compared with the LS system.

The system’s damping characteristics, including both damping ratio and damping coefficient, are experimentally determined through shock response analysis and subsequently compared with theoretical predictions, as summarized in

Table 3. Damping performance of the three vibration isolation systems under shock excitation.

Type	Theoretical Results		Experimental Results
	ξ	c/(N·s/m)	ξ	c/(N·s/m)
LS	-	-	0.0415	2103.6
CS-6 mm	0.0563	2903.6	0.0806	4128.8
CS-8 mm	0.0639	3303.6	0.0849	4355.1

.

The comparative analysis reveals that the integration of the polyurea damping structure significantly enhances the damping performance of the composite vibration isolation system, with experimental results exceeding theoretical estimations. Particularly, the CS-6 mm and CS-8 mm systems exhibit 96.27% and 107.03% increases in damping coefficients, respectively, compared to the LS system. This observed discrepancy may stem from two principal mechanisms. Primarily, the polyurea material undergoes high-strain-rate deformation under shock loading, which activates molecular chain mobility and subsequent rupture of doubly coordinated hydrogen bonds between polyurea molecules. This bond dissociation process dissipates considerable energy, thereby enhancing the damping characteristics. Secondarily, inherent variations in both the peak magnitude and temporal duration of the shock excitation introduce measurement uncertainties in the shock response, consequently elevating the derived damping parameters (damping ratio and damping coefficient).

4.3. Vibration Isolation Performance

Notwithstanding the metal lattice structure’s operation in the linear elastic regime, significant variations are observed in its dynamic stiffness and damping behavior when subjected to vibrational loads compared to shock loading scenarios. Through swept-frequency excitation testing of the metal lattice vibration isolation system, the resonant frequency is determined to be 73.55 Hz with a corresponding response peak of 53.5384, as derived from the vibration transmissibility curve. Experimental characterization yields a stiffness of 6.031 × 10⁶ N/m and a damping coefficient of 243.49 N·s/m for the metal lattice structure. The vibration transmissibility curves for the LS, CS-6 mm, and CS-8 mm vibration isolation systems were calculated, as shown in Figure 13a. Through swept-frequency testing of the shaking table, the vibration transmissibility curves for the LS, CS-6 mm, and CS-8 mm systems were obtained, as shown in Figure 13b.

Table 4. Theoretical and experimental results of sweep-frequency responses.

Type	Theoretical Results		Experimental Results
	Natural Frequency/Hz	Peak Value	Natural Frequency/Hz	Peak Value
LS	73.55	53.54	73.55	53.60
CS-6 mm	74.50	20.59	73.63	32.41
CS-8 mm	74.60	15.76	73.63	26.28

shows the theoretical and experimental results of sweep-frequency responses. The LS vibration isolation system demonstrates the highest resonance peak (53.60), followed by the CS-6 mm (32.41) and CS-8 mm (26.28) systems, with the composite systems achieving up to 50.97% peak attenuation. In addition, the natural frequencies remain virtually unchanged. Thus, the introduction of the polyurea damping structure enhanced the vibration isolation effect.

The system’s damping ratio and damping coefficient were calculated using Equation (4) and subsequently compared with theoretical values, as summarized in

Table 5. Damping performance of the three vibration isolation systems under sweep-frequency excitation.

Type	Theoretical Results		Experimental Results
	ξ	c/(N·s/m)	ξ	c/(N·s/m)
LS	-	-	0.0093	486.98
CS-6 mm	0.0243	1286.98	0.0154	807.03
CS-8 mm	0.0318	1686.98	0.0190	995.47

. The experimental results are consistent with the trend of the theoretical solution but are smaller than the theoretical results. This might be because the damping capacity was insufficient because of the excessively small vibration displacement. However, after the introduction of the polyurea damping structure, the damping coefficient and damping ratio of the system were significantly enhanced. The damping coefficient of the CS-8 mm vibration isolation system was the largest, increasing from 486.98 N·s/m of the LS vibration isolation system to 995.47 N·s/m, an increase of 104.42%.

The research focus of this paper lies in exploring a method that can be applied in extreme environments to enhance the damping performance of the system while ensuring a large load-bearing capacity. The response characteristics of the vibration isolation system under vibration and shock are related to its stiffness, damping ratio, and load mass. The load mass adopted in this paper is 56.54 kg. In the existing traditional vibration isolation research of lattice structures, in references [6,37], the load masses are 1 kg and 90 g, respectively, which obviously increases the damping ratio of the system and thereby reduces the peak value of vibration transmissibility. Meanwhile, their materials are both acrylonitrile butadiene styrene (ABS), which has poor radiation resistance and anti-aging ability. Under the shock excitation, the maximum response peak decay is not significant. This is because the peak of the shock response is greatly influenced by the stiffness, while the damping ratio has a relatively small effect on the peak of the shock response. In reference [30], as the damping ratio increased from 0.05 to 0.3, the peak response only decreased from 17.87 m/s² to 15.60 m/s². The damping ratio mainly affects the decay rate. In this study, in the later stage of the decay process, such as around 0.1 s, the peak responses of LS, CS-6 mm, and CS-8 mm are 4.51 m/s², 3.02 m/s², and 1.72 m/s², respectively, showing a significant convergence speed of the shock response. In reference [26], the damping ratio of the 316 L-made BCC lattice structure after filling with hard damping material is 0.007. In conclusion, the damping effect of the method presented in this paper is significant.

5. Conclusions

A parallel polyurea integration method was proposed to effectively enhance the damping properties of metal lattice structures, thereby achieving superior vibration isolation and shock attenuation capabilities. The metal lattice structure was used for load-bearing capacity while incorporating parallel polyurea viscoelastic elements used for enhanced damping and energy dissipation. A novel vibration isolation system featuring this metal lattice–polyurea parallel composite structure was designed, with its corresponding theoretical model developed. Comprehensive analyses were conducted to evaluate the system’s damping characteristics, vibration isolation performance, and shock mitigation capability. The experimental setup of the metal lattice–polyurea parallel composite structure vibration isolation system was built and verified through semi-sinusoidal shock tests and swept-frequency tests. Both theoretical and experimental results demonstrate that, compared with the metal lattice structure, the damping performance of the composite structure is improved significantly. Under shock excitation, the maximum peak value of the shock response of the composite structure with the introduction of the polyurea damping structure decreases, while the decay rate of the shock response is accelerated. Thus, the shock resistance effect is enhanced. Under swept-frequency excitation, the peak response of the composite structure significantly decreases, while the natural frequency remains unchanged, demonstrating better vibration isolation performance.

This study offers a novel approach to enhancing the damping performance of metal lattice structure vibration isolation systems, improving their shock resistance and vibration isolation effectiveness. It also provides insights for the future development of vibration isolators suitable for conditions with high radiation, constrained spaces, large load-bearing capacity, low stiffness, and improved damping performance. In addition, there is a potential application in vibration isolation for steel domes by introducing metal lattice–polyurea parallel composite structures between the steel dome and its lower supporting structure.