The energy consumption characteristics of a new type of energy dissipating vibration-damping fastener Open Access

Rail transit has become a prominent form of transportation in contemporary urban transit systems due to compact spatial requirements, substantial capacity, high speed, and punctuality. It has demonstrated significant efficacy in alleviating urban traffic congestion and enhancing the quality of life in densely populated areas, making it a preferred means of transportation for urban residents.¹ However, the rapid development of rail transportation presents growing concerns regarding the detrimental effects of vibration and noise pollution. The vibration and noise produced by the contact between the wheels of trains and rails significantly impact passenger comfort.² This noise is primarily transmitted between rails, tunnels, and car bodies, while a portion of the vibrational energy is also dispersed to the surrounding soil, leading to secondary structural noise in the buildings along the rail, which significantly disrupts the daily lives of residents along the line.^3–6 Therefore, considering the wheel and rail system as a means to inhibit undesirable vibrations and noise has emerged as a viable, cost-effective solution option, which specifically targets the noise source of the vibrational energy generated during train operation. Vibration-damping fasteners have been widely adopted and applied for this purpose due to their simplicity, practicality, substantial impact, and cost-efficacy.^7–9 

As core components connecting the rails to the rail foundation, fasteners play an indispensable role in the structural rail system. They securely fix the rails in the appropriate position in the rail foundation via anchoring bolts, effectively limiting longitudinal and lateral rail movement and preventing them from overturning.¹⁰ Considering that urban rail transit is often located in densely populated areas, the vibration- and noise-damping properties of fasteners are critical. The elastic properties of fasteners are used to improve the vibration and noise reduction performance while vibration-damping fasteners usually use elastic polymer materials as under-rail rubber pads to absorb and dissipate vibrational energy.⁸ According to the structural and force deformation characteristics of elastic elements, vibration-damping fasteners can be divided into medium vibration-damping (e.g., double-layer nonlinear fasteners) and high-vibration-damping fasteners (e.g., shear and compression types).¹¹ Ning¹² analyzed the structure of double-layer nonlinear vibration-damping fasteners and proposed a new type of compression plate design, which exhibited a vibration-damping effect of 8.9 dB. Therefore, exploring new vibration-damping fasteners capable of efficient vibration isolation and energy dissipation is essential for both research and practical applications.

Existing vibration-damping fasteners mainly use rubber as the vibration-damping element. As the stiffness of rubber elastic components increases, the viscous damping decreases, exhibiting elastic frequency dependent dynamic stiffness characteristics.¹³ Wei et al.¹⁴ examined high-speed railroad fastening systems and found that the elastic rubber element displayed noticeable temperature-dependent stiffness characteristics, which had a significantly negative impact on its ability to reduce vibration and noise. In addition, rubber primarily functions as a vibration isolation element, reducing the transmission of vibrations to the foundation. However, the undissipated vibration energy may intensify the vibrations of the track itself.^15–17 Consequently, the focus of the research is on developing vibration-damping fasteners with stable isolation performance and effective energy dissipation capabilities. High-damping metal, a unique type of damping alloy, possesses both the necessary strength for structural materials and the ability to efficiently convert vibrational energy into heat energy during internal dissipation.¹⁸ This alloy relies on the generation and movement of twinned interfaces in its internal microstructure to absorb vibrational energy and significantly reduce vibration and noise.^19,20 According to their microscopic energy dissipation mechanisms, damping alloys are generally categorized into complex-phase, dislocation, ferromagnetic, twin-crystal, and hyperplastic types, as well as some for which the damping mechanism has not yet been completely clarified, such as Fe–Mn and Fe–Ni–Mn alloys.^21–24 A comparison between the mechanical and damping characteristics of various damping alloys shows that manganese–copper (Mn–Cu) damping alloys (twinned-type damping alloys) exhibit exceptional mechanical properties. Furthermore, the damping properties of these alloys demonstrate a relatively lower reliance on temperature and external environmental factors.¹² Therefore, Mn–Cu damping alloys have been extensively employed in engineering applications. Yang et al.²⁵ designed an aircraft skin wall plate with a free damping layer structure, which reduced structural stiffness and increased the loss factor to enhance its vibration and noise reduction capability. Zhang and Lei²⁶ developed a damping alloy sheet for ships. After aging treatment, the material structure shows a clear and neat martensitic structure. Under the action of alternating stress, its movement or sliding can effectively absorb vibration energy, achieving the function of vibration reduction and noise reduction. Compared with traditional polymers, damping alloys display excellent damping and mechanical properties, which can be regarded as materials with structural and functional advantages. The energy dissipation mechanism mainly relies on the reversibility of microtwin interfaces during periodic motion triggered by the thermoelastic martensitic phase transition at the microscopic level of the material. The subsequent static hysteresis between the strain and the stress converts vibrational energy to thermal energy, facilitating dissipation. Chen et al.²⁷ used a reverse torsion pendulum and vibration testing device to study the damping performance of Mn–Cu damping alloy and its vibration reduction performance of components. The results showed that Mn–Cu damping alloy has not only excellent mechanical properties but also significant damping performance, and the damping performance increases rapidly with the increase of strain amplitude. These findings hold significant theoretical and practical implications for understanding and designing metallic materials with high damping capabilities.

To address the damping capacity and energy dissipation deficiencies of existing damping fasteners, this study establishes a theoretical model of a double-layer bearing rail system to investigate the effect of damping fastener stiffness and loss factors on the rail vibration attenuation rate. The nonlinear mechanical properties of the damping alloy are analyzed in depth to establish its principal mechanical model. This paper proposes a novel approach for incorporating high-damping alloys to create a new type of energy dissipating vibration-damping fastener (NEDF) capable of effective vibration isolation and energy dissipation, which are assessed via a rail system hammering test. This study presents a novel strategy for effective noise and vibration management in rail transportation systems.

Considering the practical application context, the vibration-damping fasteners in the rail system examined in this study displayed a low level of stiffness, while that of the rail and under-rail support section was relatively high. Therefore, vibration-damping fasteners play a crucial role in determining the rail vibration attenuation rate. The system was simplified to a Timoshenko beam model, where the beam was supported by vibration-damping fasteners and the rail plate in the vertical direction. The entire system was modeled as a mass-spring-mass-spring system. This simplified model helped to effectively analyze and understand the dynamic response characteristics of the rail system.^28–30 

Table I shows the key parameters of the internationally used UIC60 rail. L denotes the beam length. The length-to-slenderness ratio of the beam is obtained as GAL²/EI = 34.6 with the fastener spacing as d. When the beam length-to-slenderness ratio exceeded 30, it is accurate to describe it as a Timoshenko beam.³¹ 

This section calculated the theoretical model proposed above using the relevant rail and rail plate parameters listed in Table I. Stiffness and damping factor are the critical factors influencing the vibration reduction and noise attenuation capabilities of fasteners.³³ Therefore, the rail system fastener criteria were adjusted to study the impact of changes in stiffness and damping factors on rail vibration attenuation rate. The specific experimental design included the following: (1) when a fixed fastener mass was 12.5 kg and the stiffness was 33 kN/mm, the rail vibration attenuation rate was evaluated when the fastener damping factor changed from 0.1 to 1;(2) at a fixed fastener mass of 12.5 kg and a damping factor of 0.2, the rail vibration attenuation rate change was assessed when the fastener stiffness was adjusted from 15 to 50 kN/mm.

The theoretical calculation results are shown in Figs. 3(a) and 3(b), highlighting the following phenomena:

1. At lower frequencies ω, the double-bearing rail system exhibited significant vibration attenuation characteristics due to the presence of first-order occlusion regions, with the bearing expressed as the equivalent mass, that is, $meq=−sω/ω2$⁠. Based on the parameters listed in Table I and Eq. (6), the relationship between the equivalent mass of the bearing m_eq and the mass of the fastener m_d can be deduced as shown in Fig. 4(a). The relationship curve at two specific frequency points ω_c1 and ω_c2 could be ordered according to their numerical magnitudes. The orbital system at these two frequency points satisfied the m_d + m_eq = 0 and $mdω2−sw=0$ conditions, at which point the orbital mass was completely offset by the bearing structure. Therefore, these two frequency points were considered intrinsic to the double-bearing orbital system. Liu et al.³² found that when ω < ω_c1, the rail system entered a low-frequency occlusion region, equalizing the real and imaginary wave number sections, which prevented wave propagation and increased the vibration attenuation rate.

2. The orbital system entered the first-order cutoff region at a higher frequency ω, while the vibration attenuation rate showed a continuous decline. When the system entered the second-order blocking region, the vibration attenuation rate reached the first peak at 500 Hz, which was attributed to the termination of free-wave propagation during this frequency interval. The equivalent mass m_eq and $sω$ were combined to calculate the equivalent stiffness curves, as shown in Fig. 4(b), in which the two key frequencies are labeled with vertical lines $ω1=st/md$ and $ω2=sd+st/md$⁠. According to Eq. (6), the dynamic stiffness $sω$ at ω₁ goes to zero while it tends to infinity at ω₂. In addition, ω₁ corresponded to the fastener mass m_d and rail plate stiffness s_t, while the resonance frequency of ω₂ corresponded to the resonance frequency of the fastener mass m_d and the composite stiffness of the rail plate and the under-rail spacer. In the ω_c1 < ω < ω₂, the frequency range, the mass per unit length of the equivalent beam is m_d + m_eq. The wave propagated as a free wave, while the imaginary part of its wave number was zero. The free wave propagated without attenuation, while the rail vibration attenuation rate continued to decrease, reaching the lowest point at ω₂ at almost zero. When the bearing equivalent stiffness became infinite and changed the sign, the free wave propagation at the ω₂ terminated, the rail system went into the second-order occlusion region of the complex wave state, and the free wave propagation was truncated again above the frequency ω_c2, producing the first vibration attenuation rate peak.

3. In the high-frequency region, the free wave propagation was similar to that of an unsupported rail. A unique “pinned–pinned” vibration region was evident, showing higher rail-vehicle system vibration due to discontinuous rail bearings³² when the rail system changed from continuous to periodic, with a frequency of about 1070 Hz. This was independent of the other rail system parameters and was only related to the fastener spacing and propagation speed of the mechanical wave in the rail.

4. As shown in Fig. 3(a), the vibration attenuation rate of the first-order occlusion, first-order cutoff, and high-frequency zones increased gradually at a higher fastener loss factor. Although the vibration attenuation rate of the second-order occlusion zone peaks decreased, its average value improved. Overall, the rail vibration attenuation rate increased significantly at a higher fastener loss factor.

5. As shown in Fig. 3(b), the rail vibration attenuation rate in the entire frequency band increased at a higher fastener stiffness, especially in the second-order occlusion zone, showing an elevated vibration attenuation rate peak.

In summary, the theory provides an important theoretical basis for the application of alloy high-vibration-damping fasteners in rail systems. Therefore, the vibration-damping fastener design should improve the stiffness and loss factor to increase the rail vibration attenuation rate.

The twinned Mn–Cu damping alloy is an excellent vibration-damping material widely used in the mechanical, electronic, and military industries. It undergoes stress martensitic transformation when elastically deformed under external forces at room temperature, dissipating vibrational energy through an interfacial slip between martensite and parent phase austenite. This energy dissipation mechanism exhibits significant hyperelastic and hysteresis characteristics in the ontological relations. Unlike traditional linear elastic metallic materials, Mn–Cu damping alloys must avoid plastic deformation in practical engineering applications since they are essentially nonlinear elastic materials. Therefore, this study used the nonlinear elastic Ogden model and hyperelastic–viscoelastic PRF model in the Abaqus software to characterize the nonlinear mechanical properties of Mn–Cu damping alloys. The material parameters of the PRF model cannot be obtained directly from the mechanical experimental results but must be converted according to the material parameters of the linear viscoelastic model (e.g., Prony series).³⁴ This method provides an effective theoretical framework for accurately describing the complex mechanical behavior of Mn–Cu damping alloys.

This study used the experimental data to perform a series of uniaxial tensile tests for hyperelastic model fitting to investigate the hyperelastic properties of the Mn–Cu damping alloy (Mn–20Cu–5Ni–2Fe, at. %). The models were categorized into the polynomial, Ogden, reduced polynomial, and Marlow models based on their specific theoretical compositions. Strict criteria were established for the test conditions and the preparation of the specimens used in the experiments. Three bar specimens with consistent compositional ratios (Mn–20Cu–5Ni–2Fe, at. %), and thicknesses, widths, and total lengths of approximately (2 ± 0.2), (15 ± 0.2), and (150 ± 0.2) mm, were selected and allowed to stand in laboratory conditions (room temperature of ∼23 °C) for 48 h before testing.

As shown in Fig. 5(a), the uniaxial tensile test followed the ISO 6892-1:2019³⁵ standard and was performed using an electronic universal tensile testing machine at a specimen elongometric scale of 80 mm and a strain-controlled method at a tensile strain rate of 0.00025s-1. To ensure data reliability, three test repetitions were averaged using all the axial tensile stress–strain data. The uniaxial tensile test results, as shown in Fig. 5(b), illustrated the typical hyperelastic properties of the Mn–Cu damping alloy during the elastic deformation stage. Specifically, the stress–strain curve slope decreased and then stabilized as the strain increased.

The main linear viscoelastic models include the Prony series, the Maxwell model, and the Voigt model. The Prony series defines viscoelastic behavior and is commonly used in the engineering field. The relaxation modulus is used to evaluate the key viscoelastic parameters of the fundamental mechanical properties of a material, which are usually defined by the stress or strain time histories obtained via relaxation tests. However, using conventional relaxation tests to determine the relaxation modulus of materials such as Mn–Cu damping alloys is challenging and may lead to significant errors, affecting the accuracy of subsequent mechanical analysis. To address this problem, the present study employed dynamic mechanical analysis (DMA) frequency scanning experiments to obtain the modulus vs the frequency curves, while the Prony series parameters defining the linear viscoelasticity were acquired via appropriate parameter transformations.³⁶ This provides a new approach for the accurate evaluation of the Mn–Cu damping alloy mechanical properties.

The DMA frequency scanning experiments were performed using bar-shaped rectangular Mn–Cu damping alloy specimens of 20 nm long, (3.00 ± 0.01) mm wide, and (0.77 ± 0.01) mm thick, as shown in Fig. 6(a). The samples were obtained using wire cutting equipment and polished with 400 and 800 grit sandpaper to remove the cut marks from the surfaces. Considering the high modulus properties of the Mn–Cu damping alloy, the experiments were performed according to the ISO 6721-5:2019³⁷ standard and were tested using a 20 mm three-point bending mode on a NETZSCH DMA242E instrument (Germany). The experiments were established with a strain amplitude of 0.02%, while DMA frequency sweep tests were performed in a temperature range of −90–50 °C and a frequency sweep range of 0.01–100 Hz. The experiment was repeated three times for each condition to obtain average results.

Figure 6(b) presents the storage modulus and loss modulus frequency curves. The results showed that both the storage and loss moduli rose as the frequency increased from 0.01 to 100 Hz. The storage modulus rose from 76.4 to 78.5 GPa, showing an increase of about 2.7%, while the loss modulus increased from 4.8 to 5.8 GPa, which was ∼17.2% higher.

The Prony series model parameters were obtained by selecting some of the features on the main storage and loss modulus curves and solving them iteratively. Table III shows the linear viscoelastic Prony series parameters.

Table IV shows the PRF model parameters obtained via Eq. (27).

For structural designs with specific stiffness requirements, common engineering solutions include helical springs, disk springs, and leaf springs. Among these, leaf springs are characterized by their strong load-bearing capacity and uniform deformation under stress. Consequently, this paper proposes that the load-bearing and energy dissipation capabilities of the vibration-damping fastener be provided by leaf springs. The newly designed novel energy-dissipative vibration-damping fastener (NEDF), as shown in Fig. 9, measures 320 mm in length, 245 mm in width, and 70 mm in height, and consists of four main components: the load-bearing part, metal clips, leaf spring assembly, and support. The leaf spring assembly is composed of three high-damping alloy leaf springs, each 150 mm wide, with arc lengths of 220, 200, and 180 mm, respectively, and an arc angle of 55°. It is worth noting that the disk spring located at the top has been thickened at both ends to stably perform its load-bearing function. Two metal clips are positioned near the ends to secure the three high-damping alloy leaf springs, a design that mitigates the adverse impact of metal clips on the deformation of the damping alloy leaf springs under load. The leaf spring assembly is placed on the load-bearing part via the leaf spring supports and is fixed to the track slab by the load-bearing part.

In this section, the Finite Element Method (FEM) of the NEDF is established based on its dimensional parameters. As shown in Fig. 9(a), the FEM consists of fundamental components including the rail, the load-bearing part, the leaf spring assembly, and the leaf spring support. Referencing actual working conditions, the specific settings in the finite element model are as follows:

1. Material properties: The materials for support are specified as 304 stainless steel, with a density of 7.8 g/cm³, an elastic modulus of 210 GPa, and a Poisson’s ratio of 0.3. The material for the leaf spring assembly is specified as Mn–Cu damping alloy, with a density of 6.9 g/cm³; its hyperelastic and nonlinear viscoelastic parameters are detailed in Tables III and IV To enhance the efficiency of the finite element computation, the rail and load-bearing part, which do not undergo deformation, are set as rigid bodies, while the remaining components are set as elastic materials.

2. Contact settings: The components of the NEDF were assembled in ABAQUS. The leaf spring assembly and the leaf spring supports were constrained using a Tie constraint, and the leaf spring supports and the load-bearing part were also constrained using a Tie constraint. Interlayer contact within the leaf spring assembly was defined using contact constraints. The leaf spring assembly and the rail were constrained using a Tie constraint, with the friction coefficient set to 0.3 for all contact interfaces.

3. Loading settings: For the simulation of static stiffness, a concentrated load method was used, with the wheel-rail force from actual experiments serving as a reference. The load gradually increased from 0 to 20 000 N in a vertical downward direction over a duration of 60 s. For the simulation of dynamic stiffness, a preload of 15 000 N was first applied to the vibration-damping fastener. Then, a sinusoidal force load with an amplitude of 5000 N and a frequency of 4 Hz was applied, and the time-history data of force and displacement at the excitation point was collected.

4. Constraint settings: To ensure stability, the load-bearing part was fully constrained, while the rail was allowed to displace only in the vertical direction.

5. Mesh division: In this study, the mesh was generated using the ABAQUS “mesh part” function, with the Element Library for all components set to “Standard” and the geometric order set to “Linear.” All components of the NEDF were meshed using the C3D8R element type for the tetrahedral mesh. The overall mesh size was approximately set to 4 mm, with the FEM model consisting of 124 058 nodes and 97 995 elements. The leaf spring component's mesh consisted of 29 859 nodes and 22 680 elements.

The FEM simulation results are shown in Fig. 10. The simulated static and dynamic stiffness are 14.740 and 14.726 kN/mm, respectively. Compared to traditional compression type fasteners, the static stiffness of the NEDF is close to the static stiffness of the compression type fasteners, which is 15.895 kN/mm. At a frequency of 4 Hz, the area of the force–displacement curve of the NEDF is larger than that of the compression type fasteners, indicating that the vibration-damping energy dissipation characteristics of the NEDF are superior at 4 Hz. Notably, the dynamic stiffness of the NEDF shows little variation compared to its static stiffness, while the dynamic stiffness of the compression type fasteners increases to 20.224 kN/mm. This suggests that the dynamic stiffness of the NEDF has a lower frequency dependency compared to compression type fasteners, which ensures that the fastener maintains its damping performance under high-frequency vibrations. As shown in Fig. 10(b), the maximum strain of the NEDF is 0.6%, all occurring in the leaf spring assembly, indicating that this structure can effectively induce deformation in the high-damping alloy leaf springs under load, thereby enhancing its damping performance.

To demonstrate the low-frequency dependency of the NEDF stiffness, this study performed simulation calculations of the force–displacement curves for both the NEDF and compression type fasteners at four different frequencies: 4, 20, 40, and 80 Hz. The simulation results are shown in Figs. 11(a) and 11(b). By analyzing the force–displacement curves, the dynamic stiffness and damping factors of the NEDF and compression type fasteners at different frequencies were obtained, as presented in Figs. 11(c) and 11(d). By comparison, the following conclusions are made:

1. With the increase in frequency, the dynamic stiffness of the NEDF shows minimal variation, with a change rate of 6.04%; whereas the dynamic stiffness of the compression type fasteners exhibits significant variation, with a change rate of 20.49%. This indicates that the NEDF can maintain relatively low dynamic stiffness under high-frequency vibrations compared to compression type fasteners, which is beneficial for fully exploiting its damping characteristics.

2. The damping factor of the NEDF is higher than that of the compression type fasteners at all four frequencies, and it increases with rising frequency. In contrast, the damping factor of the compression type fasteners decreases with increasing frequency. This demonstrates that the NEDF has superior damping performance compared to compression type fasteners, and its damping performance is further enhanced under high-frequency vibrations.

To verify the vibration-damping performance of the NEDF, hammering tests were conducted on both the NEDF and compression type fasteners to obtain the rail vibration acceleration data for different fastener assemblies. Specialized data acquisition and signal processing tools were utilized during the rail vibration acceleration analysis to assess the transfer function and one-third-octave amplitude–frequency curves. Finally, the rail vibration attenuation rate was calculated to evaluate the performance of the alloy high-vibration-damping fasteners.

This experiment was conducted with reference to the standards “GB/T 14412-2005, Mechanical vibration and shock. Mechanical mounting of accelerometers,”⁴¹ “GB/T 2298-1991, Mechanical vibration and shock-Terminology,”⁴² and “EN 15461:2008+A1:2010, Railway applications - Noise emission - Characterization of the dynamic properties of track sections for pass by noise measurements.”⁴³ Under hammering load conditions, the vibration attenuation characteristics of the rail were recorded at one-third octave frequency points, with a test frequency range of 50–2000 Hz. The rail was subjected to vertical hammering using an IEPE medium-sized force hammer to test the vertical rail response when using compression type fasteners and NEDF. The rail vibration frequency response function (FRF) was then solved to calculate the rail vibration attenuation rate at the one-third-octave frequency point of the crossover frequency. Table V shows the test equipment used, while Fig. 12 illustrates the site configuration of the hammering test.

This test measured the rail vibration attenuation characteristics recorded at one-third octave frequency points in hammer load conditions in a test frequency range of 50–2000 Hz.

As shown in Fig. 13, A(x) represented the FRF amplitude of a one-third-octave frequency point at x distance from the accelerometer arrangement point (point c). The rail-radiated power was proportional to the FRF amplitude, which was integrated along the length of the rail $∫0∞Ax2dx$⁠.

The installed compression type fastener and DENF were evaluated. The rail was attached to the track plate using ten groups of fasteners at 0.6 m intervals. Figure 13 shows the acceleration sensor and hammering positions. After connecting the instrumentation in accordance with the measurement point layout scheme, the sampling frequency was set to 40000 Hz to ensure normal signals in each channel, the sensitivity coefficients of which were confirmed before testing. Then the hammer load was applied, the excitation and response signals on the rails installed on the fasteners were collected. FRF test was performed. Three hammer tests were carried out at each measuring point to take the average, and the FRF was recorded in the form of one-third octave spectrum.

The rail vibration attenuation rate results of the one-third-octave spectrum were obtained after installing the compression type fastener and NEDF (Fig. 14):

1. A rail vibration amplitude graph comparison indicated that installing alloy high-vibration-damping fasteners reduced the rail vibration amplitude faster over time than the compression type fastener, showing a stronger vibration energy dissipation capacity.

2. The experimental results were compared with the theoretically calculated curves to examine the typical first-order occlusion, first-order cutoff, second-order occlusion, and high-frequency regions of a double-layer bearing rail system. The performance of the pinned-pinned vibrational region was insignificant due to the standard requirement that the experimental results should be expressed in terms of discrete one-third-octave frequency points. Overall, the experimental test results were consistent with the theoretically calculated patterns.

3. When the vibration frequency of the rail system entered the second-order occlusion zone, the alloy high-vibration-damping fasteners showed significantly higher vibration attenuation rates, especially around 400 Hz, where the increase reached a maximum value of 2.718 dB/m compared with the compression type fasteners.

4. The alloy high-vibration-damping fasteners exhibited considerable vibration dissipation ability in the second-order occlusion zone and at each subsequent test point. They showed 78.6% and 51.9% improvement in the second-order occlusion and high-frequency zones, respectively, compared with the compression type fasteners. These results indicated that installing NEDF underneath the rails effectively reduced vibration.

This paper proposes a new type of energy dissipating vibration-damping fastener (NEDF) for improving the vibration attenuation capacity of rails. A theoretical model of a double-layer bearing rail system is used to examine the effect of fastener stiffness and damping factors on the rail vibration attenuation rate. An intrinsic damping alloy model is established, and its Prony level and PRF model parameters are determined. These parameters are combined with actual operational conditions to design a new type of energy dissipating vibration-damping fastener (NEDF), while its static and dynamic stiffness is simulated to investigate its vibration isolation ability. Hammering tests were conducted after installing the NEDF and compression type fasteners in the rail system to comparatively evaluate the damping characteristics of the NEDF. The specific conclusions are as follows:

1. For the periodic double-layer support rail system, the rail vibration attenuation rate is generally higher at low frequencies and initially decreases with increasing frequency before increasing again. Peaks are observed due to the resonance between the fastener stiffness and the composite stiffness of the rail pad and under-rail pads, as well as peaks caused by the “Pinned–Pinned mode.”

2. The theoretical model of the periodic double-layer bearing rail system is tested, showing that enhancing the fastener stiffness and loss factor increases the rail vibration attenuation rate.

3. The simulation compared the static and dynamic stiffness of NEDF and compression type fasteners. Although the static stiffness values of both fasteners are almost identical, the damping factor of the NEDF is higher than that of the compression type fasteners, indicating that the NEDF has a stronger damping capability.

4. The simulation calculated the force–displacement curves of the NEDF and compression type fasteners at different frequencies. The simulated results indicate that the dynamic stiffness of the NEDF exhibits lower frequency dependency compared to the compression type fasteners. In addition, the damping factor of the NEDF increases with frequency, whereas the damping factor of the compression type fasteners decreases with frequency. This demonstrates that the NEDF has effective vibration-damping and noise-reduction capabilities, particularly for high-frequency noise.

5. Hammering tests were performed on the rail systems assembled with NEDF and compression type fasteners, respectively. Compared with compression type fasteners, the vibration attenuation rates of NEDF were 78.6% and 51.9% higher in the second-order occlusion and high-frequency areas, while they displayed significantly improved energy dissipation capacity.

The authors have no conflicts to disclose.

Yan Liu: Conceptualization (equal); Data curation (equal); Writing – original draft (equal). Jiansen Zhu: Data curation (equal); Formal analysis (equal); Methodology (equal). Xianpu Yuan: Formal analysis (equal); Supervision (equal); Writing – review & editing (equal). Runhua Fan: Formal analysis (equal); Methodology (equal). Yuan Yuan: Data curation (equal); Methodology (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.