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As an efficient, environmentally friendly, and economical urban public transportation tool, the subway has significant advantages compared to other urban public transportation tools and plays an irreplaceable role in the urban rail transit system. While the subway brings many conveniences to people, its operation has also brought a series of problems to urban development and residents’ lives, especially the vibration and noise problems generated by the subway have become unavoidable and urgent problems to be solved. The traditional wave barriers have a certain effect on attenuating and suppressing the vibration generated by the subway, but it has shortcomings in terms of the width and quantity of elastic wave bandgap (BG), so its application in low-frequency vibration reduction and isolation of subway systems is greatly limited. In order to broaden the elastic BG width and quantity of the wave barrier, this paper designs a novel phononic-like crystal subway wave barrier (PLCSWB) for subway vibration isolation based on locally resonant theory. Firstly, the dispersion curves of the novel PLCSWB are calculated using the improved plane wave expansion method and finite element method (FEM), and compared with the dispersion curves of traditional phononic crystal (PC) wave barriers. Secondly, the frequency response function of the novel PLCSWB is calculated using FEM to evaluate its attenuation effect on vibration, and the energy distribution characteristics at its BG boundary are analyzed. Then, the main factors affecting the BG of the novel PLCSWB are analyzed, and a spring–mass system equivalent model of the novel PLCSWB is established to theoretically estimate its BG range. Finally, the vibration data of the tunnel wall monitored on site are used to analyze and verify the vibration isolation effect of the novel PLCSWB. The results show that the novel PLCSWB opens five low-frequency BGs in the 200Hz frequency band, which increased the total width of the opened BGs by 49% compared to traditional PC wave barriers. In the frequency range of the BG, the attenuation value of the novel PLCSWB to vibration is mostly above 30dB, and the energy distribution inside the structure is mainly concentrated in the primitive cell that controls the BG, indicating good attenuation and control effects on vibration. The main factors affecting the BG of the novel PLCSWB are the density of the scatterer material, the elastic modulus, and the thickness of the wrapping layer material. Moreover, during subway operation, the novel PLCSWB has a good attenuation effect on the vibration transmitted from the tunnel wall to the soil. Among them, the maximum vibration acceleration amplitude of the novel PLCSWB with nine rows is reduced by 47%, and the vibration isolation performance is remarkable. The relevant research results of this paper provide a novel approach and method for the study of subway vibration reduction and isolation, and can also provide specific references for the design and development of wave barriers.

Quasi-zero Stiffness (QZS) isolators offer significant advantages in low-frequency vibration isolation. Nonetheless, the complexity of the structure and the limited load adaptability hinder the practical application of such isolators. Therefore, this paper proposes a novel load-adjustable QZS isolator based on a compliant mechanism. By integrating the positive stiffness of the curved beam and the negative one of the inclined beam, a comprehensive design strategy for the QZS flexible beam is introduced. The optimal geometric parameters of the structure are determined using a genetic algorithm, and the finite element simulations are employed to numerically validate the QZS characteristics of the structure as well as the low-frequency vibration isolation performance. Leveraging the same structural design and a kind of temperature-sensitive materials-Thermoplastic Polyurethane (TPU), a unit cell of load-adjustable QZS isolator controlled by electric heating is developed and fabricated via 3D printing. Static and dynamic tests are conducted to explore the QZS platform characteristics and vibration isolation performance of the isolator subjected to various voltage inputs. The results demonstrate that the QZS characteristics of the isolator can be effectively regulated by adjusting the input voltage, ensuring effective low-frequency vibration isolation under different loads. Moreover, the incorporation of serial and parallel arrangements of unit cells could further enhance the range of load adjustability. This study offers novel insights into the design of load-adjustable QZS isolators.

It has been commonly assumed that an inerter–stiffness–damping isolator mounts on a rigid foundation, however, there exists a strong interaction among the vibration source, isolator, and the base structure for systems with flexible or nonrigid bases. This paper investigates a system consisting of an isolation object, mounted on flexible base plate through an inerter–spring–damping isolator. The steady-state response of the plate-exerted point force excitation can be obtained by using the eigenfunction expansion theorem and expressed by the eigenfunctions and natural frequencies of the system. The four-pole parameter of the inerter can be modeled from the formula calculation or its properties. The transmissibility relation of the proposed system is obtained by using the four-pole parameter theory, which is validated by creating the simulation model in Abaqus software. The power transmission ratio as an isolation performance index is proposed by the mobility relationship among the isolation object, the isolator, and the base. The novelty of this study is that the vibration transmissibility with the flexible base has a much better roll-off rate and anti-resonance peak than that of the rigid base in the high-frequency range, although the resonant peak is generated. A comprehensive parameter analysis shows that the isolation performance can be designed and adjusted by the thickness, material of the plate and the position of the isolator. The effects of feedback control on the resonant peak mitigation of the proposed system are discussed in detail based on Resonant Control, Positive Position Feedback, and Fractional Order Positive Position Feedback. The $H_2$ optimization criterion is employed to obtain the optimal damping parameters of positive position feedback.

The quasi-zero stiffness (QZS) structure is capable of achieving a satisfactory low-frequency vibration isolation effect. However, the majority of current QZS structure designs are complex, comprising a single working load and a relatively limited QZS zone. This paper presents the development of a multi-quasi-zero (MQZS) stiffness vibration structure based on a circular shallow arch structure. The static compression of the unit structure was studied in detail using the theoretical derivation, and finite element simulation, which can achieve multiple loads and a big QZS zone using the symmetrical and orthogonal connections, respectively. An analytical solution for the transfer rate was derived by solving the nonlinear dynamic equations of the system using the Harmonic Balance Method (HBM). In comparison to the conventional QZS system and the linear system, the vibration isolation frequency of the MQZS system is reduced by 75%, and the vibration transmissibility is reduced by 22dB at the same frequency. Furthermore, the findings based on 3D printing demonstrate that the designed MQZS isolator exhibits an effective low-frequency vibration isolation effect and has promising potential for meeting the requirements of integration and lightweight design.

Nonlinear vibration isolators with high-static-low-dynamic-stiffness (HSLDS) can achieve low-frequency isolations, while they are usually applicable to a limited range of payload mass. To address the issue, a reconfigurable HSLDS isolator is proposed based on compliant structures. The isolator can be assembled as a unilateral configuration and a bridge-type configuration, exhibiting low-frequency isolations for both light and heavy payloads in the experiments. To reveal the mass adaption mechanism of the proposed isolator, a theoretical analysis is performed. The restoring force of the compliant structure is characterized by a beam constraint model and validated by a finite element analysis and experiments. The reconfiguration of the isolator changes the geometric constraint of the structure during deformations. The unilateral structure exhibits weakly softening stiffness in the experimental range. The bridge-type configuration demonstrates strongly softening and negative stiffness, presenting obvious HSLDS at large deformation. The vibration equation of the isolator is established based on the restoring forces of both configurations and the frequency responses are obtained through a harmonic balance method. The frequency responses under different masses, different excitations and different damping ratios are investigated. A further discussion on the mass adaption range is provided. This work provides a new insight into realizing HSLDS isolators applicable to a wide range of payload mass by the reconfiguration of basic compliant structures.

Ocean waves are abundant in energy; however, they also cause ships to sway and can disrupt the operation of precision equipment. Harvesting energy from ocean waves and isolating vibrations in marine precision equipment have long posed significant challenges due to the inherently low-frequency nature of ocean waves. This study proposes a dynamic-constrained nonlinear (DCN) stiffness method for low-frequency energy harvesting and vibration isolation. A generalized mathematical model of the DCN stiffness system is established, and its semi-analytical solution is derived using the harmonic balance method and the arc-length extension method. Finally, various application scenarios for energy harvesting and vibration isolation using the nonlinear stiffness method are explored. The results demonstrate that the DCN stiffness method can significantly enhance the performance of low-frequency wave energy, capture and provide excellent low-frequency vibration isolation. Notably, this method exhibits a strong adaptive capability to excitation compared to traditional nonlinear stiffness methods.

This paper deals with the problem of optimum design of a foundation for rotating machinery with a view to minimize vibration transmission from a machine source to its supporting structure. The problem of analysis and optimization of the installation systems of machinery has been extensively researched on the assumption of a rigid supporting structure. The design based on a rigid supporting structure model is reasonable for the installation of machinery in many real engineering situations. However, this rigid support based model may not be appropriate for the problem studied herein where the machinery is to be installed on a relatively flexible supporting plate. Thus, a generalized mathematical model of mobility power flow is developed in this paper, with a rotating machine as vibration source, resilient mounts as isolator, and a flexible supporting plate as receiver. The objective of minimizing vibration transmission is realized by optimization of stiffness coefficients of resilient mounts with a constraint on the vibration level of the machine. The design objective is chosen as the minimization of the power flow transmitted to the flexible supporting plate through the resilient mounts at the excitation frequency of the machinery. Both a single excitation frequency and a range of excitation frequencies are considered. A gradient-based mathematical programing method is selected for its advantage of efficiently solving the current type of optimization problem with multiple mounts and multi-degree-of-freedom vibration transmission. The sensitivities of the objective and the constraint functions with respect to the design variables are derived analytically. The design and performance of the optimized machinery foundation is illustrated and discussed using several numerical examples. The optimized mounting system is suitable for the installation case of a rotating machine with a low or medium service speed on a flexible supporting plate structure.

The primary objective of this fundamental research is to investigate the mechanical properties of the disk spring when the friction at the contact edges is asymmetric and varies with the load. The contact mechanics study shows that the static friction and static friction coefficient on fractal surfaces change depending on the normal load. In this paper, a fractal contact model based on the W-M function is used to explore the connection between the static friction and the normal load. Subsequently, taking into account the asymmetry of the contact surface at the edge, the variable static friction coefficient is brought into the existing model to obtain an improved static model of the disk spring. Different fractal dimensions, frictional states and free heights are considered under quasi-static loading condition, the relative errors between this paper and the method using Coulomb friction are also calculated, and experimental validation was performed. The static stiffness and force hysteresis of the disk spring for different forms of asymmetric variable friction are discussed. It is shown that using the variable friction model can improve the computational accuracy of the disk spring model under small loads and help to improve the design and control accuracy of preload and vibration isolation equipment using the disk spring as a component.

In the current paper, the quasi-zero stiffness effect caused by the pseudo elastic effect of Shape Memory Alloy (SMA) spring in vibration isolator is modeled and analyzed. The recovery force of the SMA spring is modeled as a non-convex one. A macroscopic differential model is employed to describe the hysteretic dynamics and pseudo elasticity of the SMA spring. It is illustrated that the resonant frequency of the proposed isolation system is close to zero. Numerical simulations are presented in studying the influence of the excitation frequencies on vibration isolation performance. It shows that a quasi-zero dynamic stiffness is achieved; the feasibility of the proposed system for ultra-low frequency excitation isolation is validated.