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Vehicle seat vibrations significantly affect driver and passenger comfort. This study proposes a 3D-printed seat cushion incorporating a double-diamond cell structure designed for low-frequency vibration isolation. Characterized by quasi-zero stiffness (QZS), this structure was analyzed through analytical and simulation approaches to determine its vibration transmissibility. A machine learning-based response surface method enabled performance prediction and sensitivity analysis of key design parameters, revealing that link element length and spring stiffness most influence peak transmissibility. Unlike previous seat suspension designs focusing on X-shaped suspension supports, this approach provides an efficient means of optimizing the seat cushion’s vibration isolation performance without extensive simulations or complex analytical solutions.

Local resonance structure (LRS) can effectively suppress wave transmission, but the design of LRS with tunable band gaps is still a challenge. This work proposes an LRS with two tunable band gaps, where the first bandwidth is successfully enlarged almost five times, and finally a low-frequency broadband with 60–420 Hz is obtained with the second disappearing because of the remarkable modification of band gaps obtained only by adjusting the stiffness rather than by large deformation or changing geometric configuration in traditional methods. The mechanism of tunable band gaps would have important implications for designing metamaterials with broadband, and potential applications for vibration and noise attenuation.

A novel concept of a nonlinear oscillator is proposed, based on a bistable element, which operates around an unstable equilibrium point. Contrary to the Quasi-Zero Stiffness oscillators, a totally different redistribution of the stiffness elements is followed, so that any level required static stiffness for the entire system can be maintained. This oscillator is designed to present the same overall (static) stiffness around the system equilibrium point, the same mass and to use the same damping element as a reference classical linear SDOF oscillator. Once such an oscillator is optimally designed, it is shown to exhibit an extraordinary apparent damping ratio, which is several orders of magnitude higher than that of the original SDOF system, especially in cases where the original damping of the SDOF system is extremely low. This damping behavior is not a result of a novel additional extraordinary energy dissipation mechanism, but a result of the phase difference between the positive and the negative stiffness elastic forces; this is in turn a consequence of the proper redistribution of the stiffness and the damping elements. This fact ensures that an adequate level of elastic forces exists throughout the entire frequency range, able to counteract the inertial and the external excitation forces. Consequently, a resonance phenomenon, which is inherent in the original linear SDOF system, cannot emerge in the proposed oscillator.

Variable stiffness vibration isolator (VSVI) can be switched between the low stiffness state and high stiffness state, respectively suitable for spacecraft requirement in cutting off the jitter transmitted from the bus to high accuracy payload and for avoiding long term adjustment during the process of attitude maneuver. For the advantage stated, the mechanism of VSVI is investigated for several types, considering the following factors: parallel manipulator with positive and negative stiffness components, structure with nonlinearity stiffness characteristics, smart materials or mechanisms, and maglev configuration. The design objectives of variable mechanisms are summarized into three indexes: adjustment range of stiffness, a lower limit of resonant frequency, and region with quasi-zero stiffness. Experimental studies for related isolators were presented, and the typical configuration or schematic diagram was shown under each index. As for the application of VSVI in spacecraft, research on the two significant problems, i.e. dynamic modeling and non-collocated control problem, is investigated for the design of control law of VSVI’s stiffness. Besides the complete description of spacecraft flexibility, variable stiffness characteristic that leads to a time-varying system and is easily coupled with the maneuvering process is worthy of more attention. Finally, challenges and future research are suggested for improving the performance in spacecraft application.

To reduce the natural frequency of air isolators and realize low or ultra-low frequency air/magnetic composite vibration isolation with large payloads, a magnetically repulsive negative stiffness permanent magnetic array (MRNSPMA) is proposed. Specifically, we utilize cuboidal permanent magnets to form a spatial array that is mechanically repulsive in the horizontal direction and structurally parallel in the vertical direction. The superiority of MRNSPMA in achieving high amplitude negative stiffness is verified. Furthermore, the effects of structural parameters on vibration transmissibility under the base and force excitations are investigated with the introduction of MRNSPMA. The displacement transmissibility, the force transmissibility and the frequency corresponding to the peak transmissibility are significantly reduced, validating the promise of MRNSPMA for improving the isolation performance of cutting-edge scientific experimental systems and facilities.

Active suspension technique normally provides the best vibration mitigation performance at the cost of high-energy consumption. In contrast, the energy consumption of a semi-active suspension is normally much smaller than that of an active suspension, whereas the control performance is compromised as well. Observing the core issue that caused such a phenomenon is that the existing semi-active control force, unlike the active control force, shall always oppose to the relative motion of the actuator (i.e. clipping phenomenon). This paper subsequently proposes a novel semi-active vehicle suspension system that incorporates a passive negative stiffness (NS) spring and a semi-active damper (SD) to realize uncompromised active control force while consuming energy of a typical semi-active suspension system. In specific, the proposed system allows for decomposition of the target active control force and tracked via the collaboration of the NS and SD components. Herein, the NS element is capable of releasing the store potential energy that subsequently eases the aforementioned clipping phenomenon of a traditional semi-active suspension. In this paper, besides the relevant clarifications on the system topology and working mechanism, its feasibility and performance enhancement are also validated via systematic numerical simulations of a vehicle suspension; and the results indicate, for the first time, that the proposed semi-active suspension can fully track the active control force and subsequently achieve unprecedented control performance comparable to an active controller.

A control strategy combining cubic displacement feedback nonlinear control and proportional-differential (PD) linear control is used to control the vibration performance of the maglev system. The maglev system is divided into positive stiffness maglev system, quasi-zero stiffness maglev system and negative stiffness maglev system according to the linear stiffness value of maglev system. Firstly, an improved multi-scale method is used to analyze the vibration characteristics of suspension in the positive stiffness state of the maglev system. Secondly, the influence of control parameters on train vibration amplitude and vibration center displacement under quasi-zero stiffness is studied. Finally, the vibration characteristics of the train when the maglev system is in negative stiffness are analyzed by numerical simulation. The maglev system exhibits the worst vibration performance under negative stiffness compared with positive stiffness and quasi-zero stiffness. The suspension frame is easy to enter the chaotic motion state, and its vibration center is easy to deviate from the equilibrium position and produce large displacement when the maglev system is in the negative stiffness state. The control results show that the control strategy combining the cubic displacement feedback nonlinear control with the PD linear control can make the maglev system exhibit better vibration characteristics under positive and quasi-zero stiffness.

Base isolation proves to be an effective vibration control strategy for buildings. However, the base-isolation floor (BIF) may undergo substantial displacements. To improve the seismic performance of base-isolation system, this paper proposes a multi-performance economical optimization procedure (MPEOP) for exploring the optimal parameters of base isolation system with tuned inerter negative stiffness damper (BIS-TINSD) subjected to non-stationary seismic excitation. The simplified analysis model for BIS-TINSD is developed, followed by the formulation of the state-space representation. The non-stationary seismic excitation is represented as a stationary Gaussian process with a time-modulating function based on the Clough–Penzien spectrum, and combining the equations of motion with seismic excitation results in the augmented state-space representation of structure-damper-excitation, followed by the formulation of differential Lyapunov equation. The multi-objective performance economical index is proposed, in which the performance optimization objective is defined as a weighted combination of base isolation floor displacement and superstructure acceleration, and the economic optimization objective is set as the support stiffness. The Pareto optimal fronts (POF) are adopted to deal with optimal objectives. The examination of optimal design parameters is extended under real earthquake records. The results demonstrate the effectiveness of the MPEOP, and indicate the advantages of the BIS-TINSD compared with the inerter amplify damper (IAD) and negative stiffness inerter damper (NSID).

Transmission loss of acoustic metamaterials (AM) made of double thin plates with magnetic (negative) stiffness was analyzed using theory, finite element analysis and experimental techniques. The theoretical formulation was done using a rectangular duct below the first cut off frequency, the model is then validated against finite element method and experiment. Two cubic magnets were used, their interaction force and the resulted magnetic stiffness were calculated. The sound transmission loss (STL) of the structure is calculated for plane wave condition, the addition of magnetic mass shifts STL peaks to the lower frequency compared to a structure without mass. The slight increase in STL for small negative stiffness in experiment is not enough to cancel the effect of air compressibility. However, a significant enhancement could be expected if negative stiffness can be made large enough in the double thin plates. The developed AM can be employed as a prospective sound engineering control at low frequency.