To break through the limitations of the traditional vibration isolation system in the low-frequency and resonance region, this study designed a nonlinear quasi-zero stiffness (QZS) element structure composed of a negative stiffness bistable sinusoidal beam and a positive stiffness arc Euler beam in parallel. The finite element model and restoring force expression of the element structure were established by static analysis. The restoring force of the element structure and the parameter conditions with QZS characteristics near the equilibrium position were obtained. The experimental data show that the bistable QZS element structure has a wide QZS region, which verifies the accuracy of the theoretical model and finite element analysis. Based on the static analysis results, the nonlinear dynamic model of the QZS element structure is further established. The influence of system parameters and excitation amplitude on the vibration isolation performance and response stability of the system was studied using the harmonic balance method (HBM). In addition, based on the vibration isolation model of the bistable QZS element structure, a vibration isolation base with high static and low dynamic stiffness characteristics is designed. The vibration isolation performance of the base is verified by the dynamic experiment. This study provides a new design paradigm for the miniaturized and integrated vibration isolation system of special equipment, and its bistable QZS mechanism shows significant engineering application potential in broadening the effective vibration isolation frequency band.
Nonlinear coupled transversal–longitudinal vibrations of a thin rotating beam attached to a rigid hub are investigated in the paper. The analytical model is based on Euler–Bernoulli beam theory, extended to accommodate a moderately large displacement field and modest geometrical nonlinearities. The governing partial differential equations (PDEs) of motion are derived from Hamilton’s principle for clamped-free boundary conditions. The complete set of three PDEs involving transversal and longitudinal vibrations and angular velocity is expanded up to the third perturbation order. Then, the longitudinal motion, which includes effects arising from the structure’s rotation, has been reduced to the transverse motion. Moreover, the assumption of constant angular velocity is made, and finally a new original reduced (condensed) single d.o.f. model of the rotating beam is proposed. Next, the PDEs are reduced to ODEs by means of the Galerkin method, and the final form of the condensed transversal–longitudinal dynamics of the rotating beam is obtained. The effect of angular velocity and nonlinear coupling terms on the softening or hardening of the resonance curves is demonstrated. Moreover, the importance of the preset angle in contributing to the Coriolis force in system dynamics is studied.
Understanding snap-through instability and dynamic behavior is vital for designing lightweight, damage-tolerant components and preventing catastrophic failure in structural applications. This study presents a comprehensive analytical, experimental, as well as numerical investigation of the nonlinear snap-through instability and dynamic behavior of 3D-printed architected sandwich spherical meta-shells with bamboo fiber-reinforced polylactic acid (PLA) composite face-sheets. The proposed structure combines lightweight architected star-shaped cellular cores with sustainable bio-composite face-sheets to achieve enhanced stiffness, stability, and vibration performance. Using Hamilton’s principle, a nonlinear shell model is established within the framework of the First-Order Shear Deformation Theory (FSDT), while geometric nonlinearity is represented through the von-Kármán formulation. The governing equations are solved through the Ritz method employing Chebyshev polynomial expansion, while the cylindrical arc-length technique is adopted to accurately trace complex snap-through equilibrium paths. The present work investigates the influence of two practically important loading conditions, namely concentrated loading (CL) and uniformly distributed loading (UDL), on the nonlinear snap-through response of architected spherical meta-shells. The analytical model is first verified against benchmark solutions available in the literature. Additionally, a 3D finite element model is developed to capture the true physical dynamic behavior of the complex architected geometry, which is evaluated experimentally through impact hammer modal testing on a baseline pure PLA fused deposition modeling (FDM)-fabricated specimen. Following these evaluations, an extensive parametric study is carried out to examine the influence of shell geometry, architected core characteristics, thickness ratio, fiber volume fraction, loading scenarios, and support conditions on nonlinear vibration and snap-through responses. The developed bio-inspired architected sandwich meta-shells offer an efficient lightweight alternative for multifunctional structural systems that demand enhanced stability, excellent energy absorption, and outstanding dynamic performance.
The electrochemical performance of batteries is critically influenced by evolving interparticle contact in composite electrodes. While significant contact stresses trigger structural degradation and capacity fading, the reestablishment of electrical contact between active particles facilitates capacity recovery. Herein, an electro-chemo-mechanical coupling model in the Eulerian description is developed to investigate the effects of contact behaviors on the electro-chemo-mechanical responses in electrodes. The proposed model simultaneously describes mechanical and electrical contact among active particles, and the Eulerian description accommodates the associated geometrical changes. Crucially, the model reproduces the capacity recovery phenomenon. The results show that significant contact stress suppresses lithium accumulation in the contact region. It is found that the electrically isolated particle is activated due to interparticle contact. At the early stage of contact, lithiation is transiently reversed into delithiation and then suppressed in the highly lithiated particle, whereas lithiation is promoted in the low lithiated particle. Ultimately, the two particles evolve with a uniform degree of lithiation. This concurrent lithiation of both particles contributes to an increase in the total amount of lithium intercalated, leading to capacity recovery. The proposed model provides insights into the complex interplay among interparticle contact behaviors, interfacial reaction kinetics, and electrode capacity evolution.
