This paper investigates the vibration behavior of the thermo-piezoelectric semiconductor (TPES) microplate on a fractional-order viscoelastic Pasternak foundation with moving laser load. The relationship between the electrochemical potential and carrier density is derived for the first time. And the symplectic elastic method is applied to TPES microplate. The field is still in its early stages and represents a frontier demanding further exploration. The present study yields several key insights into the coupled thermoelastic behavior of the microplate. At the constitutive level, the nonlocal elasticity softens both stiffness and damping. Damping exhibits a universal peak and the position of this peak is related to the natural frequency and relaxation time of the foundation. Regarding the piezoelectric-semiconductor coupling, carrier density modulates the interaction through the Debye length, with strongest coupling when the Debye length is equal to the thickness of the microplate. In terms of modal characteristics, mode shapes transition systematically from bending to torsion/ rotation with increasing mode order. For the forced vibration induced by a moving laser load, the critical velocity for resonance is accurately predicted by the decoupled critical velocities from the sideband formula. As the excitation frequency increases, the dominant mode shifts from low mode to higher mode, due to natural frequency matching. Overall, these findings provide a theoretical basis for the design and control of microplate resonators under moving thermoelastic excitation.
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.
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.
Traditional energy harvesting devices generally suffer from poor adaptability to low-frequency environments, making it difficult for them to cope with diverse conditions. This paper proposes a stiffness-adjustable electromagnetic induction energy harvesting device comprising four sets of inclined springs connected to adjustable gears, a central vertical spring, and an inertial amplifier mechanism. By altering the rotational angle of the gears, the geometric configuration and parameters of the springs are modified, thereby regulating the system’s dynamic stiffness, natural frequency, and potential energy characteristics and enabling stiffness adjustment for different environmental vibration conditions. The electromechanically coupled dynamical equations are established, and the nonlinear restoring force is approximated using a ninth-order odd-polynomial fitting method. The harmonic balance method is employed to obtain amplitude-frequency response curves. Slowly varying harmonic coefficients are introduced to analyse the stability of periodic solutions. The fourth-order Runge-Kutta method is used to generate maps of RMS load voltage and average output power. Numerical results indicate that the proposed configuration can produce large-amplitude cross-well vibrations over low-frequency and broadband ranges. Coexisting responses and two-dimensional basin sections are computed for bistable, tristable, and quasi-zero-stiffness configurations to examine the dependence of steady-state responses on initial conditions. Finite-duration pulse excitation is used to investigate transitions among coexisting responses. Changing the pulse application time can cause the system to return to its original response, switch between potential wells, or reach a large-amplitude cross-well response. These results provide a theoretical and numerical basis for state regulation in electromagnetic energy harvesters operating under low-frequency excitation.
