Acta Mechanica最新文献

This paper examines the problem of a piezomagnetic right-angle plane with irregular boundaries using the boundary element method. It considers SH waves and line source loads as external forces acting on the piezomagnetic right-angle plane. The effectiveness of the boundary element method is demonstrated through two different numerical examples. Firstly, in the absence of line source loads, the paper analyzes the dynamic characteristics in the first example by employing the image method and Graf addition theorem. Then, it introduces Green’s identities and solves the Green’s function in infinite three-dimensional space. In the second example, the paper investigates the dynamic characteristics when irregular boundaries are subjected to line source loads using the boundary element method. The results elucidate the influence on the dynamic stress concentration factor and magnetic field intensity concentration factor under appropriate conditions. Additionally, the analytical solutions are compared with finite element solutions to validate the accuracy of the conclusions presented in this study.

The converse flexoelectric effect can be applied to control thin-shell structures. In this paper, the vibration control of a conical shell with multiple flexoelectric actuators is studied. In order to investigate the actuation performance of the flexoelectric patch, this study analyzes the electric field gradient, modal forces, and displacement of a conical shell driven by the flexoelectric patch and their relationships with the design parameters. In the physical model, the AFM probe is positioned on the upper surface of the flexoelectric patch to create a high-intensity non-uniform electric field within the flexoelectric actuator. In turn, generates internal stress in the flexoelectric actuator patch through the converse flexoelectric effect. The case study shows that the high-intensity non-uniform electric field generated by the AFM probe has nearly zero contribution to the electric field in areas far from the contact point. As a result, the stress generated by the converse flexoelectric effect primarily concentrates near the AFM probe, with the size and shape of the flexoelectric patches having minimal influence on the actuation. Based on the assumption of small deformation and linear displacement, considering the vibration control of multiple flexoelectric actuators on the truncated conical shell, the lateral displacement results controlled by multiple flexoelectric actuators can be calculated by the superposition principle. When multiple flexoelectric actuators work together, the same flexoelectric actuator in different positions may induce opposite lateral displacements at a specific point on the surface of the truncated conical shell. This can result in the cancellation of vibrational displacements produced by the flexoelectric actuators. Approximate optimal distribution positions for the multi-channel flexoelectric actuators were determined through experimental simulations. In this study, the superior vibration suppression capabilities of multi-channel flexoelectric actuators are highlighted through a comparative analysis with single-channel configurations, demonstrating their effectiveness in controlling complex vibration modes in conical shell structures.

Factors such as the memory effect of viscoelastic materials and the influence of microcantilever deflection still pose challenges in the mechanical modeling, mathematical solution, and material parameter identification for AFM indentation-relaxation experiments to characterize the viscoelastic properties of cells. This paper aims to provide a rational mechanical model for interpreting the detection signals in AFM indentation-relaxation experiments. Considering the contribution of microcantilever deflection under the Euler beam assumption to the viscoelastic indentation force, the Lee-Radok’s model was updated. Combining a piecewise integration method and a time-domain differential method, we derived the implicit/explicit governing equations of the probe-cell viscoelastic indentation forces under ramp-hold protocol. After building the finite element (FE) model, we examined the effect of microcantilever deflection on the acquired data in FE simulation results and the updated model predictions, and compared our updated model with relevant experiments. Then, we proposed a new two-stage (TS) approach for parameter extraction and compared the differences between this new approach and the classic single-stage (SS) approach, thus the strategy for suppressing parameter extraction error was presented. The results validate that the transient modulus extracting by the classical SS approach is essentially an equivalent transient modulus dependent on the ramp loading history, which incurs a divergence in identification of cellular viscoelastic parameter; whereas the new TS approach is valid at a broader range of loading conditions due to explicitly reflecting the dependence of viscoelastic material parameters on ramp loading history. These conclusions provide a theoretical foundation and reference for the advancement of AFM-based detection techniques for cellular mechanical properties.

In this study, analytical solutions are presented for the flexural–torsional coupled vibration response analyses of thin-walled beams under bidirectional moving random loads. Based on classical Euler–Bernoulli and Vlasov beam theories, the governing dynamic equations considering the influence of additional torque have been established. The modal superposition method, the Laplace transform, and the Duhamel's integral technique have been employed to obtain the average value and standard deviation of beam displacements in vertical, lateral, and torsional directions. For the validation of the proposed formulations, the results obtained in this paper are compared with the results acquired by the Newmark-β method and the Monte Carlo method. Comparisons of the results prove the accuracy of the suggested formulations. Through the parametric analysis, it is confirmed that the position where the average value reaches its maximum is related to the load velocity. But the maximum standard deviation always occurs at the end of the beam, which decreases with the growth of velocity and the drop in span. When the velocity does not exceed 30 m/s, the displacement response is mainly controlled by low-order modes.

At present, rigid-flexible coupling systems have been used in various engineering fields extensively, due to task demands, the systems have become complex increasingly, and thus, it is crucial to study the dynamic problems and active control of rigid-flexible coupling systems. Piezoelectric materials with electromechanical coupling phenomenon have great applications in active control of rigid-flexible coupling systems. In the current study, the active control of rigid-flexible coupling rectangular thin plate is investigated based on piezoelectric effect. The dynamic model of rigid-flexible coupling piezoelectric rectangular thin plate is established first using the Hamilton’s principle, and its discrete form is obtained using the superposition method. The dynamic equations of the system are numerically solved using the Newmark-β method. The active control of the rigid-flexible coupling system has been carried out. Case studies show that, for rigid-flexible coupling rectangular thin plate, the rigid motion will drive the vibration of flexible thin plate, and the vibration of the flexible thin plate can cause rigid body motion. The piezoelectric patch can achieve active control of rigid body motion and flexible plate vibration simultaneously. The active control effect is related to the distribution position and thickness of the piezoelectric patch, as well as the excitation voltage. The closer the piezoelectric patch is to the edges of the rectangular thin plate, the better the active control effect on the rigid body motion. The closer the piezoelectric patch is to the center of the rectangular thin plate, the better the active control effect on the flexible plate vibration. Furthermore, the thicker the piezoelectric patch, the greater the excitation voltage, and the better the active control effect. The conclusion of the current work has direct and important engineering applications.

This work compares the effect that two categories of passive dampers have on the vibratory motion of a bridge modeled as simply supported uniform beam, namely the fixed versus the moving tuned mass damper (TMD). Assuming that the suspension system of the moving vehicle performs like a TMD, its effect on the vibratory motion at points on the beam is studied by juxtaposing it with the performance of the same system placed at a specific location on the bridge span. In both cases, the vehicle suspension is modeled as a single degree-of freedom (SDOF) system with a mass, a stiffness and a damping element. Specifically, we first examine the eigenproblem of this combined structural system comprising the bridge, the moving mass and the TMD, to compute spectrograms that show the time–frequency evolution of the eigenfrequencies for both fixed and moving TMD cases. Subsequently, we examine vibrations at a point close to center span of the beam and produce energy measures to contrast fixed versus moving TMD effectiveness, which changes over time thus making it impossible to produce a concrete measure.

Nonlinear vibration isolators can offer a high static stiffness alongside a low dynamic stiffness and so they have better isolation performance than conventional linear devices. In this paper, the models of the one-degree-of-freedom (DOF) and two-DOF bottom-springs grounded (BG) nonlinear vibration isolators with quasi-zero stiffness (QZS) characteristic are analyzed. In order to further improve the isolation performance of the 2-DOF BG nonlinear QZS vibration isolator, the H-infinity optimal control problem based on output feedback is studied. The nonlinear element of the vibration isolator is linearized by Taylor series expansion and ignoring the higher order term and then the whole nonlinear system is decomposed into linear part and nonlinear part. The output feedback H-infinity optimal controller designed for the linear part is proved to be the H-infinity optimal controller of the original nonlinear system. The controller has constraints, and the constraint equation contains input-related terms. The solution methods recorded in the existing literature are invalid for this situation. Therefore, a new linear matrix inequality for solution is given in this paper. To test the performance of the controller, numerical simulation is studied under the typical harmonic excitation. The results show that the designed controller for the 2-DOF BG nonlinear QZS vibration isolator has a good vibration isolation effect.

To accurately predict transient thermoelastic diffusion responses of the metallic solids in nanoscale heating condition, this work aims to establish a nonlocal dual-phase-lag Cattaneo-type thermoelastic diffusion theory by simultaneously consider the nonlocal effects of elastic deformation, heat and mass transport with the aid of Eringen’s nonlocal continuum mechanics. The proposed model is applied to investigate 1D transient dynamic response for copper-metallic layered structure by using eigenvalue approach. The influences of nonlocal characteristic lengths on the structural dynamic responses and wave propagations are evaluated and discussed.

Refill friction stir spot welding (RFSSW) has found several industrial applications, especially in the transportation and automotive sectors. However, modeling the RFSSW process has been tackled mainly with empirical approaches. At the same time, the key physical phenomena involved have been explained and predicted by a few numerical studies in the literature. This study uses a fully Lagrangian method, smoothed particle hydrodynamics (SPH), for the simulation of RFSSW. The Lagrangian particle method simulates materials undergoing large deformation, interface dynamic changes, void formations, material temperature, and strain evolution without using complex tracking schemes often required by traditional grid-based methods. As a relevant example, magnesium-to-steel welding simulation is presented by accounting for all the main thermo-mechanical phenomena involved. Temperature, stress, and strain field histories as well as material flow taking place during the process, are determined as characteristic aspects for qualification of RFSSW; the proposed computational approach is validated by comparing the predicted and experimentally measured welding temperature. The results obtained demonstrate that SPH is a reliable tool for welding design and process optimization and provides the information related to the involved physics needed to precisely evaluate the quality, the mechanical characteristics, and the material flow of the joined region.