No abstract

The nonlinear free vibration of an axially translating viscoelastic beam with an arbitrarily varying length and axial velocity is investigated. Based on the linear viscoelastic differential constitutive law, the extended Hamilton's principle is utilized to derive the generalized third-order equations of motion for the axially translating viscoelastic Bernoulli-Euler beam. The coupling effects between the axial motion and transverse vibration are assessed under various prescribed time-varying velocity fields. The inertia force arising from the longitudinal acceleration emerges, rendering the coupling terms between the axial beam acceleration and the beam flexure. Semi-analytical solutions for the governing PDE are obtained through the separation of variables and the assumed modes method. The modified Galerkin's method and the fourth-order RungeKutta method are employed to numerically analyze the resulting equations. Further, dynamic stabilization is examined from the system energy standpoint for beam extension and retraction. Extensive numerical simulations are presented to illustrate the influences of varying translating velocities and viscoelastic parameters on the underlying dynamic responses. The material viscosity always dissipates energy and helps stabilize the transverse vibration.

Full-scale simulations of a (Magnetorheological) MR damper are carried out for revealing its hysteretic behaviors associated with implementation of semi-active control using the routine of computational fluid dynamics. By virtue of the structural symmetry of the MR damper, a two-dimensional configuration for finite element simulation is built up. Herschel-Bulkley model is employed to represent the property of the MR fluid, of which the control parameters and their relevances to the input current are addressed. Typical cases involving sinusoidal and irregular displacements, steady and transient currents loaded upon the MR damper are investigated. Numerical investigations reveal that the damper force has a positive correlation with input current, excitation amplitude and excitation frequency. The full-scale simulation is proved to exhibit a sound accuracy through the validation of experimental data. It provides a logical manner revealing the true performance of MR dampers under desirable operating modes in practice, and can be readily integrated with the gain design of the associated semi-actively controlled structure. This progress bypasses the technical challenge inherent in the traditional tests with low-frequency cyclic loadings due to the limitation of experimental setup. Besides, comparative study between two-dimensional and three-dimensional configuration simulations of the MR damper shows that former has a better applicability, which can be carried out on a low-cost platform.