Papers by Author: Xiao Dong Zhu

Abstract: The nonlinear dynamic equation of a laminated beam subject to parametrically deterministic excitation is derived based on the general von Karman-type equations and the Reddy third-order shear deformation plate theory. The first mode parametric resonance is taken into consideration using Galerkin approach. The modulation equations are obtained with the method of multiple scales. The frequency-amplitude and force-amplitude characters are investigated. Results show that the nonlinear behaviors belong to hardening effect.

Abstract: The first mode parametric resonance of a laminated beam subject to narrow-band random excitation is taken into consideration. The method of multiple scales is used and the stochastic jump and bifurcation have been investigated aiming at the stationary joint probability of the response of the system by using finite difference method. Results show that stochastic jump occurs mainly in the region of triple valued solution. The higher is the frequency, the more probable is the jump from the stationary nontrivial branch to the trivial one, whereas the most probable motion gradually approaches the trivial one when the band width becomes higher.

Abstract: The clearances, which universally exist in the joint parts of mechanical systems, are a main cause of various operation deteriorating problems, including noises generating, material wearing, even the early fatigue of members. In this paper, a new method to determine the clearance magnitude in the beam support is proposed with the description of a numerical example. The growing clearance will increase the vibration period of realistic system, and the accurateness of measurement is relevant to the frequency resolution of the instrument. Through the time series of the midpoint response of a simply supported beam, the period of the first modal free vibration can be obtained using the FFT Algorithm. Only two responses from different initial conditions are needed to identify the magnitude of the clearance. It is estimated the accurateness could be below 15%. The investigation also suggests this free vibration period approach may be adapted to handle the energy losses situations with the damping ratio considered in the formulas.