A recursive formulation is proposed for the method of reverberation-ray matrix (MRRM) to exactly analyze the free vibration of a multi-span continuous rectangular Kirchhoff plate, which has two oppo- site simply-supported edges. In contrast to the traditional MRRM, numerical stability is achieved by using the present new formulation for high-order frequencies or/and for plates with large span-to-width ratios. The heavy computational cost of storage and memory are also cut down. An improved recursive formulation is further proposed by modifying the iterative formula to reduce the matrix inversion op- erations. Numerical examples are finally given to demonstrate the effectiveness and efficiency of the proposed recursive formulae.
<正>This work presents an approach named direct displacement method to investigate the free axisymmetric vibrat...
Yun WANG School of Mechanical Engineering,Hangzhou Dianzi University,Hangzhou,Zhejiang 310018,China Rong-qiao XU,Hao-jiang Ding Department of Civil Engineering,Zhejiang University,Hangzhou,Zhejiang 310058,China
An analytical solution is obtained for transient torsional vibration of a finite hollow cylinder with initial axial stress. The cylinder is subjected to dynamic shearing stress at the internal surface and is fixed at the external surface. The basic equations are presented and the solution is obtained by means of Fourier series expansion technique and the separation of variables method. The effects of the initial stress on the natural frequencies and transient torsional responses are presented and discussed.
In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we present an error estimate between the homogenization solution u0(x) and the exact solution uε(x) on the Sobolev space L∞(Ω).
HE WenMing1,2 & CUI JunZhi3 1Department of Mathematics,Wenzhou University,Wenzhou 325035,China
