Forced and free vibrations of composite beams solved by an energetic boundary functions collocation method

Abstract

For the analyze of forced and free vibrations of composites with periodically varying interfaces, we develop an energetic boundary function method. Three types of beams under different homogeneous boundary conditions and a sequence of boundary functions for each type beam are given, which automatically satisfy the homogeneous boundary conditions. Then we derive an energy equation and construct the energetic boundary functions by further satisfying the energy equation. The solution of forced vibration is expressed in terms of energetic boundary functions as the numerical bases, and then we can derive the linear system to decide the expansion coefficients by a simple collocation technique. To find out the natural frequencies of composite beams we iteratively solve the varying linear systems which include the unknown natural frequencies, and at each iteration we employ the Rayleigh quotient to calculate the natural frequencies until convergence. Through numerical tests we find that the energetic boundary function methods are highly efficient and very accurate for solving the proposed vibration problems of composite beams.