The forced Motion of a Nonconservatively Loaded Elastic System

摘要

The solution of a non-self adjoint boundary value problem, having both time derivatives of the dependent variable and known time-dependent functions in the boundary conditions, is obtained by means of Williams' method. Because the problem is nonself-adjoint, the usual form of the modified orthogonality condition for the eigenfunctions is no longer applicable, and must be replaced by a modified biorthogonality condition relating the eigne-functions of the original system to those of its adjoint. Plots of displacement versus time and mode shapes are given. In solving the problem, a heretofore unclear limitation of Williams' method is pointed out. (Author)