Solution of the Moving Mass Problem Using Complex Eigenfunction Expansions

Abstract

A new solution technique is developed for solving the moving mass problem for nonconservative, linear, distributed parameter systems using complex eigenfunction expansions. Traditional Galerkin analysis of this problem using complex eigenfunctions fails in the limit of large numbers of trial functions because complex eigenfunctions are not linearly independent. This linear dependence problem is circumvented by applying a modal constraint on the velocity of the distributed parameter system (Renshaw, A. A., 1997, J. Appl. Mech., 64 , pp. 238–240). This constraint is valid for all complete sets of eigenfunctions but must be applied with care for finite dimensional approximations of concentrated loads such as found in the moving mass problem. Numerical results indicate that the proposed method is competitive with Galerkin’s method with real trial functions in terms of accuracy and rate of convergence. [S0021-8936(00)00604-8]