Inverse mass matrix via the method of localized lagrange multipliers

Abstract

An efficient method for generating the mass matrix inverse of structural dynamic problems is presented, which can be tailored to improve the accuracy of target frequency ranges and/or wave contents. The present method bypasses the use of biorthogonal construction of a kernel inverse mass matrix that requires special procedures for boundary conditions and free edges or surfaces, and constructs the free-free inverse mass matrix employing the standard FEM procedure. The various boundary conditions are realized by the the method of localized Lagrange multipliers. In particular, the present paper constructs the kernel inverse matrix by employing the standard FEM elemental mass matrices. It is shown that the accuracy of the present inverse mass matrix is almost identical to that of a conventional consistent mass matrix or a combination of lumped and consistent mass matrices. Numerical experiments with the proposed inverse mass matrix are carried out to validate its effectiveness when applied to vibration analysis of bars, beams and plain stress problems. This article is protected by copyright. All rights reserved.