Vibrations of structures

Abstract

This chapter presents that the method considered in the chapter is an important branch of the finite element analysis of structures and like static analysis, it is an extension of the matrix displacement method. In addition to needing the stiffness matrices, it will be necessary to introduce the mass matrix as well and like the stiffness matrix, the elemental mass matrix will be derived by energy methods. The elemental mass matrix, which is always symmetrical, is a matrix of equivalent nodal masses that dynamically represent the actual distributed mass of the element. Transformation of the elemental mass matrix from local to global coordinates and assemblage of the mass matrix of the entire structure are carried out in a manner similar to that adopted for the stiffness matrices. If a beam or a rigid-jointed plane frame has a number of additional masses at certain nodes, then the mass matrix of the structure must have added to it the magnitudes of these additional masses, together with their corresponding mass moments of inertia, to the appropriate nodes.