Consistent mass matrix of distributed mass beam element with linear elastic connections

Abstract

     When analyzing structures subjected to dynamic loadings, it is necessary to determine the mass matrix of these systems. The simplest procedure for defining the mass matrix of any structure is to assume that the distributed mass is concentrated at the points at which the translational displacements are defined and the distribution of the mass to these points being determined by static, in this case the result of problem depend on the number of lumped-mass. This paper deal with a procedure establishing the consistent mass matrix of distributed mass beam element with semi-rigid connections at the ends, based on the shape functions of beam. The convenience of consistent mass procedure greatly reduce the element to a MDOF system and augment the exact degree of solution.