Analytical formulation of dynamic stiffness

Abstract

The dynamic stiffness matrix method enables one to model an infinite number of natural modes by means of a small number of unknowns. The method has been extended to skeletal structures with uniform or non-uniform, straight or curved, damped or undamped beam members. For two-dimensional structures, if one of the dimensions can be eliminated by means of the Kantorovich method, the method still applies. However, for more complicated systems, analytical formulation of the dynamic stiffness is tedious. A computer assisted analytical method is introduced here for any structural members the differential governing equations of which are expressible in matrix polynomial form. Complex arithmetics are used to cater for all possible classification of the characteristic roots. Numerical examples are given and are compared with existing results.