Incorporation of Lagrangian Multipliers into an algorithm for finding exact natural frequencies or critical buckling loads

Abstract

An existing algorithm enables natural frequencies or critical load factors to be found with certainty when “exact” stiffness matrices are used. This algorithm is extended to permit Lagrangian Multipliers to be used to couple the “exact” stiffness matrices of component structures to represent connections between the structures. The new algorithm also permits coupling of the stiffness matrices for different assumed wavelengths of sinusoidal response of a given structure with the stiffness matrices of other structures to satisfy required constraint conditions. The algorithm applies to problems formulated using real or complex arithmetic.