A unified method for constructing the dynamic boundary stiffness and boundary flexibility for rod, beam and circular membrane structures

Abstract

In this paper, the dynamic boundary stiffness and boundary flexibility for rod, beam and circular membrane structures are analytically derived using the dual integral formulation. Two approaches, the real- and the imaginary-part kernels are employed to determine the dynamic boundary stiffness and boundary flexibility. The continuous system for a circular membrane can be transformed into a discrete system with a circulant matrix. Based on the properties of circulant, the analytical solution for dynamic boundary stiffness and dynamic boundary flexibility in the discrete system can be derived. The exact formulae for the dynamic boundary stiffness and boundary flexibility matrices of a rod, a beam and a circular membrane are obtained. Also, the calculation for the static flexibility using the pseudo-inverse technique is discussed.