Direct Global Stiffness Matrix Method for 3-D Truss Dynamics

Abstract

Abstract This paper deals with the acoustical design goal for a new approach in submarine architecture calling for the use of an internal truss to support the ship’s control and living spaces in the forward section. The acoustical design goal is to minimize truss vibration over a broad band of frequency through the application of passive damping treatments. Damping can be placed in three generic locations: 1) in or along the truss members, 2) in the joints between members, and 3) in dynamic absorbers placed at discrete locations along the truss members. This paper develops the framework for evaluating ways to achieve the stated acoustical goal. We outline the formulation of the Direct Global Stiffness Matrix method (DGSM), which is used to relate externally applied forces and moments at truss joints to joint displacements everywhere on the truss. The model is kinematically constrained by matching welded boundary conditions at the joints, and the joint displacements are computed by a sparse matrix inversion method. From these displacements, wave amplitudes for each of the three wave types, longitudinal, torsional, and flexural, may be computed on any of the beam members. An example of the use of this method illustrates the sensitivity of the global energy decay rate to the truss damping parameters, which are the only free parameters of the model. [Work sponsored by ARPA/ONR]