General Dynamic Shape Functions and Stiffness Matrix of Timoshenko Beam and Their Application to Structure-borne Noise on Ships

Abstract

The general dynamic shape functions and stiffness matrix of a Timoshenko beam are derived and used to establish the stiffness equations for an entire structural system. All the effects of rotary inertia of the mass, shear distortion, mass and structural dampings, axial force, elastic-spring and dashpot foundation are included in this formulation. These stiffness equations can then be easily modified to account for the influences from the concentrated dynamic properties. Both the low-and high-frequency dynamic responses are discussed generally, with special emphasis on the latter case. The problem of structure-borne noise on ships is also studied as an example for application.