Dynamic Stiffness Matrix With Timoshenko Beam Theory and Linear Frequency Solution for Use in Compliant Mechanisms

Abstract

Abstract The kinetostatic and dynamic formulation of planar-compliant mechanisms is investigated by making use of the dynamic stiffness method based on Timoshenko beam theory. This research is prompted by the significance of considering both the shear deformation and rotary inertia for short and thick flexure beams widely used in compliant mechanisms. We investigate the problem by developing the frequency-dependent dynamic stiffness matrix with the pseudo-static characteristic for a threefold purpose. The first is to show that a closed-form dynamic stiffness matrix of flexure beams in power series of frequency including the shear deformation and rotary inertia is effective that is parameter-insightful and from a computational standpoint concise. Second, a programmable stiffness and mass assembling procedure is developed to build the kinetostatic and dynamic model for compliant mechanisms in a general sense. The third target is to accelerate the calculation efficiency of dynamic stiffness model by employing a linear solution strategy of natural frequencies which is beneficial for parameter optimization iteration. The presented approach is demonstrated by applying the parameter influence analysis and dimension synthesis of a bridge-type compliant mechanism widely used in micro-displacement and/or force amplifications