A dynamic Timoshenko beam constraint model for use in compliant mechanisms with intermediate deformation ranges

Compliant mechanisms undergoing intermediate deformation ranges can be found in many applications, including large-stroke precision positioning stages, robotic pivots, energy harvesters and micro-electro-mechanical systems, etc. However, the geometric nonlinearity often leads to great design challenges. A dynamic Timoshenko beam constraint model (DTBCM) is herein reported to capture the nonlinear force-displacement relationship of flexure beams undergoing large-amplitude vibrations, including the effects of shear deformation and rotary inertia. Two equivalent dynamic stiffness matrices of the DTBCM are also derived for two-node flexure beams in the presence of axial forces and nodal displacements, respectively. With a full matrix operation, the presented DTBCM enables a concise modeling process, and hence offers a straightforward tool for nonlinear kinetostatic and dynamic analyses of complex serial-parallel configurations. The influence of shear deformation and rotary inertia on the nonlinear stiffness and particularly on the amplitude-dependent resonance frequency is discussed through two case studies. The geometric nonlinearities of dynamic stiffening and weak stiffness softening are, respectively, observed with the two case studies.