Abstract
A dynamic model of an L-shaped multi-beam joint structure is presented to investigate the nonlinear dynamic behavior of the system. Firstly, the nonlinear partial differential equations (PDEs) of motion for the beams, the governing equations of the tip mass, and their matching conditions and boundary conditions are obtained. The natural frequencies and the global mode shapes of the linearized model of the system are determined, and the orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to derive a set of nonlinear ordinary differential equations (ODEs) that govern the motion of the L-shaped multi-beam jointed structure. The accuracy of the model is verified by the comparison of the natural frequencies solved by the frequency equation and the ANSYS. Based on the nonlinear ODEs obtained in this model, the dynamic responses are worked out to investigate the effect of the tip mass and the joint on the nonlinear dynamic characteristic of the system. The results show that the inertia of the tip mass and the nonlinear stiffness of the joints have a great influence on the nonlinear response of the system.
Highlights
A multi-beam jointed structure composed of multiple beams and flexible joints is widely used as a component on spacecrafts in the field of aerospace engineering, such as in solar arrays and large antenna support structures
The terms asj are resulted from the axial force of the beams caused by the foundation motion, the terms bsjk are resulted from the axial forces of the beams caused by the elastic motion of the beams, the terms csjkr represent the geometric nonlinearities of the beams and the nonlinear stiffness of the joints, and the terms dsjkr represent the inertial nonlinearities of the beams and the tip mass
A comparison of the natural frequencies obtained from the frequency equation and the finite element software ANSYS (Version 16.0, ANSYS Inc, Canonsburg, PA, USA) is presented so to verify the accuracy of the model, and the first four global mode shapes of the L-shaped multi-beam structure are given
Summary
A multi-beam jointed structure composed of multiple beams and flexible joints is widely used as a component on spacecrafts in the field of aerospace engineering, such as in solar arrays and large antenna support structures. Nayfeh et al [5,6,7] investigated the nonlinear motion of the L-shaped beam structure with lumped masses, and experimentally confirmed that the structure exhibits a chaotic response when subjected to small excitation with twoto-one internal resonance. Wei et al [28,29] proposed a dynamic modeling approach to derive a reduced-order analytical model for a multi-beam structure with nonlinear joints Based on this model, they studied the influence of the nonlinear stiffness and the damping of the joint on the attitude and the position of the spacecraft during maneuvering. They demonstrated that very small variations in either the stiffness or the tip mass can alter the type of bifurcation, which can potentially be applied for using parametrically excited micro-cantilever beams as sensing devices
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