Nonlinear Dynamic Modeling and Analysis of an L-Shaped Multi-Beam Jointed Structure with Tip Mass

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.

An Analytical Dynamic Model for Vibration Suppression of a Multi-Span Continuous Bridge by Tuned Mass Dampers

“…The roots of Equation ( 32) represent the natural frequencies of the system, which are denoted in ascending order by ω 1 , ω 2 , • • • . Once the r-th natural frequency, ω r , of the bridge system is solved by Equation (32), the corresponding vector, φ r , can be determined by Equation (31).…”

“…In recent years, Wei and Cao proposed a methodology suitable for obtaining the mode functions of complex flexible structures. The process of obtaining the mode functions is simple and straightforward, and has been utilized to model the dynamic behavior of flexible space manipulators [30], multi-beam jointed structures [31,32], and flexible spacecraft with jointed solar wings [33,34]. Based on this methodology, the presented work is devoted to obtaining the mode functions in analytical form for the purpose of establishing the analytical dynamic model of the multi-span bridge with TMDs.…”

Dynamic Modeling and Analysis of Spacecraft with Multiple Large Flexible Structures

“…However, the global mode is not as direct as the assumed mode, and how to accurately obtain the global mode of the system becomes the key point. Based on the development of the GMM, Wei and Cao applied it to the dynamic modeling and analysis of flexible spacecraft with jointed solar wings [27,28], flexible space manipulators [29], and multi-beam jointed structures [30,31].…”

Investigations on Nonlinear Dynamic Modeling and Vibration Responses of T-Shaped Beam Structures

“…The research indicated that appropriate joint stiffness can reduce the overall vibration of the structure due to the coupling relationship between flexible rods and flexible joints. Recently, Wei et al [23,[28][29][30] derived a reduced-order analytical model for multi-beam structures connected with hinges associated with a nonlinear rotational spring. Based on this model, they investigated the effect of the nonlinear stiffness and damping of the joints on the attitude and position of a spacecraft during maneuvering.…”