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Nonlinear dynamic modeling of planar moving Timoshenko beam considering non-rigid non-elastic axial effects

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Abstract

Due to the importance of vibration effects on the functional accuracy of mechanical systems, this research aims to develop a precise model of a nonlinearly vibrating single-link mobile flexible manipulator. The manipulator consists of an elastic arm, a rotary motor, and a rigid carrier, and undergoes general in-plane rigid body motion along with elastic transverse deformation. To accurately model the elastic behavior, Timoshenko’s beam theory is used to describe the flexible arm, which accounts for rotary inertia and shear deformation effects. By applying Newton’s second law, the nonlinear governing equations of motion for the manipulator are derived as a coupled system of ordinary differential equations (ODEs) and partial differential equations (PDEs). Then, the assumed mode method (AMM) is used to solve this nonlinear system of governing equations with appropriate shape functions. The assumed modes can be obtained after solving the characteristic equation of a Timoshenko beam with clamped boundary conditions at one end and an attached mass/inertia at the other. In addition, the effect of the transverse vibration of the inextensible arm on its axial behavior is investigated. Despite the axial rigidity, the effect makes the rigid body dynamics invalid for the axial behavior of the arm. Finally, numerical simulations are conducted to evaluate the performance of the developed model, and the results are compared with those obtained by the finite element approach. The comparison confirms the validity of the proposed dynamic model for the system. According to the mentioned features, this model can be reliable for investigating the system’s vibrational behavior and implementing vibration control algorithms.

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Correspondence to M. R. Homaeinezhad.

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Abbasi Gavari, M., Homaeinezhad, M.R. Nonlinear dynamic modeling of planar moving Timoshenko beam considering non-rigid non-elastic axial effects. Appl. Math. Mech.-Engl. Ed. 45, 479–496 (2024). https://doi.org/10.1007/s10483-024-3086-9

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  • DOI: https://doi.org/10.1007/s10483-024-3086-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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