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

Applied mathematics and mechanics(English Edition) 2024年第3期45卷 479-496页

作者： m.a.basi gavari m.R.HOmAEINEZHAD Faculty of mechanical Engineering K.N.Toosi University of TechnologyTehran 19991-43344Iran

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 consists of an elastic arm,a rotary motor,and a rigid carrier,and undergoes general in-plane rigid body motion along with elastic transverse *** accurately model the elastic behavior,Timoshenko’s beam theory is used to describe the flexible arm,which accounts for rotary inertia and shear deformation *** 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 *** 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 *** addition,the effect of the transverse vibration of the inextensible arm on its axial behavior is *** the axial rigidity,the effect makes the rigid body dynamics invalid for the axial behavior of the ***,numerical simulations are conducted to evaluate the performance of the developed model,and the results are compared with those obtained by the finite element *** comparison confirms the validity of the proposed dynamic model for the *** to the mentioned features,this model can be reliable for investigating the system’s vibrational behavior and implementing vibration control algorithms.

关键词： planar moving Timoshenko beam non-rigid non-elastic axial effect as-sumed mode method(Amm) nonlinear motion analysis

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