Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length

Wang, L. H.; Hu, Ziqi; Zhong, Zheng; Ju, J. W.

doi:10.1007/s00707-010-0287-8

Cited by 40 publications

(8 citation statements)

References 35 publications

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“…The standard linear solid model has been employed in modelling axially traveling viscoelastic beams. Wang et al [12] investigated the effect of an arbitrary varying length on the nonlinear free vibration of an axially translating viscoelastic beam. Chen and his co-workers worked on the steady-state responses of the axially traveling strings [13] and beams [14] with the standard linear solid model.…”

Section: Introductionmentioning

confidence: 99%

Primary resonance of traveling viscoelastic beam under internal resonance

Ding

Huang

Mao

2016

Appl. Math. Mech.-Engl. Ed.

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Under the 3:1 internal resonance condition, the steady-state periodic response of the forced vibration of a traveling viscoelastic beam is studied. The viscoelastic behaviors of the traveling beam are described by the standard linear solid model, and the material time derivative is adopted in the viscoelastic constitutive relation. The direct multi-scale method is used to derive the relationships between the excitation frequency and the response amplitudes. For the first time, the real modal functions are employed to analytically investigate the periodic response of the axially traveling beam. The undetermined coefficient method is used to approximately establish the real modal functions. The approximate analytical results are confirmed by the Galerkin truncation. Numerical examples are presented to highlight the effects of the viscoelastic behaviors on the steady-state periodic responses. To illustrate the effect of the internal resonance, the energy transfer between the internal resonance modes and the saturation-like phenomena in the steady-state responses is presented.

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Section: Introductionmentioning

confidence: 99%

Primary resonance of traveling viscoelastic beam under internal resonance

Ding

Huang

Mao

2016

Appl. Math. Mech.-Engl. Ed.

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“…Here, b 1 and l 1 are given by the autonomous set of equation (20). In order to obtain steady-state responses, i.e.…”

Section: Primary Resonance Case: (! % )mentioning

confidence: 99%

“…The effect of gyroscopic inertia and geometric stiffening on the dynamics of manipulator with high speed and payload has been demonstrated in the work. Investigation of the nonlinear free vibration of an axially translating viscoelastic beam with an arbitrarily varying length and axial velocity has been carried out by Wang et al 20 The beam has been modeled as Euler-Bernoulli element and extended Hamilton's principle has been employed to derive the third-order governing equation of motion. The influence of beam extension and retraction along with the material viscosity on the vibration of beam has been demonstrated.…”

Section: Introductionmentioning

confidence: 99%

Position analysis and nonlinear phenomena of flexible manipulator with generic payload mounted on a moving base

Kumar

Pratiher

2020

Proceedings of the Institution of Mechanical Engineers, Part K:

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The investigation of the end-point trajectory and the nonlinear oscillation of elastic manipulator with offset payload mounted on moving base has been carried out by demonstrating the modal parameters and dynamic responses of a bi-directionally deflected rotating flexible link manipulator. A large deflection model of a flexible rotating manipulator considering both transverse and axial deformation, dynamics of rotating hub, generic payload, and rigid motion of platform has been derived. Initially, modal analysis has been studied to graphically illustrate the eigenfrequencies and corresponding eigenspectrums, while it has been noted that the system possesses distinct and different vibration characteristics as compared to that of a system without offset payload. A smooth sinusoidal input torque has been imparted to the joint to assess the time dependency factors and parameters, which describe its position inaccuracy over time. Finally, the investigation of influence of essential system attributes on the nonlinear behavior and system instabilities under resonance conditions by analyzing the steady-state solutions has been accomplished. The effect of payload parameters such as mass, inertia, and offset, along with the inertia and stiffness of actuator on the frequency response curves has been demonstrated graphically. This work exhibits that the system’s dynamics diversely evolve with a change of offset parameters while system loses its stability due to saddle-node bifurcations. The present result offers specific guidelines towards the design and control aspects of flexible manipulators based on the selection of offset parameters.

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“…However, over the long run, the transient stability at a number of instants is not meaningful to describe the dynamics of the time-varying parameter system. Wang et al [30] investigated the total energy of transverse vibrations with respect to time for the deploying beam, from which the tendency of the transient dynamics could be determined. Zhu and Ni [31] proposed the concept of energy density to the dynamics of translating media with varying length.…”

Section: Introductionmentioning

confidence: 99%