Effect of Method Type on the Response of Continuum Vibro‐Impact

Wei, Hongtao; Li, Gang; Guo, Pan; Zhao, Jun

doi:10.1155/2019/2718502

Cited by 4 publications

(2 citation statements)

References 28 publications

(46 reference statements)

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“…The RMTM is a novel approach derived from the classical Mode Transfer Method (MTM) techniques, emphasizing the concept of "relative." Specifically, during a mode transition, the previous mode "state" is recorded, and the post-transition "state" is treated as an iterative motion relative to the preceding state [22]. Building on this idea [23], it not only facilitates the study of complex structural impact vibration but also addresses vibration problems with changing boundary conditions that cannot be modeled using external forces.…”

Section: Introductionmentioning

confidence: 99%

Study on the variable length simple pendulum oscillation based on the relative mode transfer method

Yu,

Ma,

Shi

et al. 2024

PLoS ONE

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In this study, we employed the principle of Relative Mode Transfer Method (RMTM) to establish a model for a single pendulum subjected to sudden changes in its length. An experimental platform for image processing was constructed to accurately track the position of a moving ball, enabling experimental verification of the pendulum’s motion under specific operating conditions. The experimental data demonstrated excellent agreement with simulated numerical results, validating the effectiveness of the proposed methodology. Furthermore, we performed simulations of a double obstacle pendulum system, investigating the effects of different parameters, including obstacle pin positions, quantities, and initial release angles, on the pendulum’s motion through numerical simulations. This research provides novel insights into addressing the challenges associated with abrupt and continuous changes in pendulum length.

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Section: Introductionmentioning

confidence: 99%

Study on the variable length simple pendulum oscillation based on the relative mode transfer method

Yu,

Ma,

Shi

et al. 2024

PLoS ONE

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“…The Galerkin approximation has been used to solve the governing partial differential equations (PDEs) of the string. The set of ordinary differential equations (ODEs) obtained from the Galerkin approach are in modal coordinates, and the imposition of impact constraints upon the modal system is a challenging task (Vyasarayani et al, 2010; Wagg and Bishop, 2002; Wei et al, 2019). To avoid such difficulties, we use a transformation to convert the modal system into its physical coordinates by discretizing the string in space (Issanchou et al, 2017; Van Walstijn and Bridges, 2016).…”

Section: Introductionmentioning

confidence: 99%

Galerkin–Ivanov transformation for nonsmooth modeling of vibro-impacts in continuous structures

Samukham

Khaderi

Vyasarayani

2020

Journal of Vibration and Control

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This work deals with the modeling of nonsmooth vibro-impact motion of a continuous structure against a rigid distributed obstacle. Galerkin’s approach is used to approximate the solutions of the governing partial differential equations of the structure, which results in a system of ordinary differential equations. When these ordinary differential equations are subjected to unilateral constraints and velocity jump conditions, one must use an event detection algorithm to calculate the time of impact accurately. Event detection in the presence of multiple simultaneous impacts is a computationally demanding task. Ivanov (Ivanov A 1993 “Analytical methods in the theory of vibro-impact systems”. Journal of Applied Mathematics and Mechanics 57(2): pp. 221–236.) proposed a nonsmooth transformation for a vibro-impacting multi-degree-of-freedom system subjected to a single unilateral constraint. This transformation eliminates the unilateral constraints from the problem and, therefore, no event detection is required during numerical integration. This nonsmooth transformation leads to sign function nonlinearities in the equations of motion. However, they can be easily accounted for during numerical integration. Ivanov used his transformation to make analytical calculations for the stability and bifurcations of vibro-impacting motions; however, he did not explore its application for simulating distributed collisions in spatially continuous structures. We adopt Ivanov’s transformation to deal with multiple unilateral constraints in spatially continuous structures. Also, imposing the velocity jump conditions exactly in the modal coordinates is nontrivial and challenging. Therefore, in this work, we use a modal-physical transformation to convert the system from modal to physical coordinates on a spatially discretized grid. We then apply Ivanov’s transformation on the physical system to simulate the vibro-impact motion of the structure. The developed method is demonstrated by modeling the distributed collision of a nonlinear string against a rigid distributed surface. For validation, we compare our results with the well-known penalty approach.

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A New FEM Approach for a Continuum Vibro-impact Response Based on the Mode Transfer Principle

Wei

Sun²,

Xu³

et al. 2022

J. Vib. Eng. Technol.

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Effect of Method Type on the Response of Continuum Vibro‐Impact

Cited by 4 publications

References 28 publications

Study on the variable length simple pendulum oscillation based on the relative mode transfer method

Study on the variable length simple pendulum oscillation based on the relative mode transfer method

Galerkin–Ivanov transformation for nonsmooth modeling of vibro-impacts in continuous structures

A New FEM Approach for a Continuum Vibro-impact Response Based on the Mode Transfer Principle

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