The self-excited vibrations of an axially retracting cantilever beam using the Galerkin method with fitted polynomial basis functions

Hua, Hongliang; Liao, Zhenqiang; Zhang, Xiangyan

doi:10.1007/s12206-017-1204-z

Cited by 7 publications

(1 citation statement)

References 17 publications

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“…where k j is the jth root of the transcendental equation chk j cosk j ¼ �1. 30 After substituting equations ( 20) and ( 21) into equations ( 14) and ( 15), the integral of the weighted formula in the entire region [0,1] is equal to 0. The following equations after organizing are obtained:…”

Section: Discretization and Solution Of Dynamic Equationsmentioning

confidence: 99%

Effect of composite preforms weaving parameters on weaving capability based on vibration characteristics

Lin

Wang

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

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In terms of the composite preforms weaving process, the influence of the length, width, height and speed of the weaving needle on the weaving capacity is analyzed. According to the calculated kinetic energy, potential energy, and virtual work of the weaving needle and the guide array, the system dynamic equation is established based on Hamilton’s principle, and the discrete processing is performed. According to the state equation, the Runge-Kutta method is used to solve the vibration response of the weaving needle free end. The correctness of the theoretical model is verified with ADAMS by analyzing the system dynamics. The variation of the free end vibration response was studied with time under different parameters. It is found that the velocity, length, and height parameters of the weaving needle have a greater influence on the vibration amplitude and the deflection of the equilibrium position. The comprehensive influence of velocity and size parameters on the weaving capability is discussed. Based on the above results, the analysis concludes that the width of the weaving needle has the smallest influence on weaving capability. The short-high weaving needles have great weaving capability. The increase in velocity can reduce the vibration amplitude and improve the weaving efficiency, but there is a limit to the improvement of the weaving capability.

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Section: Discretization and Solution Of Dynamic Equationsmentioning

confidence: 99%