软铁磁矩形薄板多种模式的联合共振分析

IF 1.5 Q3 MECHANICS
Xiaofang Kang, Xinzong Wang, Qingguan Lei, Zhengxing Zhu, Ziyi Sheng, Fuyi Zhang
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引用次数: 0

摘要

本文研究了磁场环境下软铁磁矩形薄板的非线性本构和内部共振特性。推导了软铁磁矩形薄板在同质简谐激励作用下的非线性偏微分运动方程。利用 Galerkin 方法,通过假定的单边固定三边简单支撑条件建立了多自由度非线性微分方程系统。通过多尺度法求解非线性微分方程系,得到了两个模态在简谐力作用下的主共振和内共振响应。系统响应的数值结果表明,当简谐力的频率接近其中一个模态(一阶或二阶模态)导致其共振时,另一个模态也会发生内部共振。磁场会对系统的共振响应产生抑制作用,也会影响系统的运动状态。内部共振提供了一种将能量从高阶模式传递到低阶模式的机制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Joint Resonance Analysis in Multiple Modes of Soft Ferromagnetic Rectangular Thin Plate
In this article, the nonlinear principal and internal resonance properties of a soft ferromagnetic rectangular thin plate are investigated in a magnetic field environment. The nonlinear partial differential equation of motion of a soft ferromagnetic rectangular thin plate is derived under the effect of homogeneous simple harmonic excitation. The system of nonlinear differential equations with multiple degrees of freedom is established by the assumed one-sided fixed trilateral simply support condition using the Galerkin’s method. The system of nonlinear differential equations is solved by the multiscale method to obtain the response of two modes under the simple harmonic force at the principal and internal resonance. The numerical results of the system response show that when the frequency of the simple harmonic force is close to one of the modes (first-order or second-order mode) causing it to resonate, the other mode will also resonate internally. The magnetic field can have an inhibiting effect on the resonant response of the system and also affect the kinematic state of the system. The internal resonance provides a mechanism for transferring energy from a high mode to a lower mode.
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来源期刊
CiteScore
1.70
自引率
8.30%
发文量
0
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