Xu Yan, Shang Xinchun, Xu Ke
National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083, China.
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China.
Sensors (Basel). 2024 Aug 21;24(16):5390. doi: 10.3390/s24165390.
Taking the nonlocal effect into account, the vibration governing differential equation and boundary conditions of a magnetostrictive composite cantilever resonator were established based on the Euler magnetoelastic beam theory. The frequency equation and vibration mode function of the composite cantilever were obtained by means of the separation of variables method and the analytic solution of ordinary differential equations. The lateral deflection, vibration governing equations, and boundary conditions were nondimensionalized. Furthermore, the natural frequency and modal function of the composite beam were quantitatively analyzed with different nonlocal parameters and transverse geometry dimensions using numerical examples. Compared with the results without considering the nonlocal effect, the influence of the nonlocal effect on the vibration characteristics was analyzed. The numerical results show that the frequency shift and frequency band narrowing of the magnetostrictive cantilever resonator are induced by nonlocal effects. In particular, the high-frequency vibration characteristics, such as vibration amplitude and modal node of the composite beam, are significantly affected. These analysis results can provide a reference for the functional design and optimization of magnetostrictive resonators.
考虑非局部效应，基于欧拉磁弹性梁理论建立了磁致伸缩复合悬臂梁谐振器的振动控制微分方程和边界条件。采用变量分离法和常微分方程解析解，得到了复合悬臂梁的频率方程和振型函数。对横向挠度、振动控制方程和边界条件进行了无量纲化处理。此外，通过数值算例定量分析了不同非局部参数和横向几何尺寸下复合梁的固有频率和模态函数。与不考虑非局部效应的结果进行对比，分析了非局部效应对振动特性的影响。数值结果表明，非局部效应导致磁致伸缩悬臂梁谐振器出现频移和频带变窄现象。特别是，复合梁的高频振动特性，如振动幅值和模态节点，受到显著影响。这些分析结果可为磁致伸缩谐振器的功能设计和优化提供参考。
