Abstract

This paper investigates the size-dependent nonlinear primary resonant dynamics of truncated conical microshells (TSMs) made of magnetostrictive facesheets with a functionally graded material (FGM) under external magnetic field and mechanical harmonic soft excitation. To accomplish this purpose, a framework is established using a microstructure-dependent third-order shear deformation shell (TSDS) model based on nonlocal strain gradient continuum elasticity. By employing discretized differential operators achieved from generalized differential quadrature (GDQ) technique, a numerical solution is adopted to acquire nonlocal strain gradient amplitude- and frequency-responses for the primary resonant dynamics of FGM-TCMs. The jump phenomenon related to the loss of first stability branch and jumping down to lower stable branches could occur in the nonlinear primary resonances of FGM composite TCMs. It is illustrated that frequency-response bends to right by the hardening-type of nonlinearity. This pattern is enhanced by nonlocal size effect, which is weakened under strain gradient size dependency. Also, it can be observed that at higher material gradient index values, the hardening-type of nonlinearity enhances and nonlocal strain gradient frequency-response bends to right more considerably.

摘要

本文研究了在外部磁场和机械谐波软激励下，由具有功能梯度材料 (FGM) 的磁致伸缩面板制成的截锥形微壳 (TSM) 的尺寸相关非线性初级共振动力学。为了实现这一目的，使用基于非局部应变梯度连续体弹性的微观结构相关三阶剪切变形壳 (TSDS) 模型建立了一个框架。通过采用从广义微分正交 (GDQ) 技术获得的离散微分算子，采用数值解来获取 FGM-TCM 初级共振动力学的非局部应变梯度振幅和频率响应。在 FGM 复合 TCMs 的非线性初级共振中，可能会发生与第一稳定分支丢失和跳到较低稳定分支相关的跳跃现象。通过非线性的硬化型说明频率响应向右弯曲。这种模式通过非局部尺寸效应得到增强，在应变梯度尺寸依赖性下减弱。此外，可以观察到，在较高的材料梯度指数值下，非线性的硬化型增强，非局部应变梯度频率响应向右弯曲得更多。