引用本文: 陈琦, 马连生, 郭章新. 功能梯度材料梁自由振动的线性与非线性振动. 力学与实践, 2023, 45(3): 520-525.
Chen Qi, Ma Liansheng, Guo Zhangxin. Linear and nonlinear vibration of free vibration of functional gradient material beams. Mechanics in Engineering, 2023, 45(3): 520-525.
 Citation: Chen Qi, Ma Liansheng, Guo Zhangxin. Linear and nonlinear vibration of free vibration of functional gradient material beams. Mechanics in Engineering, 2023, 45(3): 520-525.

## LINEAR AND NONLINEAR VIBRATION OF FREE VIBRATION OF FUNCTIONAL GRADIENT MATERIAL BEAMS

• 摘要: 基于数值模拟和理论分析两种方法，研究了功能梯度材料(functional gradient materials，FGM) 梁自由振动下的线性与非线性振动问题。通过解析法求解了FGM梁在经典理论下以及一阶剪切理论下的力学行为，得到了FGM梁在简支和固端约束下的固有频率。理论分析了不同边界条件、不同梁理论下、梯度指数、长细比等因素对于FGM梁固有频率的影响；不论经典梁理论还是一阶剪切理论，随着梯度指数的增加，FGM梁的固有频率都随之减小。通过ABAQUS 仿真模拟，得到FGM梁数值模拟下的非线性固有频率。将理论解与数值解进行对比，完善力学模型。在多种理论下，利用解析法和数值模拟的方法，给出FGM梁结构振动响应的线性与非线性解。

Abstract: Based on both numerical simulation and theoretical analysis, the linear and nonlinear vibration problems for free vibration of beams with functional gradient materials (FGM) are investigated. The mechanical behaviors of FGM beams under classical theory and first-order shear theory are solved analytically, the inherent frequencies of FGM beams under simple support and solid end restraint are obtained.The theory analyses different conditions that influence the inherent frequence of the FGM beams, including different boundary conditions, different beam theories, gradient index, slenderness ratio and so on. Regardless of classical beam theory or first-order shear theory, with the increase of gradient index, the inherent frequency of FGM beams decreases accordingly. The nonlinear inherent frequency of FGM beam under numerical simulation is obtained by ABAQUS simulation. The theoretical solutions are compared with the numerical solutions to verify each other and improve the mechanical model. The aim is to give linear and nonlinear solutions of the structural vibration response of beams with FGM under multiple theories, using analytical methods and numerical simulations.

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