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首页> 外文期刊>International journal of mechanics and materials in design >Nonlinear vibration analysis of third-order shear deformablefunctionally graded beams by a new method based on directnumerical integration technique
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Nonlinear vibration analysis of third-order shear deformablefunctionally graded beams by a new method based on directnumerical integration technique

机译：一种基于Directnumerical Integration技术的新方法，三阶剪切可变形函数分析的非线性振动分析

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摘要

This study investigates the nonlinear vibration and dynamic response of a beam made of functionally graded material (FGM) within the framework of the improved third-order shear deformable theory. The beam is subjected to a concentrated moving load, and the included angle of the load direction and axial direction varies with time. Considering the von Karman geometric nonlinearity, the nonlinear formulations of the FGM beam is derived. The Newmark method in conjunction with the Newton-Raphson iteration is adopted to analyze the dynamic response of the beam. A new method, based on a direct numerical integration technique for the matrix form motion equation, is presented to study the nonlinear vibration of the FGM beam. The proposed method overcomes the problem of signal determination for the solution of the eigenvector equation that often leads to nonconvergence or a false result of the nonlinear eigenvalue equation. In relation to the numerical results, the effects of material property distribution, vibration amplitude on the nonlinear dynamic behavior of the FGM beams, and the energy transference phenomenon are discussed in this paper.
机译：本研究研究了通过改进的三阶剪切可变形理论的框架内由功能渐变材料（FGM）制成的光束的非线性振动和动力响应。梁经受浓缩的移动载荷，并且载荷方向和轴向的角度随时间而变化。考虑到von Karman几何非线性，导出了FGM光束的非线性配方。采用与牛顿释放迭代结合的纽马克方法来分析光束的动态响应。提出了一种基于用于矩阵形式运动方程的直接数值积分技术的新方法，以研究FGM光束的非线性振动。所提出的方法克服了对实际vector方程的解决方案的信号确定的问题，这些方程通常导致非线性特征值方程的非计因素或假结果。本文讨论了与数值结果，材料性质分布，振动幅度对FGM光束的非线性动力学行为的影响以及能量转移现象。

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