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首页> 外文期刊>Applied Mathematical Modelling >Free vibration analysis of axially functionally graded nanobeam with radius varies along the length based on strain gradient theory
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Free vibration analysis of axially functionally graded nanobeam with radius varies along the length based on strain gradient theory

机译：基于应变梯度理论的半径沿长度方向变化的轴向功能梯度纳米束的自由振动分析

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In this study the vibration of axially functionally graded material (AFGM) nanobeam is investigated by using strain gradient theory. In so doing, Euler-Bernoulli beam model is used, the nanobeam surroundings are modeled as visco-Pasternak foundation, and the beam has simply-supported boundary conditions. The governing equations and boundary conditions are derived by using Hamilton's principle, and differential quadrature method (DQM) is used to discretize equations of motion and solve the vibrational problem with simple-simple and clamped-clamped boundary conditions. The results demonstrate that the effect of the variation of Young's modulus, density, the diameter of the nanobeam, and size parameter along the length on the natural frequency of the nanobeam is significant. In addition, the effects of the stiffness and damping of the visco-Pasternak foundation on the natural frequency of the nanobeam are studied.
机译：在这项研究中，使用应变梯度理论研究了轴向功能梯度材料（AFGM）纳米束的振动。在这种情况下，使用Euler-Bernoulli光束模型，将纳米束周围环境建模为粘滞Pasternak基础，并且该光束具有简单支持的边界条件。利用汉密尔顿原理导出控制方程和边界条件，并采用微分求积法（DQM）离散化运动方程，并通过简单的边界约束条件解决了振动问题。结果表明，杨氏模量，密度，纳米束直径和尺寸参数沿长度的变化对纳米束固有频率的影响是显着的。此外，还研究了粘滞式Pasternak基础的刚度和阻尼对纳米束固有频率的影响。

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