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Effects of pores different distributions on vibrational behavior of functionally graded porous cylinder applying Haar wavelet computational technique

机译：应用Haar小波计算技术的孔隙分布对功能梯度多孔圆柱振动行为的影响。

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摘要

This paper presents an analytical solution based on the Haar wavelet method for investigation of vibration behavior of a functionally graded porous cylinder of finite length. Here, different types of porosity distributions are considered. Also, mass density and modulus of elasticity of porous materials are changed continually and gradually in the thickness direction by a function. Meanwhile, boundary conditions are assumed to be classic and elastic. The governing equations for the functionally graded porous cylinder are obtained by the employment of first-order shear deformation theory. Then the proposed numerical approach is implemented to achieve the frequency parameters of the cylinder. Next, in order to ensure the present method, the results generated in this study are compared by the other researchers' results. More, the vibrational behavior of the structure is studied for different porosity distributions: symmetric, stiff non-symmetric, soft non-symmetric distribution and uniform distribution. As well as, the effects of geometric and boundary parameters and boundary conditions are discussed. The results indicate that the porosity distributions of symmetric, stiff non-symmetric and soft non-symmetric distribution increase the frequency parameters. It can be attributed to the effects of the increase in the inertia of cross-section and stiffness in these types of porosity distributions.
机译：本文提出了一种基于Haar小波方法的分析解决方案，用于研究功能梯度有限长度的多孔圆柱的振动行为。这里，考虑了不同类型的孔隙率分布。而且，多孔材料的质量密度和弹性模量通过函数在厚度方向上连续且逐渐变化。同时，边界条件被认为是经典且有弹性的。利用一阶剪切变形理论获得了功能梯度多孔圆柱体的控制方程。然后采用所提出的数值方法来实现圆柱体的频率参数。接下来，为了确保本方法的有效性，将本研究中产生的结果与其他研究人员的结果进行比较。此外，研究了结构在不同孔隙率分布下的振动行为：对称，刚性非对称，软非对称分布和均匀分布。此外，还讨论了几何和边界参数以及边界条件的影响。结果表明，对称，刚性非对称和软非对称分布的孔隙率分布增加了频率参数。这可以归因于在这些类型的孔隙度分布中横截面惯性和刚度增加的影响。

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