Propagation of Elastic Waves along a Cylindrical Rod of Micropolar Elastic Solid with Stretch under Impedance Boundary Conditions

Indian journal of science and technology Pub Date : 2024-04-16 DOI:10.17485/ijst/v17i15.322

G. Rajkumar, K. Somaiah, K. Narasimharao, B. Venkateswararao

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Abstract

Objective: The objective of this article is to derive the dispersion relations of elastic waves along a cylindrical rod of homogeneous, isotropic micropolar elastic solid with stretch under impedance boundary conditions. Method: The basic equations and constitutive relations are converted into cylindrical coordinates and solved by adopting the method of plane harmonic solution. Findings: Displacements, micro rotations, and micro stretch relations are derived analytically. The dispersion relations pertaining to elastic waves with using impedance boundary conditions also derived analytically and these relations are compared with the results of Tomar. Novelty: With the use of the MATLAB program, the effects of impedance parameters, micropolarity and stretch are discussed for a particular model. The speed of the elastic wave is proportional to the ratio of the impedance parameter in microstretch elastic solids, but there is no significant effect of the impedance ratio in micropolar elastic solids. Keywords: Elastic Waves, Cylindrical rod, Micropolarity, Micro stretch, Impedance Boundary Conditions

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阻抗边界条件下弹性波沿具有拉伸作用的微极性弹性固体圆柱杆的传播

目的：本文旨在推导在阻抗边界条件下，沿均质、各向同性、带拉伸的微多极弹性固体圆柱杆的弹性波的频散关系。方法：将基本方程和构成关系转换为圆柱坐标，并采用平面谐波解法求解。结果：通过分析得出了位移、微旋转和微拉伸关系。使用阻抗边界条件也能分析得出与弹性波有关的频散关系，并将这些关系与 Tomar 的结果进行了比较。新颖性：利用 MATLAB 程序，讨论了阻抗参数、微拉伸和拉伸对特定模型的影响。在微拉伸弹性固体中，弹性波的速度与阻抗参数的比值成正比，但在微极性弹性固体中，阻抗比值没有显著影响。关键词弹性波圆柱杆微极性微拉伸阻抗边界条件

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Indian journal of science and technology

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