Forced Vibration Analysis in Axisymmetric Functionally Graded Viscothermoelastic Hollow Cylinder Under Dynamic Pressure
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RESEARCH ARTICLE
Forced Vibration Analysis in Axisymmetric Functionally Graded Viscothermoelastic Hollow Cylinder Under Dynamic Pressure Dinesh Kumar Sharma1 • Himani Mittal1 • Sita Ram Sharma2
Received: 24 April 2018 / Revised: 8 July 2019 / Accepted: 11 July 2019 The National Academy of Sciences, India 2019
Abstract The forced vibrations of axisymmetric inhomogenous isotropic viscothermoelastic hollow cylinder under periodic dynamic pressure have been studied. The material was taken inhomogenous due to easy exponent law in radial direction. By applying time harmonics variation technique, the partial differential equations were converted into ordinary differential equations. These ordinary differential equations were solved by applying series solution of matrix Fro¨benius method analytically to represent displacement, temperature and stresses. Numerically simulated outcomes were presented graphically to express the effect of functionally graded material disk for different values of grading parameter. With the increase in value of grading index, variation of field functions go on decreasing. The variation of field functions show high variation in homogenous materials in contrast to low variation in inhomogeneous materials. Keywords Forced vibrations Dynamic pressure Inhomogenous Fro¨benius method De-hoop stress
& Dinesh Kumar Sharma [email protected] Himani Mittal [email protected] Sita Ram Sharma [email protected] 1
Department of Mathematics, School of Basic and Applied Sciences, Maharaja Agrasen University, Baddi, District Solan, HP 174103, India
2
Chitkara University School of Engineering and Technology, Chitkara University, Baddi, District Solan, HP 174103, India
1 Introduction Functionally graded materials (FGMs) also known as graded materials are generally many-sided phase composites having continuously changing properties. Depending on the positions of the material, the properties of these materials are not uniformly distributed across the whole material. Chen [1] had studied the problem of elastic medium based on spherically isotropic material bounded by two concentric spherical surfaces. Honarvar and Sinclair [2] have derived mathematical expressions for plane acoustic waves in transversely isotropic elastic cylinder. Dai et al. [3] presented numerical method to analyze the elasto-thermodynamic long hollow cylinder prepared by functionally graded materials in radial direction under symmetric mechanical and thermal loads. Keles and Tutuncu [4] have studied the free and forced vibration analysis of functionally graded transversely isotropic elastic hollow cylinder in radial direction by using easy exponent law and represented the stresses, displacements and temperatures under dynamic loads. Othman et al. [5] have presented a mathematical model based on normal mode analysis in which two-dimensional viscothermoelastic (VTE) problem has been investigated in the medium with two relaxation time parameters for the temperature distribution, thermal stresses and the di
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