Journal
JOURNAL OF VIBRATION AND CONTROL
Volume 25, Issue 19-20, Pages 2567-2579Publisher
SAGE PUBLICATIONS LTD
DOI: 10.1177/1077546319861810
Keywords
Viscoelastic; elasticity; cylindrical shell; vibration; three-dimensional
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In this research based on theory of elasticity, free vibration behavior of a viscoelastic cylindrical shell with different boundary conditions is studied. A constitutive equation for viscoelastic material is assumed to obey the Boltzmann model and Poisson's ratio is held to be constant. Moreover, the Prony series is used to model time dependent modulus of elasticity. Governing equations of motions for simply-supported edges conditions are solved analytically using the state-space technique along the radial coordinate and the Fourier series method along the axial and circumferential directions. In the case of other edges condition a semi-analytical solution is employed by using the differential quadrature method instead of Fourier series solutions. It is worthy to note before solving the problem, that the Laplace transform is employed to convert governing differential equations from the time-domain into the Laplace domain. Then, validation of the present formulation is performed by comparing the numerical results with those published in the literature. Finally, effect of viscoelastic properties, boundary conditions, the thickness-to-radius ratio and length-to-radius ratio on the frequency behavior are studied.
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