Vibration analysis of viscoelastic tapered micro-rod based on strain gradient theory resting on visco-pasternak foundation using DQM

다국어 초록 (Multilingual Abstract)

In the present work, based on strain gradient theory, the free vibration analysis of tapered viscoelastic micro-rod resting on visco-Pasternak foundation is investigated. The material properties of micro-rod are assumed the visco-elastic and modeled as the Kelvin-Voigt.

Using Hamilton's principle and energy method, the governing equation of motion of viscoelastic micro-rods is derived, then this obtainedequation using the differential quadrature method (DQM) for different boundary conditions is solved. In this study, the effects of variousparameters such as the structural damping coefficient, Winkler and Pasternak foundation modulli, damping coefficient of the elastic mediumand material length scale parameters on the non-dimensional natural frequencies of viscoelastic micro-rod are investigated. Theresults show that with an increase in the Winkler and Pasternak coefficients, the natural frequency increases as well as the obtained nondimensionalnatural frequencies by MCST and SGT decrease by increasing the material length to radius ratio. It can be seen that the nondimensionalfrequency for SGT is higher than that of the other theories. It is shown that the non-dimensional frequencies increase byincreasing the damping coefficient for all theories. Moreover, at the specified value of damping coefficient of the elastic medium, thevariation of non-dimensional natural frequency is approximately smooth.

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