The influence of strain gradient theory on the free vibration analysis of viscoelastic tapered nanorodusing DQM

In this article, the free vibration analysis of tapered viscoelastic Nano-rod based on strain gradient theory isinvestigated. The material properties of nano-rod are assumed the visco-elastic and modeled as the Kelvin-Voigt.Applying Hamilton's principle and energy method, the governing equation of motion of viscoelastic micro-rods isobtained, then this equation using the differential quadrature method (DQM)for different boundary conditions is solved.Also, the effects of various parameters such as the structural damping coefficient, Winkler and Pasternak foundationmodulus, damping coefficient of the elastic medium and material length scale parameters on the frequencies ofviscoelastic Nano-rod are investigated. The results show that the obtained non-dimensional natural frequencies byMCST and SGT decrease by increasing the material length to radius ratio. It can be seen that the non-dimensionalfrequency 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.

کلیدواژه ها:

Vibration analysis ، Viscoelastic tapered nano-rod ، Strain gradient theory ، DQM