Vibration analysis of nanobeam in thermal environment

Nanostructures are used widely in nanotechnology and nanodevice in recent years and this thesis paper presents the implementation of perturbation method for the vibration analysis of simple and fixed supported Euler-Bernoulli nanobeams resting on Winkler-Pasternak and nonlinear foundation in thermal environment. Considering the thermal loading, the equations of motion of the Euler-Bernoulli nanobeam are obtained using modified couple stress theory and nonlocal elasticity theory. The effect of thermal loadings on the free vibration of the Euler-Bernoulli nanobeam is presented. Hamilton's principle is employed for obtaining differential equation of motion of nanobeam in cooperation with suitable boundary conditions. An approximate solution of the presented system is developed considering the method of multiple scale, which is one of the perturbation techniques. The effects of temperature, Winkler and Pasternak parameters, nonlinear foundation parameter as well as effects of the simple-simple and clamped-clamped boundary conditions on the vibrations, are determined and presented numerically and graphically.