Explicit frequency equations of free vibration of a nonlocal Timoshenko beam with surface effects

摘要: Considerations of nonlocal elasticity and surface effects in micro- nanoscale beams are both important for the accurate prediction natural frequency. In this study, governing equation a Timoshenko beam with is established by taking into account three types boundary conditions: hinged–hinged, clamped–clamped clamped–hinged ends. For hinged–hinged beam, an exact explicit frequency obtained. However, beams, solutions corresponding equations must be determined numerically due to their transcendental nature. Hence, Fredholm integral approach coupled curve fitting method employed derive approximate fundamental equations, which can predict values high accuracy. short, conditions proposed exhibit directly dependence on elasticity, residual stress, shear deformation rotatory inertia, avoiding complicated numerical computation.