Free vibration of an ultra-fast-rotating-induced cylindrical nano-shell resting on a Winkler foundation under thermo-electro-magneto-elastic condition

Abstract

Recently, ultra-fast-rotating-induced cylindrical nano-shells subjected to electro-magnetic fields are used as a water pump. An enormous centrifugal acceleration (up to 1011 g), which is surpassed by five orders of magnitude acceleration in the fastest centrifuges available today, on such nano-structure would have a considerable effect on the vibration and buckling behavior of the structure. In order to predict the first natural frequency and the critical angular velocity of a thermo-electro-magneto-elastic single-layer cylindrical nano-shell resting on a Winkler foundation, the governing equations of motion are derived based on the Hamiltonian Principle and by using first shear deformation theories in conjunction with modified couple stress theory. The effects of the centrifugal acceleration are considered in the formulation. For different boundary conditions, GDQ method is applied as a numerical solution and an analytical solution is presented for the simple-simple boundary conditions at the end of the nano-cylinder. The contributions of the centrifugal acceleration, angular velocities, electrical field, magnetic field, elastic foundation and boundary conditions are investigated. The convergency of the results as well as the verification of the solutions with available results in the literature are presented in details.