Analyzing dynamic characteristics of nonlocal porous graded beams under impulse and thermal loading

In the framework of nonlocal strain gradient theory, the dynamic responses of a porous functionally graded (FG) nano-size beam under half-sine impulse load and thermal environment. The half-sine impulse load has been modeled as a point load located on the top surface of the nano-size beam. The exerted impulse load leads to the transient vibrations of the nano-size beam at a prescribed time. The porous beam has been described with two pore distributions named even-type and uneven-type pores. The formulation has been developed based upon the refined beam model while the equations will be solved numerically using differential quadrature (DQ) method. Finally, the dynamic deflections in transient region will be derived with the usage of Laplace transform technique. It will be indicated that temperature variation, pore distribution and nano-scale factors have remarkable influences on dynamic resonse of the nano-size beam subjected to sine-type impulse loads.