On viscoelastic transient response of magnetically imperfect functionally graded nanobeams

This research focuses on transient response of porosity-dependent viscoelastic functionally graded nanobeams subjected to dynamic loads and magnetic field as well. The material properties of the nanobeams with changing gradually along thickness direction is presented by modified power law function. In this research, nonlocal strain gradient theory (NSGT) in framework of a quasi 3D beam theory, which is capable of including thickness stretching effect, are employed. In order to capture the internal damping effect in the model, Kelvin-Voigt visco constitutive model is applied. Applying Hamilton's variation, the governing equations are obtained, and Navier as well as inverse Laplace transform methods are utilized to solve them analytically. Eventually, some parametric investigations are conducted to display the sensitivity of transient response to porosity coefficient, internal damping, volume fraction, length to thickness ratio, position of point load, magnetic field as well as small size parameters. It is manifested that by raising the magnetic field and length scale parameter (LSP), the oscillation amplitudes diminish whereas the number of periodic cycles of the nanobeams increases and the systems are damped much faster.