Nonlinear statics and dynamics of porous functional-gradient nanobeam taking into account transverse shifts

In this paper, nonlinear mathematical models of functionally gradient porous nanobeams are constructed taking into account transverse shifts. Transverse shifts are described using kinematic models of the second (S. P. Timoshenko) and third approximations (Sheremetyev – Pelekh). From the Sheremetyev – Pelekh model, as a special case, the kinematic models of the second (S. P. Timoshenko) and first approximation (Bernoulli – Euler) follow. Geometric nonlinearity is accepted according to T. von Karman, nanoeffects are accepted according to the modified Yang moment theory of elasticity. The required equations are derived from the Ostrogradsky – Hamilton principle. An efficient algorithm has been developed that allows us to consider both static and chaotic dynamics problems. Numerical examples are given.