Abstract:

Following the modified theory of beams with the effect of shear deformation, a generalized Hamilton variational principle with three displacements and two rotational angles is established in which the material of pile obeys one of the thrice nonlinear constitutive relations. A mathematical model of dynamic behavior analysis of nonlinear elastic piles is also presented. As an application of the model, the plane coupling movement of nonlinear elastic piles is analyzed in detail. The Galerkin method and methods in nonlinear dynamic dynamics are used to study the dynamic behavior of nonlinear piles with long time. To consider the effect of the boundary condition, the dynamic behavior of plies with three different boundary conditions is considered. Also, the qualitative properties of the Galerkin systems with 1-order and 2-order truncation are calculated and compared numerically.

Key words: thrice nonlinear elastic material; Hamilton variational principle; plan coupling movement; nonlinear dynamics