Nonlinear free vibration analysis of granular soil layer using perturbation technique

In this study, natural frequency of single layer homogeneous and horizontal alloys under one-dimensional harmonic vibrations was studied. If the ground surface, the rock surface and the boundaries between the soil layer and the rock layer are considered horizontally, the lateral extent of the deposit has no influence on the response and in this case the soil layer may be considered as a semi-infinite and horizontal layer. In such cases, when the soil is affected by seismic excitation at the base, only shear deformations occur in the soil. The nonlinear soil behavior resulting from cyclic loading is investigated by free vibration modification in the properties of the dynamical deformation of the granular soil, such as damping ratio and normalized stiffness using a new approach to the dynamic equilibrium equation governing the behavior of a freedom-degree system. So, by deriving a nonlinear equation of motion, it is possible to solve this equation by the perturbation technique. Then the natural frequency of the system will be determined analytically. It was seen that the nonlinear natural frequency depends on the response amplitude and with increasing of amplitude it increases. In other words, the system behavior is of hardening type. The analytical method for determining the response of a freedom-degree system has good agreement with the numerical method of solving the free equation such as the Runge-Kutta method.