s.a.a. hosseini

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.

This paper investigates the optimal configuration for a partially two-layered circular capacitive microplate subjected to AC-DC electrostatic actuation. To this end, the static deflection due to DC electrostatic actuation, natural frequency of vibration about static position and primary resonance response due to AC electrostatic actuation are studied. Primarily, the nonlinear equations of motion are derived through classical laminated plate theory (CLPT). Then, the static position and natural frequency of vibration around static position are obtained using Galerkin approach. The linear mode shapes of non-uniform microplate i.e. a microplate coated as partial by a second layer are used as comparison functions. The forced vibration equations around static position are separated using Galerkin method, and solved by the multiple scale perturbation theory. Firstly, the impact of changes in the second layer radius on the variations of static and dynamic response of the system is studied while its thickness remains constant. Then, the effect of changes in the second layer thickness is studied while its radius remains constant. Finally, the impact of simultaneous change in the radius and thickness of the second layer is studied while its volume remains constant.