This paper presents new exact 3-D (three-dimensional) elasticity closed-form solutions for out-of-plane free vibration of thick rectangular single layered FG (functionally graded) plates and thick rectangular homogeneous plate coated by a functionally graded layer with simply supported boundary conditions. It is assumed that the plate is on a Winkler-Pasternak elastic foundation and elasticity ...

In this paper, the effect of anisotropy on the free vibration of laminated rectangular plate supporting a localized patch mass is investigated. The two variable refined plate theory is applied to define the third order displacement field of a composite rectangular plate. The plate is considered to have simply supported boundaries. The equations of motion for rectangular plate are obtained by ca...

Free vibration of soil often occurs during earthquakes. Since the vibration caused by earthquake does not have (steady state harmonic vibration) continuity, the alluvium vibrates with its natural frequency between two natural seismic waves. This study evaluates the effect of piles on the period of free vibration of a soil layer using numerical method. In the first stage, using analytical equati...

this research is carried out to design and manufacturing of lathe vibration tool and their tests. firstly, one-dimensional vibration tool is designed and made of the bending vibration mode. one-dimensional vibration tool with half piezoelectric rings is considered to excite the bending mode of tool. structure of vibration tool is designed in abaqus software about 20 khz and then is made with re...