Vibrations of a Three-Layer Circular Step Plate under Periodic Impact

Abstract

Forced oscillations of a three-layer circular plate with step-variable thickness of the outer layers are analyzed. The deformation of the plate is described with the zig-zag theory. In thin border layers of plate Kirchhoff’s hypotheses are valid. In a relatively thick in thickness medium layer Timoshenko’s hypothesis on the straightness and incompressibility of the deformed normal is fulfilled. The equations of motion are derived from Hamilton’s variational principle. A special case of exposure is considered: periodic sequence of strokes with constant intensity. The problem is reduced to finding three required functions in each section, deflection, shear and radial displacement of the median plane of the filler. The solution is presented as a sum of quasi-static and dynamic components of the unknown displacements. Numerical results of the obtained solution are presented. The influence of the impact stress on the oscillatory character is analyzed.

Keywords

• circular three-layer plate
• plate with step-variable thickness
• forced vibration
• periodic strokes