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.

Proper normal waves in a two-layer tube taking into account the rheological properties of materials

“…), which generates a wide variety of models for describing real phenomena and does not allow creating a single mathematical model of the process in a mechanical system. Despite the large number of mathematical models of a mechanical system, mathematical methods for solving problems have been developed mainly for such systems as acoustic, whose elastic motions are described by linear differential equations [3,4]. In [5,6,7], an attempt was made to determine and optimize the dissipative characteristics, as well as the stress-strain states of mechanical systems.…”

Vibrations of an Inertial Semi-Cylindrical Cushion

“…In [6], free vibrations of a three-layer circular plate on an elastic inertial base under the influence of temperature are considered. The kinematics of a non-symmetric thickness packet is described by the broken normal hypothesis.…”