Oscillation of a circular sandwich plate on an elastic base under a parabolic loads

Аuthors

Starovoytov E. I.^*, Leonenko D. V.^**

Belarusian State University of Transport, 34, Kirova srt., Gomel, 246653, Belarus

*e-mail: dstar@mail.by
**e-mail: leoden@tut.by

Abstract

Axisymmetric forced vibrations of elastic circular three-layer plate have been studied.

The plate is fixed on elastic base. Because of the symmetry of the problem the tangential displacements in the layers are absent. On the contour of the plate assumes a rigid diaphragm that prevents relative shift layers. The padding between the carrier layer is considered easy, that allows us to neglect his work in the tangential direction. Elastic base describes the Winkler model. To describe the kinematics asymmetrical thickness package adopted broken normal hypothesis.

Solution of the problem is contained in a cylindrical coordinate system. External vertical load acting on the plate is not dependent on the angular coordinate. Applied to the plate following types of loads: locally parabolic distributed on a circle with a given radius of the concave parabolic uniformly distributed local rectangular.

Forced transverse vibrations of circular three-layer plate associated with the elastic foundation, described by a system of differential equations derived from the variational principle of Hamilton. External load and the desired solution are presented in the form of expansions in series.

Numerical results are obtained for the contour clamped circular three-layer plate, unbound and bound with a base of medium hardness. The resultant force and the parabolic rectangular loads assumed to be equal.

The dependence of the change in the deflection of circular three-layer plate associated with the elastic base of medium hardness, the radius of the spot the local distribution of the dynamic load have been found. In the absence of an elastic foundation deflections vary little. A plate associated with a deformable base deflections when distributing loads on the entire surface increases approximately twofold.

Deflection reaches maximum values during operation load on the entire outer surface of the plate. Maximum deflection of the convex parabolic load time exceeds the amount of deflection of a rectangular load of 1.35 times. Consequently, for the same magnitude of the resultant convex parabolic load more dangerous than rectangular, as in the plate causing Larger deflections. This effect is observed for the plate associated with an elastic base, both with and without it. In the absence of an elastic foundation deflections vary little. A plate connected with a deformable base deflections when distributing loads on the entire surface increases approximately twofold.

Numerical results are compared with the case of the local surface load of rectangular shape.

Keywords:

three-layer circular plate, elastic base, oscillations, parabolic loading

References

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