Axisymmetric vibration of an elastic circular plate bonded on a transversely isotropic multilayered half-space

In this paper, dynamic response of an elastic circular plate, under axisymmetric time-harmonic vertical loading, resting on a transversely isotropic poroelastic half-space is investigated. The plate-half-space contact surface is assumed to be smooth and fully permeable. The discretization techniques are employed to solve the unknown normal traction at the contact surface based on the solution of flexibility equations. The vertical displacement of the plate is represented by an admissible function containing a set of generalized coordinates. Solutions for generalized coordinates are obtained by establishing the equation of motion of the plate through the application of Lagrange’s equations of motion. Selected numerical results corresponding to the deflections of a circular plate, with different degrees of flexibility, resting on a transversely isotropic poroelastic half-space are presented.

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The Free Vibration of the Magneto-Electro-Elastic Materials Laminated Circular Plate

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.374-377.2193 ◽

2011 ◽

Vol 374-377 ◽

pp. 2193-2199 ◽

Cited By ~ 1

Author(s):

Qun Guan

Keyword(s):

Free Vibration ◽

Circular Plate ◽

Single Layer ◽

Transversely Isotropic ◽

State Variables ◽

Vibration Properties ◽

Elastic Circular Plate ◽

Symmetric Deformation ◽

Laminated Circular Plate ◽

The Given

In this paper, on the basis of the dynamic equation of material which contains transversely isotropic piezoelectric、piezomagnetic and elastic media, the state variables equation of piezoelectric、piezomagnetic and elastic circular plate in axial symmetric deformation is deduced. Under the given boundary conditions, according to the theorem of Caylay-Hamilton and applying the transfer matrix method, the solutions of state variables equation which are about free vibration of piezoelectric、piezomagnetic and elastic circular plate of single layer and multilayered are obtained. The calculation example indicates that from the varying law of the first natural frequency of the plate depending on the thickness-to-radius radio of the plate under varied conditions, the vibration properties of piezoelectric、piezomagnetic and laminated plate is related to the laminatation order of the material is gotten to know.

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Variational Formulation of Interaction between Elastic Plate and Elastic Medium under the Influence of Surface Energy

MATEC Web of Conferences ◽

10.1051/matecconf/201820601012 ◽

2018 ◽

Vol 206 ◽

pp. 01012

Author(s):

S. Tirapat ◽

T. Senjuntichai ◽

J. Rungamornrat ◽

R. K. N. D. Rajapakse

Keyword(s):

Surface Energy ◽

Circular Plate ◽

Half Space ◽

Variational Formulation ◽

Surface Elasticity ◽

Elastic Half Space ◽

Radial Coordinate ◽

Vertical Loading ◽

Elastic Circular Plate ◽

Present Solution

A variational formulation of interaction problem is presented in this paper for the analysis of an elastic circular plate under axisymmetric vertical loading resting on an isotropic elastic half-space under the influence of surface energy. The Gurtin-Murdoch surface elasticity theory is adopted to take into account the surface energy effects. The contact surface between the plate and the half-space is assumed to be smooth, and the deflected shape of the plate is represented by a power series of the radial coordinate. The undetermined coefficients in the series are determined through the minimization of the total potential energy functional of the plate-half-space system. The accuracy of the present solution is verified by comparing with existing solutions, and selected numerical results are presented to portray the influence of surface energy effects on interaction between an elastic circular plate and an elastic half-space.

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