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Solutions of vibration problems for thin infinite plates subjected to harmonic loads

Klanner M., Ellermann K.

Journal of Theoretical and Applied Mechanics

2017

Vol. 55 nr 3

949—961

New closed form solutions for harmonic vibrations of infinite Kirchhoff plates subjected to a constant harmonic ring load, a constant harmonic circular load and an alternating harmonic circular load are derived. Two different approaches are used to define the closed form solutions. The first approach uses the integration of the harmonic point force and the addition theorem for Bessel functions, while the second approach applies the Hankel transform to solve the inhomogeneous partial differential equation of the Kirchhoff plate theory. The new closed form particular solutions can especially be used in Trefftz like methods and extend their field of application.

Deflection relationships between the homogeneous Kirchhoff plate theory and different functionally graded plate theories

Cheng Z., Batra R.

Archives of Mechanics

2000

Vol. 52, nr 1

143-158

We derive field equations for a functionally graded plate whose deformations are governed by either the first-order shear deformation theory or the third-order shear-deformation theory. These equations are further simplified for a simply supported polygonal plate. An exact relationship is established between the deflection of the functionally graded plate and that of an equivalent homogeneous Kirchhoff plate. This relationship is used to explicitly express the displacements of a plate particle according to the first-order shear deformation theory in terms of the deflection of a homogeneous Kirchhoff plate. These relationships can readily be used to obtain similar correspondences between the deflections of a transversely isotropic laminated plate and a homogeneous Kirchhoff plate.