We present a systematic analysis of the eigenvalue problem associated with free vibrations of a finite piezoelectric body. The analysis is based on an abstract formulation of the three-dimensional theory of piezoelectricity. A series of fundamental properties of free vibrations of a piezoelectric body are proved concisely. The problem of free vibrations of a piezoelectric plate governed by the ...

In this paper a least squares method, using the minus one norm developed in 6] and 7], is introduced to approximate the solution of the Reissner-Mindlin plate problem with small parameter t, the thickness of the plate. The reformulation of Brezzi and Fortin is employed to prevent locking. Taking advantage of the least squares approach, we use only continuous nite elements for all the unknowns. ...

The mixed method for the biharmonic problem introduced in [12] is extended to the Reissner-Mindlin plate model. The Reissner-Mindlin problem is written as a system of first order equations and all the resulting variables are approximated. However, the hybrid form of the method allows one to eliminate all the variables and have a final system only involving the Lagrange multipliers that approxim...

Background: The first-order shear deformation theory (FSDT) for plates requires a shear correction factor due to the assumption of constant shear strain and shear stress across the thickness; hence, the shear correction factor strongly influences the accuracy of the deflection solution; the third-order shear deformation theory (TSDT) does not require a correction factor because it facilitates t...

In this paper, we consider a plate–beam system inwhich the Reissner–Mindlin platemodel is combined with the Timoshenko beam model. Natural frequencies and vibration modes for the system are calculated using the finite element method. The interface conditions at the contact between the plate and beams are discussed in some detail. The impact of regularity on the enforcement of certain interface ...

A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated. Details about the scheme implementation are provided, and the numerical results on several different types of meshes are reported.