Abstract
The object of this paper is the Saint-Venant torsion of a radially non-homogeneous, hollow and solid circular cylinder made of orthotropic piezoelectric material. The elastic stiffness coefficients, piezoelectric constants and dielectric constants have only radial dependence. This paper gives the solution of the Saint-Venant torsion problem for torsion function, electric potential function, Prandtl’s stress function and electric displacement potential function.
Highlights
Application of piezoelectric materials and structures has been increasing recently
The Saint-Venant torsion of a homogeneous, isotropic elastic cylindrical body is a classical problem of elasticity [1,2,3], which is solved using a semi-inverse method by assuming a state of pure shear in the cylindrical body so that it gives rise to a resultant torque over the end cross sections
The inhomogeneity function is piecewise continuous on the cross-sectional domain and it is given by the following formula: f (r ) = fi (r ) ri−1 < r < ri (i = 1, 2, . . . , n) r0 = R1 rn = R2 (57). It is evident for radially layered, non-homogenous, orthotropic piezoelectric hollow circular cross section that the torsion function and the electric potential function given by Eqs. (24), (25), together with all the formulae obtained before, are valid here, and we have
Summary
Application of piezoelectric materials and structures has been increasing recently. Sensors and actuators are examples of active components made of piezoelectric materials which are used widely in smart structures. Baksa [15] give a formulation of the Saint-Venant torsional problem for homogeneous monoclinic piezoelectric beams in terms of Prandtl’s stress function and the electric displacement potential function. In another paper by Ecsedi and Baksa [16], a variational formulation is presented for the torsional deformation of homogeneous linear piezoelectric monoclinic beams. Rovenski and Abramovich apply a linear analysis to piezoelectric beams with non-homogeneous cross sections that consist of various monoclinic (piezoelectric and elastic) materials [13] They give the solution procedure for extension, bending, torsion and shear. The deformation of circular cylinders made of orthotropic, radially non-homogeneous piezoelectric material is studied by means of Saint-Venant’s theory of uniform torsion. The dependence of material parameters is either described by smooth functions of radial coordinate as in the case of functionally graded materials [18,19], or the material parameters are piecewise smooth functions of the radial coordinate as in the case of radially layered circular cylinders
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