3D Analysis Of The Axisvmmetric Bending Of Circular/Annular Plates And The Free Vibrations Of Cylindrical Panels

Based on three-dimensional theory, this paper investigates the axisymmetric bending of transversely isotropic and functionally graded circular plates subject to arbitrarily transverse loads usingthedirect displacementmethod.The material properties canarbitrarilyvaryalongthethickness of the plate. The transverse load is expanded in the Fourier-Bessel series and superposition principle is then used to obtain the total response based on the results of each item of the series. For one item of the series of the load, we assume the distributions of the displacements in the radial direction and therefore only the distributions of the displacements in thickness direction are required to find. If the material properties vary in an exponential law, the exact solutions can be obtained for elastic simple support and rigidslippingsupport.which are satisfied on theevery point ofthe boundaries. Moreover, the analytical solutions are also presented for simply supported and clamped conditions, which are satisfied using Saint-Venant principle. Simultaneously, through the layer-wise method a semi-analytical solution is proposed for the case of arbitrary variation of the material properties.The method is then extended for the piezoelectric and magneto-electro-elastic circular and annular plates, in which the radial distributions of the electrical potential and magnetic potential are assumed in a similar manner as those of displacements in the corresponding elastic case. The three-dimensionally exact solutions are also obtained for some specific boundary conditions and laws of the variation of the material properties. For the cases of common boundary conditions and arbitrary variation of the material properties, some analytical solutions are presented through the layer-wise method and approximate boundary conditions by Saint-Venant principle.This paper also studies the free vibration of simply supported magneto-electro-elastic cylindrical panels. The general solutions for transverselyisotropicmagneto-electro-elasticmaterials areintroduced and the displacementfunctionsinthegeneralsolutions are expanded in trigonometric functions along the circumferential and axial directions. Then an ordinary differential equation of the displacement functions in radial direction is derived and solved. As a result, the frequency equations are obtained through the traction-free conditions on the cylindrical surfaces of the panel as well as the electric and magnetic conditions. For the torsion and thickness-shear modes, the frequency equationsin simplerforms are presented. It isfound thatthe magneto-electro-elasticcoupling effects disappeared in torsion vibration. Meanwhile, the frequencies of pure elastic materials and magneto-electro-elastic materials have an explicit relation for the thickness-shear modes. The aforementioned solutions satisfy all the governing equations and boundary conditions point by point and they are three-dimensionally exact.