Linear and nonlinear vibrations of composite plates

The work presented in this thesis deals with the linear buckling and free vibration of homogeneous plates initially and linear and nonlinear forced vibrations of laminated composite plates with and without piezoelectric materials in later parts. Equations are based on the first order shear deformable plate theory known as the Reissner-Mindlin plate theory and derived by minimizing the potential energy. All of the problems discussed in the thesis are solved by p-type solution method, which is a generalized form of the displacement based finite element method. The displacement fields are defined by polynomials of degrees much higher than those used for the geometry. The modeling of the entire middle plane of the plate considers either one or at most two domains. Special precaution is taken while interpolating the electric potential function in the thickness direction of piezoelectric materials.;The linear buckling and free vibration of square and rhombic plates with and without cut-outs are studied with various boundary conditions. Plates with no holes are solved using single domain while doubly connected plates due to circular hole at the center are analyzed with two domains. Effects of hole size, plate thickness, loading type and boundary condition on the buckling and vibration of plates are studied. Linear and geometrically nonlinear transient responses of fiber-reinforced laminated composite plates subject to transverse uniform load on the entire plate or on a circular area are examined by present method with a single domain model. Equation of motion is solved by Newmark's method along with Newton-Raphson iterative scheme. Numerical results are presented for square, rhombic, annular circular sector, and trapezoidal plates. The study is further extended to analyze the dynamic behavior of laminated composite piezoelectric plates under mechanical load, electrical load, and the combination of the two. The nonlinearity produces stiffening in the plate and this effect is observed through the reduced amplitudes of vibration and increased frequencies. Numerical results obtained from the present method, whenever compared with the data available in the open literature and also with finite element results from I-DEAS, show excellent agreement.;Keywords. buckling, displacement, electric potential, forced vibration, free vibration, hole, laminated composites, piezoelectric materials, p-type.