State-space approach is developed to analyze the bending and free vibration of a simply supported, cross-ply laminated rectangular plate featuring interlaminar bonding imperfections, for which a general linear spring layer model is adopted. The analysis is directly based on the three-dimensional theory of orthotropic elasticity and is completely exact. Numerical comparison is made, showing that although the plate theory developed in the literature behaves well for moderately thick perfect laminates it can become inaccurate when bonding imperfections are present. The special problem of the laminate in cylindrical bending is also considered, and the validity of the assumption of cylindrical bending is investigated through numerical examples. NomenclatureA = dimensionless coef cient matrix a; b; h = length, width and height of plate c i j = elastic constants E; G; ¹ = Young's modulus, shear modulus, and Poisson's ratio h k = thickness of the kth layer K i = stiffness constants of interface M k ; P k = transfer matrices of layer and interface m; n = positive integers N = number of layers in the laminate T; T i j = global transfer matrix and the elements u; v; w = displacement components in Cartesian coordinates V = dimensionless state vector z k = z coordinate of the kth interface »;´; = dimensionless coordinates ½ = mass density ratio ¾ i ; ¿ i j = normal and shear-stress components Ä, ! 0 , ! ¤ = dimensionless frequency parameters ! = circular frequency Subscripts L ; T = directions parallel and perpendicular to the bers k = kth layer or interface Superscript (k) = kth layer

The problem of a piezoceramic hollow sphere is investigated analytically based on the 3D equations of piezoelasticity. The functionally graded property of the material along the radial direction can be taken arbitrarily in the paper. Displacement and stress functions are introduced, and two independent state equations with variable coefficients are derived. By employing the laminate model, the two state equations are transformed into ones with constant variables from which the state variable solution is easily obtained. Two linear relationships between the state variables at the inner and outer spherical surfaces are established. Numerical calculations are performed for different boundary conditions imposed on the spherical surfaces.

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