Identification of mechanical properties of elastically restrained laminated composite plates using vibration data

A nondestructive evaluation method using vibration data to determine mechanical properties (material and spring constants) of elastically restrained laminated composite plates is presented. The Rayleigh–Ritz method in which a set of Legendre's polynomials is adopted to approximate the plate deflection is used to determine the theoretical natural frequencies of the elastically restrained laminated composite plates. A number of natural frequencies extracted from the impulse vibration test data of the laminated composite plates supported by elastic restraints at both the edges and centers of the plates are used in the present method to determine the mechanical properties of the plates. The sum of the squared differences function which measures the differences between the experimentally and theoretically predicted natural frequencies of the elastically restrained laminated composite plates is established. The identification of the plate mechanical properties is then formulated as a constrained minimization problem in which the mechanical properties are determined by making the sum of the squared differences function a global minimum. The feasibility and accuracy of the proposed method are studied by means of several numerical examples on the mechanical properties identification of elastically restrained laminated composite plates with different layups made of various composite materials. Experimental investigation of the mechanical properties identification of several elastically restrained laminated composite plates has been performed to illustrate the applications of the present method. It has been shown that the present method can produce good estimates of the mechanical properties of the elastically restrained laminated composite plates in an efficient and effective way.