A hybrid numerical method (HNM) is presented for analyzing transient waves in a cylinder made of functionally graded material (FGM). In the HNM, the FGM cylinder is divided into N cylindrical elements with three-nodal line in the wall thickness. The elemental material properties are assumed to vary linearly in the thickness direction to better modeol the spatial variation of material properties of FGM. The Hamilton variational principle is used to develop governing equations of the cylinder. The displacement responses are determined by employing the Fourier transfor-mations together with the modal analysis. The HNM is applied to analyze a number of FGM cylinder, and its effi-ciency is demolnstrated.

A method is presented to investigate elastic waves in functionally gradient material (FGM) plates excited by plane pressure wavelets. The FGM plate was first divided into linearly inhomogeneous elements (LIEs). A general solution for the equation of motion governing the LIE was derived. The general solution was then used together with the boundary and continuity conditions to obtain the displacement and stress in the frequency domain for an arbitrary FGM plate. The response of the plate to a pressure wavelet was obtained using Fourier transform techniques. Results obtained by the present method are compared with an existing method using homogeneous layer elements. Relationships between the surface displacement response and the material mechanical properties of FGM plates were also obtained. These relationships may be used for the material characterization of FGM plates. q1999 Elsevier Science Ltd. All rights reserved.

An analytical-numerical method is presented for analyzing dispersion and characteristic surface of waves in a circular cylinder composed of functionally graded piezoelectric material (FGPM). In this method, the FGPM cylinder is divided into a number of annular elements with three-nodal lines in the wall thickness. The elemental mechanical as well as electrical properties are assumed to vary linearly in the thickness direction so as to better model the spatial variation of the mechanical and electrical properties of FGPM. The associated frequency dispersion equation is developed and the phase velocity and slowness as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. The calculation examples provide a full understanding of the complex phenomena of elastic waves in FGPM cylinders.

The frequency and group velocity dispersion behaviors, and characteristic surfaces of waves in a hybrid multilayered piezoelectric circular cylinder are investigated. The associated frequency dispersion equation is developed using an analytical-numerical method. In this method, the cylinder is modeled using the three-nodal-line layer element; the coupling between the elastic field and the electric field is considered in each element. A system of governing differential equations of each layer element is obtained following the Hamilton Principle. The phase velocity and slowness as well as the group velocity and slowness are established in terms of the Rayleigh quotient. Six characteristic wave surfaces, e.g. the phase velocity, slowness and wave surfaces as well as the group velocity, slowness and wave surfaces, are introduced to visualize the effects of anisotropy and piezoelectricity on wave propagation. A corresponding program code is developed and numerical examples are presented for hybrid multilayered piezoelectric circular cylinders with two ratios of radius to thickness.

A computational inverse technique is presented for characterizing the material property of functionally graded material (FGM) plates, using the dynamic displacement response on the surface of the plate as input data. A modified hybrid numerical method is used as the forward solver to calculate the dynamic displacement response on the surface of the plate for given material property varying continuously in the thickness direction. A uniform crossover micro-genetic algorithm (uniform uGA) is employed as the inverse operator to determine the distribution of the material property in the thickness direction of the FGM plate. Examples are presented to demonstrate this inverse technique for material characterization of FGM plates. The sensitivity and stability to noise contamination in the input displacement response data are also investigated in detail. It is found that the present inverse procedure is very robust for determining the material property distribution in the thickness direction of FGM plates.