Xiaoshan Cao

Cut-off frequencies of Lamb waves in various functionally graded thin films

An analytical study is carried out on the cut-off frequencies of Lamb waves in freestanding thin films made of various functionally graded elastic, piezoelectric, or piezoelectric–piezomagnetic materials. Results show that the set of cut-off frequencies is a union of two series of approximate arithmetic progression, in which the differences are inversely proportional to the definite integral of a function of the material parameters along thickness. Given the simple and universal relationship between cut-off frequencies and material parameters, this study provides theoretical guidance not only for nondestructive evaluation in engineering applications but for designing high-performance sensors based on Lamb waves.

Lamb Waves in a Functionally Graded Composite Plate with Nonintegral Power Function Volume Fractions

An analytical modelling is carried out to determine the Lamb wave’s propagation behavior in a thermal stress relaxation type functionally graded material (FGM) plate, which is a composite of two kinds of materials. The mechanical parameters depend on the volume fractions, which are nonintegral power functions, and the gradient coefficient is the power value. Based on the theory of elastodynamics, differential equations with variable coefficients are established. We employ variable substitution for theoretical derivations to solve the ordinary differential equations with variable coefficients using the Taylor series. The numerical results reveal that the dispersion properties in some regions are changed by the graded property, the phase velocity varies in a nonlinear manner with the gradient coefficient, nondispersion frequency exists in the first mode, and the set of cutoff frequencies is a union of two series of approximate arithmetic progressions. These results provide theoretical guidance not only for the experimental measurement of material properties but also for their nondestructive testing.

Wentzel–Kramers–Brillouin solution of cut-off frequency for horizontal shear (SH) waves in various inhomogeneous thin films

The Wentzel–Kramers–Brillouin method is employed to study the cut-off frequencies of the horizontal shear waves in a freestanding functionally graded piezoelectric–piezomagnetic material film with the electrically and magnetically open boundary conditions. An analytical solution, which could be used in analyzing the problems of various functionally graded materials, is proven to have high precision by analytical analysis and a numerical example. The results reveal that the set of cut-off frequencies is a series of approximate arithmetic progressions. A theoretical foundation based on the relationship between the cut-off frequencies and the materials’ gradient property is established for nondestructive evaluation.

Horizontal shear waves in a parabolic cylinder piezoelectric shell

Horizontal shear (SH) waves in parabolic cylinder shells with a polling direction parallel to a generatrix are investigated. Based on the motion equation, electrical displacement equilibrium equations, piezoelectric constitutive equations, geometric equation, and the relation between electrical intensity and electrical potential, the field-governing equation in parabolic cylinder coordinates that is expressed by the displacement and electrical potential is deduced. Based on the Wentzel-Kramers-Brillouin and power series methods, ordinary differential equations are solved and the wave functions of the SH waves in a piezoelectric parabolic cylinder are determined. As a numerical example, the relation between the correction coefficient of the wave number and the frequency of the SH waves is discussed, and the structures of the waves are illustrated. Results reveal that one or more modes of the SH waves can propagate along the circumferential direction in parabolic cylinder shells. The correction coefficient of the wave number of the first modeis approximately a constant. The number of modes increases with the frequency and thickness of the shell. These results should provide theoretical guidance for evaluating curved structures non-destructively and for designing novel acoustic devices based on curved structures.

Love waves in piezoelestric layered structure with functionally graded materail half space

In this theoretical study, we investigate the propagation of Love waves in a piezoelectric layered structure. The substrate of the layered structure is a functionally graded material (FGM) in which parameters vary along thickness and in the bounded domain. Both variable substitution and power series technique, which are shown to have good convergence and high precision, are employed for the asymptotic analytical derivations of the governing equation of Love wave. The influence of the gradient coefficient of FGM on the dispersion curves, and electro-mechanical coupling factor, and the displacement amplitude distributions of Love waves in this structure are investigated. The theoretical results set guidelines not only for the design of high performance surface acoustic waves (SAW) devices using the FGM substrate, but also for the measurement of material properties of FGM half space using Love waves.