Analysis of surface waves using orthogonal functions

Abstract

A simple noniterative method using an orthonormal basis for expressing field distributions has been developed for obtaining surface-wave solutions in piezoelectric crystals. Velocity and field distributions are obtained for YZ LiNbO3 that agree with earlier works. The boundary conditions are incorporated in a manner that is easily adapted to layered structures. Dispersion curves are obtained for surface waves in LiTaO3 with a SiO2 layer at the surface; the results are in good agreement with those published earlier.

Guided wave characteristics in functionally graded piezoelectric rings with rectangular cross-sections

“…The derivatives along r and z of I(r, z) are delta (r ) and delta (z). By introducing the function I(r, z), the traction-free and open-circuit boundary conditions, i.e., T rr = T r θ = T r z = D r = 0 at r = a, r = b and T r z = T θ z = T zz =D z = 0 at z = 0, z = h, are automatically incorporated into the constitutive relations of the ring [22]:…”

“…It has been used to solve wave propagation problems in different structures, from semi-infinite structures [22] to flat plate [19] and to various curved structures [20,23], from purely elastic structures [23] to various multi-field coupled structures [19,[24][25][26], from homogeneous structures [23] to various inhomogeneous structures [22,[24][25][26]. However, the available polynomial series approach can only deal with semi-infinite structures and one-dimensional structures.…”

Dispersion curves of 2D rods with complex cross-sections: double orthogonal polynomial approach

“…After that, this approach has been used to solve various wave and vibration problems, from acoustic waves in wedges and ridges [1][2][3], to surface acoustic waves in layered [4,5] and inhomogeneous [6] semiinfinite structures. Later on, it was extended to investigate Lamb-like guided acoustic waves in multilayered [7] and functionally graded [8] finitethickness plates.…”

Mapped orthogonal functions method applied to acoustic waves-based devices

“…The illustrations do not aim at validating the mapped orthogonal functions method as this has already been done through several literature papers for both acoustic wave-based devices with guided waves 34,38,39,41 and with stationary waves. 30,31,42 The objective is rather to illustrate in a same paper the potentialities of the method for various geometries and various regimes: first a multilayered plate where the method gives, through a single calculation, all types of free ultrasonic waves, Lamb-like and SH waves, second a 2D rectangular resonator which highlights the capability of the mapped orthogonal functions method to give the forced response which includes both the thickness and lateral parasitic resonances, the latter so important in a design process, and third a 3D cylindrical resonator.…”