Guided waves in general anisotropic layered rectangular rods: An extended orthogonal polynomial approach

Abstract

The orthogonal polynomial approach has been used to solve the guided wave propagation in structures for about 20 years, but was limited until now to one-dimensional structures, that is, structures with a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. This paper extends the orthogonal polynomial approach to two-dimensional structures, that is, structures with finite dimensions in two directions, with illustration on the multilayered rectangular rod. Through numerical comparison with the available results, the validity of the extended polynomial approach is illustrated. The dispersion curves and displacement distributions of various layered rectangular rods are obtained to show their guided wave characteristics.

Keywords

Guided waves rectangular rod multilayered structure orthogonal polynomials dispersion curves displacement distribution

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References

Maradudin

Wallis

Mills

. Vibrational edge modes in finite crystals. Phys Rev B 1972; 6: 1106–1111.

Sharon

Maradudin

Cunningham

. Vibrational modes on a rectangular ridge. Lett Appl Eng Sci 1974; 2: 161–174.

Maradudin

Subbaswamy

. Edge localized vibration modes on a rectangular ridge. J Appl Phys 1977; 48: 3410–3414.

Datta

Hunsinger

. Analysis of surface waves using orthogonal functions. J Appl Phys 1978; 49: 475–479.

Kim

Hunt

. Acoustic fields and velocities for surface-acoustic-wave propagation in multilayered structures: an extension of the Laguerre polynomial approach. J Appl Phys 1990; 68: 4993–4997.

Gubernatis

Maradudin

. A Laguerre series approach to the calculation of wave properties for surfaces of inhomogeneous elastic materials. Wave Motion 1987; 9: 111–121.

Lefebvre

Zhang

Gazalet

. Legendre polynomial approach for modeling free ultrasonic waves in multilayered plates. J Appl Phys 1999; 85: 3419–3427.

Lefebvre

Zhang

Gazalet

. Acoustic wave propagation in continuous functionally graded plates: an extension of the Legendre polynomial approach. IEEE Trans Ultrason Ferroelectrics Freq Contr 2001; 48: 1332–1340.

Chen

. Wave characteristics in functionally graded piezoelectric hollow cylinders. Arch Appl Mech 2009; 79: 807–824.

10.

. Circumferential wave in functionally graded piezoelectric cylindrical curved plates. Acta Mech 2008; 198: 171–190.

11.

. Characteristics of guided waves in graded spherical curved plates. Int J Solid Struct 2007; 44: 3627–3637.

12.

. Circumferential wave in magneto-electro-elastic functionally graded cylindrical curved plates. Eur J Mech Solid 2009; 28: 560–568.

13.

. Guided thermoelastic waves in functionally graded plates with two relaxation times. Int J Eng Sci 2010; 48: 1709–1720.

14.

. Viscoelastic shear horizontal wave in graded and layered plates. Int J Solid Struct 2011; 48: 2361–2372.

15.

Taweel

Dong

Kazic

. Wave reflection from the free end of a cylinder with an arbitrary cross-section. Int J Solid Struct 2000; 37: 1701–1726.