Guided wave propagation in functionally graded fractional viscoelastic plates: A quadrature-free Legendre polynomial method

Abstract

Compared to the traditional integer-order viscoelastic model, a fractional-order derivative viscoelastic model is shown to be advantageous. A quadrature-free Legendre polynomial method combining the Weyl definition of fractional order derivative is for the first time employed to solve guided waves in functionally graded fractional viscoelastic plates. The presented method avoids a lot of numerical integration calculation in traditional polynomial method and greatly improves the computational efficiency. The effects of different graded fields and fractional orders on the dispersion and attenuation curves are illustrated. The displacement distributions, Poynting vectors and power flows are analyzed to reveal guided wave characteristics.

Keywords:

• Attenuation
• dispersion
• fractional order derivative
• functionally graded viscoelastic plate
• guided wave
• Legendre polynomial method

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [No. 51975189 and U1804134], the Training Plan of Young Key Teachers of Universities in Henan Province [No. 2018-GGJS-060], and the Open Fund for Key Laboratory of underground engineering and disaster prevention and control in Henan Province.