Guided wave propagation in functionally graded fractional viscoelastic plates: A quadrature-free Legendre polynomial method
Zhi Li, Jiangong Yu, Xiaoming Zhang, L. Elmaimouni
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.