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Thermoelastic guided wave in fractional order functionally graded plates: An analytical integration Legendre polynomial approach

机译：分数级的热弹性导波功能分级板：分析整合legendre多项式方法

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摘要

In this paper, an analytical integration Legendre polynomial approach (AILPA) is proposed to investigate the guided thermoelastic wave in functionally graded material (FGM) plates in the context of the fractional order Lord-Shulman (LS) thermoelastic theory. Coupled wave equations and fractional order heat conduction equation are solved by the presented approach, which proposes the analytical integral instead of numerical integration in the available conventional Legendre polynomial approach (CLPA). Comparison of the CPU time between two approaches indicates the higher efficiency of the presented approach. Furthermore, a new treatment of the adiabatic boundary condition for the Legendre polynomial is developed, other than the CLPA can only deal with the isothermal boundary condition. Finally, the phase velocity dispersion curves, attenuation curves, the displacement and temperature distributions for functionally graded plates with different fractional orders are analysed. Both the fractional order and relaxation time have weak influence on the elastic mode velocity, but they have considerable influence on the elastic mode attenuation.
机译：在本文中，提出了一种分析集成乘法多项式方法（AILPA），以在分数阶牧主机（LS）热弹性理论的背景下在功能渐变材料（FGM）板中的引导热弹性波。通过呈现的方法解决了耦合波动方程和分数级热传导方程，其提出了分析积分而不是可用的传统legendre多项式方法（CLPA）中的数值积分。两种方法之间的CPU时间的比较表明了所提出的方法的效率更高。此外，开发了对传说多项式的绝热边界条件的新处理，除了CLPA之外，只能处理等温边界条件。最后，分析了具有不同分数级的功能渐变板的相速度色散曲线，衰减曲线，位移和温度分布。分数顺序和弛豫时间都对弹性模式速度的影响薄弱，但它们对弹性模式衰减具有相当大的影响。

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