Dynamics of thermoelastic Lamb waves in functionally graded nanoplates based on the modified nonlocal theory.

• Thermoelastic Lamb waves in functionally graded nanoplates are studied based on integral form of modified nonlocal theory. • The Legendre polynomial approach is improved based on the proposed iterative solution integration method. • The escape frequency, which appears in differential model of modified nonlocal theory, does not exist in the integral one. • Nonlocal effect on attenuation is more notable than that on phase velocity. • Nonlocal effect strengthens attenuations before their peak frequency, but then weakens them. Based on the integral form of the modified nonlocal theory, the dispersion and attenuation characteristics of thermoelastic Lamb waves in functionally graded material nanoplates are investigated. The improved Legendre polynomial series approach is presented to conquer the difficulty of the very time-consuming integration calculation, which contains the nonlocal factor, the Legendre polynomials, rectangular window function and their derivative. An iteration solution integration method is derived by using the properties of Legendre polynomials and the integration by parts. The proposed approach possesses the advantages of a small scale of the characteristic matrix and can directly obtain the complex wave number solutions without iteration. Comparisons with the available data indicate the validity of the proposed approach. Numerical examples show that the nonlocal effect on attenuation is more notable than that on phase velocity, especially at the frequency of the maximal attenuation. Besides, the nonlocal effect is very weak at the low frequency. Importantly, the escape frequency, which appears in the results from the differential form of modified nonlocal theory, does not exist in the integral form of modified nonlocal theory. In fact, the escape frequency originates from the approximate transformation from integral model to differential model. [ABSTRACT FROM AUTHOR]