Dispersion characteristics of guided waves in functionally graded anisotropic micro/nano-plates based on the modified couple stress theory

Abstract

In this paper, the acoustic wave motion characteristics of Lamb and SH waves in functionally graded (FG) anisotropic micro/nano-plates are studied based on the modified couple stress theory. A higher efficient computational approach, the extended Legendre orthogonal polynomial method (LOPM) is utilized to deduce solving process. This polynomial method does not need to solve the FG micro/nano-plates hierarchically, which provides a more realistic analysis model for FG micro/nano-plates and has high computational efficiency. Simultaneously, the solutions based on the global matrix method (GMM) are also deduced to verify the correctness of the polynomial method. Furthermore, the effects of size and material gradient are studied in detail. Numerical results show that the size effect causes wrinkles in Lamb wave dispersion curves, and the material gradient characteristic changes the amplitude and range of wrinkles. For SH waves, the length scale parameter L x increases the cut-off frequency but does not change the overall trend of the dispersion curve; on the contrary, L z does not change the cut-off frequency but causes the dispersion curve to show an upward trend.

A Hardening Nonlocal Elasticity Approach to Axial Vibration Analysis of an Arbitrarily Supported FG Nanorod

“…С учетом интереса к композиционным материалам появились работы по исследованию композитных одномерных нано-и микроразмерных структур [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Появились также многомерные модели структур [49][50][51][52][53][54]. Теоретический анализ в рамках механики сплошной среды является важным способом изучения механического поведения этих сверхмалых элементов.…”

Low-order non-classical continuum models for the improved prediction of an anisotropic membrane lattice’s dynamics

“…For this reason, since the 19th century, considerable efforts have been concentrated on developing non-classical continuum models, capable of capturing the size-effects that appear in the discrete media. Despite the fact that the first works were undertaken in the 1960s by Mindlin [13], Eringen [14,15] or Krumhansl [16,17], among others, the interest in this matter continues at the present time [18,19], with recent works based, among others, on the strain gradient elasticity or on the modified couple stress theories, which have been commonly applied to solve problems concerning beams [20,21], membranes [22,23] or plates [24,25]. On the other hand, several works concerning non-local theories [26][27][28][29] such as the non-local strain gradient theory [30] can be found in the literature.…”

Asymptotic Analytical Solution on Lamb Waves in Functionally Graded Nano Copper Layered Wafer

“…As asymptotic methods with series form, the Legendre [24][25][26] and power series methods [27] are utilized to analyze waves in various FG structures. Especially, the Legendre series method has been applied, not only for solving wave propagation behavior of macroscopic structure [28], but also that of microstructure using the combined modified couple stress theory [29,30]. Numerical analyses of wave propagation in inhomogeneous media are also conducted.…”