Dispersion, instability, and soliton dynamics in nonlocal MEE nanoplates

IF 4 3区工程技术 Q2 MECHANICS

Acta Mechanica Pub Date : 2026-07-08 DOI:10.1007/s00707-026-04805-3

R. Karthikeyan, R. Selvamani, Samia Elattar, M. Ijaz Khan

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引用次数: 0

Abstract

This study investigates nonlinear wave propagation in nonlocal magneto-electro-elastic (MEE) sandwich nanoplates using an extended version of the Yan–Dowell framework. The governing equations account for nonlocal elasticity and multiphysical coupling, allowing for a precise description of size-dependent effects and electromechanical interactions at the nanoscale. A harmonic wave approach is used to obtain the dispersion relation, with subsequent analysis of phase and group velocities. Instability of modulation is examined, revealing a bounded instability band shaped by the balance between dispersion and nonlinearity. The impact of the nonlocal parameter and MEE coupling on bandwidth, critical wave number, and growth rate is analyzed. The nonlinear Schrödinger equation is then derived to model envelope dynamics, yielding stable envelope soliton solutions. Numerical findings indicate that soliton width and energy concentration can be adjusted via MEE coupling, enabling targeted control over wave behavior. Compared to linear wave packets, solitons exhibit enhanced localization and stability. The developed model offers a comprehensive approach for studying nonlinear wave phenomena in multifunctional nanostructures for wave guidance, energy transmission, and smart materials applications.

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非局部MEE纳米板中的色散、不稳定性和孤子动力学

本研究利用Yan-Dowell框架的扩展版本研究了非线性波在非局部磁电弹性（MEE）夹层纳米板中的传播。控制方程解释了非局部弹性和多物理耦合，允许在纳米尺度上精确描述尺寸依赖效应和机电相互作用。采用谐波法得到色散关系，并对相速度和群速度进行分析。研究了调制的不稳定性，揭示了色散和非线性之间的平衡所形成的有界不稳定性带。分析了非定域参数和MEE耦合对带宽、临界波数和增长率的影响。然后导出非线性Schrödinger方程来模拟包络动力学，得到稳定的包络孤子解。数值结果表明，可以通过MEE耦合调节孤子宽度和能量浓度，从而实现对波行为的定向控制。与线性波包相比，孤子具有更强的局域性和稳定性。该模型为研究多功能纳米结构中的非线性波动现象提供了一种全面的方法，可用于波导、能量传输和智能材料的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Mechanica 物理-力学

CiteScore

4.30

自引率

14.80%

发文量

292

审稿时长

6.9 months

期刊介绍： Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.