Local and global dynamics of a functionally graded dielectric elastomer plate

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY
Amin Alibakhshi , Sasan Rahmanian , Michel Destrade , Giuseppe Zurlo
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引用次数: 0

Abstract

We investigate the nonlinear vibrations of a functionally graded dielectric elastomer plate subjected to electromechanical loads. We focus on local and global dynamics in the system. We employ the Gent strain energy function to model the dielectric elastomer. The functionally graded parameters are the shear modulus, mass density, and permittivity of the elastomer, which are formulated by a common through-thickness power-law scheme. We derive the equation of motion using the Euler-Lagrange equations and solve it numerically with the Runge-Kutta method and a continuation-based method. We investigate the influence of the functionally graded parameters on equilibrium points, natural frequencies, and static/dynamic instability. We also establish a Hamiltonian energy method to detect safe regions of operating gradient parameters. Furthermore, we explore the effect of the functionally graded parameters on chaos and resonance by plotting several numerical diagrams, including time histories, phase portraits, Poincaré maps, largest Lyapunov exponent criteria, bifurcation diagram of Poincaré maps, and frequency-stretch curves. The results provide a benchmark for developing functionally graded soft smart materials.

功能分级介电弹性体板的局部和全局动力学
研究了电介质弹性体在机电载荷作用下的非线性振动。我们关注系统中的局部和全局动态。我们采用根特应变能函数来模拟介电弹性体。功能梯度参数是弹性体的剪切模量、质量密度和介电常数,它们由通用的全厚度幂律格式表示。利用欧拉-拉格朗日方程推导了运动方程,并采用龙格-库塔法和基于连续的方法对其进行了数值求解。我们研究了功能梯度参数对平衡点、固有频率和静态/动态不稳定性的影响。我们还建立了一种哈密顿能量法来检测工作梯度参数的安全区域。此外,我们通过绘制几个数值图,包括时程图、相位图、庞卡罗莱图、最大Lyapunov指数准则、庞卡罗莱图的分岔图和频率拉伸曲线,探讨了功能梯度参数对混沌和共振的影响。研究结果为开发功能分级软智能材料提供了参考依据。
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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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