Abstract

In this research, for the first time, a nonlinear dynamic model for large oscillation and the disk’s chaotic responses is presented. The material of the annual disk is composite layer reinforced by graphene oxide (GO) nanofillers and macro carbon fibers (CFs) and covered with a piezoelectric layer. The kinematic and nonlinear constitutive dynamic equations of the disk isare obtained by the use of the Von-Karman nonlinear theory alongside with the Hamilton’s principle. The derived nonlinear equations coupled with boundary conditions are solved numerically employing harmonic differential quadrature method (HDQM). The multiple scales method also used in the evaluation of primary resonance of the disk. The results show that inside to outside radii ratio, thickness to radius ratio as geometrical parameters, and loading condition including applied voltage and harmonic load have a substantial impact the nonlinear large oscillation, and chaotic motion of the composite disk covered with piezoelectric layer. The most interesting and significant outcome of this article is that with increasing the thickness of the piezoelectric layer, the system’s nonlinear frequency decreases and the area of instability in responses and maximum amplitude or the peak point of the backbone curve of the smart disk increases. Moreover, as the CF’s weight fraction increases, the system’s motion and dynamics change from chaotic to semi-harmonic.

摘要

在这项研究中，首次提出了大振荡和圆盘混沌响应的非线性动力学模型。圆盘的材料是由氧化石墨烯（GO）纳米填料和粗碳纤维（CF）增强的复合层，并覆盖有压电层。利用Von-Karman非线性理论和Hamilton原理得到了圆盘的运动学和非线性本构动力学方程。采用调和微分求积法（HDQM）对导出的与边界条件耦合的非线性方程进行数值求解。多尺度方法也用于评估盘的初级共振。结果表明，以内外半径比、厚径比作为几何参数，施加电压和谐波载荷等加载条件对压电层覆盖的复合圆盘的非线性大振荡和混沌运动有显着影响。本文最有趣和最重要的成果是，随着压电层厚度的增加，系统的非线性频率降低，响应不稳定的面积以及智能磁盘主干曲线的最大幅度或峰值点增加。此外，随着 CF 重量分数的增加，系统的运动和动力学从混沌变为半谐波。本文最有趣和最重要的成果是，随着压电层厚度的增加，系统的非线性频率降低，响应不稳定的面积以及智能磁盘主干曲线的最大幅度或峰值点增加。此外，随着 CF 重量分数的增加，系统的运动和动力学从混沌变为半谐波。本文最有趣和最重要的成果是，随着压电层厚度的增加，系统的非线性频率降低，响应不稳定的面积以及智能磁盘主干曲线的最大幅度或峰值点增加。此外，随着 CF 重量分数的增加，系统的运动和动力学从混沌变为半谐波。