Nonlinear flutter of variable stiffness composite plates—using a reduced-order model benefiting from a large-enough number of modes or degrees of freedom—is the subject of this research. Dynamic of such plates is enriched by different scenarios including period-n (un)stable limit cycle oscillations, quasi-periodic or chaotic solutions, along with Hopf, symmetry breaking and period doubling bifurcations. The fibre path orientation, in any individual ply of these rectangular plates, changes linearly from the left edge to the right one. The plates are subjected to a supersonic airflow. The plate’s displacement field is modelled using a third-order shear deformation theory; a p-version finite element is used to discretize the displacement components. Aerodynamic pressure due to the airflow is approximated using linear piston theory. The self-exciting vibrational full-order model (FOM) is formed by employing the principle of virtual work, and then, the ROM is extracted from the FOM using two reduction techniques, namely static condensation and modal summation method. The inclusion of a large-enough number of modes of vibration in vacuum in the latter technique is critical for the observation of, often overlooked, complex dynamic behaviour of these plates. The equations of motion representing the ROM are solved using the shooting method (to obtain stable and unstable LCOs) and using Newmark method (for stable or non-oscillatory solutions). The rich dynamics of these plates are explored with the help of vibration and flutter mode shapes, phase-plane plots, bifurcation diagrams, fast Fourier transform diagrams and Poincaré sections.

本研究的主题是可变刚度复合板的非线性颤动-使用从大量模式或自由度中受益的降阶模型。此类板块的动态性通过不同的场景得以丰富，包括周期为n（不稳定）的极限循环振荡，准周期或混沌解以及Hopf，对称破坏和周期倍增分叉。在这些矩形板的任何单个层中，纤维路径的方向从左边缘到右边缘呈线性变化。板经受超音速气流。使用三阶剪切变形理论对板的位移场进行建模。一个p-version有限元用于离散位移分量。使用线性活塞理论来估算由于气流引起的空气动力压力。利用虚功原理建立了自激振动全阶模型（FOM），然后采用静态归纳法和模态求和法两种还原技术从FOM中提取了ROM。在后一种技术中，在真空中包含足够多的振动模式对于观察这些板的复杂动态行为至关重要，而这些现象通常被忽略。使用射击方法（以获得稳定和不稳定的LCO）和Newmark方法（用于稳定或非振荡解决方案）求解代表ROM的运动方程。