Narrow Results

Both classical Fourier analysis and continuous wavelets transformation are applied to study non-linear vibrations of infinitely long flexible panels subject to longitudinal sign-changeable external load actions. First the governing PDEs are derived and then the Bubnov–Galerkin method is applied to yield 2N first order ODEs. The further used Lyapunov exponent computation is described. Transition scenarios from regular to chaotic dynamics of the being investigated plate strip are analyzed using different wavelets, and their suitability and advantages/disadvantages to nonlinear dynamics monitoring and quantifying are illustrated and discussed. A few novel results devoted to the beam nonlinear dynamics behavior are reported. In addition, links between the largest Lyapunov exponent computation and the wavelet spectrum numerical estimation are also illustrated and discussed.

In this paper, flutter and divergence instabilities of functionally graded porous plate strip reinforced with graphene nanoplatelets in supersonic flow and subjected to an axial loading are studied. The graphene nanoplatelets are distributed in the matrix either uniformly or non-uniformly along the thickness direction. Four graphene nanoplatelets distribution patterns namely, Patterns A through D are considered. Based on the modified Halpin–Tsai micromechanics model and the rule of mixture, the effective material properties of functionally graded plate strip reinforced with graphene nanoplatelets are obtained. The aerodynamic pressure is considered in accordance with the quasi-steady supersonic piston theory. To transform the governing equations of motion to a general eigenvalue problem, the Galerkin method is employed. The flutter aerodynamic pressure and stability boundaries are determined by solving standard complex eigenvalue problem. The effects of graphene nanoplatelets distributions, graphene nanoplatelets weight fraction, geometry of graphene nanoplatelets, porosity coefficient and porosity distributions on the flutter and divergence instabilities of the system are studied. The results show that the plate strip with symmetric distribution pattern (stiffness in the surface areas) and GPLs pattern A predict the highest stable area. The flutter and divergence regions decrease as the porosity coefficient increases. Besides, the critical aerodynamic loads increase by adding a small amount of GPL to the matrix.