Abstract
The nonlinear vibrations and responses of a laminated composite cantilever plate under the subsonic air flow are investigated in this paper. The subsonic air flow around the three-dimensional cantilever rectangle laminated composite plate is considered to be decreasing from the wing root to the wing tip. According to the ideal incompressible fluid flow condition and the Kutta–Joukowski lift theorem, the subsonic aerodynamic lift on the three-dimensional finite length flat wing is calculated by using the Vortex Lattice (VL) method. The finite length flat wing is modeled as a laminated composite cantilever plate based on Reddy’s third-order shear deformation plate theory and the von Karman geometry nonlinearity is introduced. The nonlinear partial differential governing equations of motion for the laminated composite cantilever plate subjected to the subsonic aerodynamic force are established via Hamilton’s principle. The Galerkin method is used to separate the partial differential equations into two nonlinear ordinary differential equations, and the four-dimensional nonlinear averaged equations are obtained by the multiple scale method. Through comparing the natural frequencies of the linear system with different material and geometric parameters, the relationship of 1 : 2 internal resonance is considered. Corresponding to several selected parameters, the frequency-response curves are obtained. The hardening-spring-type behaviors and jump phenomena are exhibited. The influence of the force excitation on the bifurcations and chaotic behaviors of the laminated composite cantilever plate is investigated numerically. It is found that the system is sensitive to the exciting force according to the complicate nonlinear behaviors exhibited in this paper.
Highlights
There are few research works dealing with the complex nonlinear dynamics of the structure which is simplified as a laminated composite cantilever plate subjected to subsonic air flow
Some literature reviews on nonlinear vibrations of plates were given by Chia [2, 3] and Mehar and Panda [4]. e nonlinear vibrations of laminated composite spherical shell panels were entirely investigated by Mahapatra et al [5,6,7,8,9]. e vibration, bending, and buckling behaviors about the functionally graded sandwich structure have been investigated by Mehar et al [10,11,12,13] and Kar and Panda [14,15,16]
Singh et al [30] used the higher-order shear deformation plate theory to study the dynamic responses of a geometrically nonlinear laminated composite plate lying on different elastic foundations
Summary
In order to calculate the lift on the wing surface by using the vortex lattice method, the Biot–Savart law is used to calculate the induced velocity on the control point. E total velocity induced by a horseshoe vortex at a point (x, y, z) representing a surface element (i.e., the nth panel element) is the sum of the various components calculated by equations (6a)–(6c).
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