Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

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.

Effects of Unbalanced Lamination Parameters on the Static Aeroelasticity of a High Aspect Ratio Wing

“…Using the Euler description method, the differential form of three-dimensional conservation N-S equation in Cartesian coordinate system is as follows [30][31][32][33]:…”

“…By introducing the theory of high-order shear deformation plates, the shear correction factor was successfully eliminated and the accuracy of transverse shear stress was improved. Liu et al's [30] laminated plate is studied in the nonlinear response of a subsonic condition, using the Hamilton's principle, the composite laminated plate is established in subsonic aerodynamic force motion control of nonlinear partial differential equation, and the frequency response curve under different parameters is obtained; thus, the exciting force and laminated plate structure provide reference for the coupling problem.…”

Piezoelectric Performance of a Symmetrical Ring-Shaped Piezoelectric Energy Harvester Using PZT-5H under a Temperature Gradient

“…Combining Equations ( 5)~( 12), the electric field distribution e 3 can be obtained, and its equation is shown in Equation (13).…”

“…Researchers have proposed various structures to improve the piezoelectric efficiency of piezoelectric energy harvesters. The cantilever has a low resonance frequency and is easy to integrate with a microelectromechanical system (MEMS), and therefore it is a focus issue in the energy harvester field [ 13 , 14 ]. Z.J.…”

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

“…6,7 It should be mentioned that due to limitation in production of FG nanocomposites with continuously varying volume fraction of nanofillers in the thickness direction, the layer-wise approach is suggested. 6,7 The high performance rotating blades have different applications in modern technologies; [8][9][10][11][12][13][14][15][16] for example, they are used as helicopter blades, airplane propellers, wind turbines, and industrial fans. 17 One way to increase the performance of various rotating structures is to add a concentrated mass into them.…”