Nonlinear Oscillations of a Composite Stepped Piezoelectric Cantilever Plate with Aerodynamic Force and External Excitation

Yan Liu () and Wensai Ma ()
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Yan Liu: School of Physics and Astronomy, China West Normal University, Nanchong 637002, China
Wensai Ma: Department of Mechanics, Inner Mongolia University of Technology, Hohhot 010051, China

Mathematics, 2023, vol. 11, issue 13, 1-30

Abstract: Axially moving wing aircraft can better adapt to the flight environment, improve flight performance, reduce flight resistance, and improve flight distance. This paper simplifies the fully unfolded axially moving wing into a stepped cantilever plate model, analyzes the structural nonlinearity of the system, and studies the influence of aerodynamic nonlinearity on system vibration. The model is affected by aerodynamic forces, piezoelectric excitation, and in-plane excitation. Due to Hamilton’s principle of least action, the mathematical model is established based on Reddy’s higher-order shear deformation theory, and using Galerkin’s method, the governing dimensionless partial differential equations of the system are simplified to two nonlinear ordinary differential equations, and then a study of the influence of the various engineering parameters on the nonlinear oscillations and frequency responses of this model is conducted by the method of multiple scales. It was found that the different values of a 5 , a 6 , b 6 and b 8 can change the shape of the amplitude–frequency response curve and size of the plate, while different symbols a 7 and b 7 can change the rigidity of the model. The excitations greatly impact the nonlinear dynamic responses of the plate.

Keywords: axially moving wings; stepped cantilever plate; piezoelectric composite material; nonlinear vibration; frequency responses; bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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