Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation

Guo, Xiang; Zhang, Wei; Yao, Minghui

doi:10.1007/s11431-010-0074-8

Cited by 22 publications

(4 citation statements)

References 29 publications

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“…For instance, in 2012, Amabili et al [22] performed numerous experiments and numerical simulations to examine the large-amplitude vibrations of plates with concentrated masses. Also, in 2010 and 2014, Zhang et al [23,24] carried out nonlinear dynamics analysis by deploying a rectangular cantilever plate and a simply supported thin rectangular plate, which were made of orthotropic and angle-ply composite laminates, respectively.…”

Section: Introductionmentioning

confidence: 99%

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

Liu

2023

Mathematics

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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 a5, a6, b6 and b8 can change the shape of the amplitude–frequency response curve and size of the plate, while different symbols a7 and b7 can change the rigidity of the model. The excitations greatly impact the nonlinear dynamic responses of the plate.

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Section: Introductionmentioning

confidence: 99%

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

Liu

2023

Mathematics

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“…Yeh [10] presents a novel analytical approach utilizing fractal dimension criteria and the maximum Lyapunov exponent to characterize the conditions, which can potentially lead to the chaotic motion of a simply supported thermo-mechanically coupled orthotropic rectangular plate undergoing large deflections. Guo et al [11] analyzed the nonlinear oscillations and chaotic dynamics of a four-edge simply supported angle-ply composite laminated rectangular thin plate subjected to the in-plane and transverse loads. The asymptotic perturbation method is used to derive the four averaged equations under 1:1 internal resonance.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations

Mousa

Sayed

Eldesoky

et al. 2014

Int. J. Dynam. Control

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The aim of this paper is to investigate the stability of a simply supported laminated composite piezoelectric rectangular plate under combined excitations. Analysis of the amplitude and phase modulation equations with the associated nonlinear interaction coefficients, as provided by the multiple scale analyses of various 1:1 internal resonance conditions and primary resonance case, where ω 2 ∼ = ω 1 and 3 ∼ = ω 1 is considered. The method of multiple time scale is applied to solve the non-linear differential equations describing the system up to the second-order approximation. All possible resonance cases at this approximation order are extracted. The stable/unstable periodic solutions are determined and are presented through frequency response plots. The analytical results are verified by comparing them with those of numerical integration of the modal equations. The influence of different parameters on the dynamic behavior of the composite laminated piezoelectric rectangular plate is studied. Variation of the some parameters leads to multivalued amplitudes and hence to jump phenomena. A comparison with the available published work is reported.

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“…The case of 1 : 1 internal resonance and primary parametric resonance is considered. Guo et al [3] studied the nonlinear dynamics of a four-edge simply supported angle-ply composite laminated rectangular thin plate excited by both the in-plane and transverse loads. The asymptotic perturbation method is used to derive the four averaged equations under 1 : 1 internal resonance.…”

Section: Introductionmentioning

confidence: 99%

Vibration, Stability, and Resonance of Angle-Ply Composite Laminated Rectangular Thin Plate under Multiexcitations

Sayed

Mousa

2013

Mathematical Problems in Engineering

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An analytical investigation of the nonlinear vibration of a symmetric cross-ply composite laminated piezoelectric rectangular plate under parametric and external excitations is presented. The method of multiple time scale perturbation is applied to solve the nonlinear differential equations describing the system up to and including the second-order approximation. All possible resonance cases are extracted at this approximation order. The case of 1 : 1 : 3 primary and internal resonance, whereΩ3≅ω1,ω2≅ω1, andω3≅3ω1, is considered. The stability of the system is investigated using both phase-plane method and frequency response curves. The influences of the cubic terms on nonlinear dynamic characteristics of the composite laminated piezoelectric rectangular plate are studied. The analytical results given by the method of multiple time scale is verified by comparison with results from numerical integration of the modal equations. Reliability of the obtained results is verified by comparison between the finite difference method (FDM) and Runge-Kutta method (RKM). It is quite clear that some of the simultaneous resonance cases are undesirable in the design of such system. Such cases should be avoided as working conditions for the system. Variation of the parametersμ1,μ2,α7,β8,ω1,ω2,f1,f2leads to multivalued amplitudes and hence to jump phenomena. Some recommendations regarding the different parameters of the system are reported. Comparison with the available published work is reported.

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Nonlinear dynamics of angle-ply composite laminated thin plate with third-order shear deformation

Cited by 22 publications

References 29 publications

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

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

Nonlinear stability analysis of a composite laminated piezoelectric rectangular plate with multi-parametric and external excitations

Vibration, Stability, and Resonance of Angle-Ply Composite Laminated Rectangular Thin Plate under Multiexcitations

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