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Nonlinear vibrations and internal resonance of pretwisted rotating cantilever rectangular plate with varying cross-section and aerodynamic force
https://orcid.org/0000-0003-1971-7530
Highlights Nonlinear dynamics and internal resonance are studied for pretwisted rotating plate. Governing equations of motion are established for pretwisted rotating cantilever plate. Method of multiple scales is applied to obtain averaged equations. Pretwisted rotating blade exhibits hardening and softening nonlinear behaviors. Periodic, quasi-periodic and chaotic vibrations exist.
Abstract This paper investigates the complex nonlinear vibrations and internal resonance of the rotating blade subjected to the aerodynamic force, which is simplified to a pretwisted rotating cantilever rectangular plate with the varying cross-section and varying rotating speed. Considering the effects of the cross-section warping, pretwisted and presetting angles, the nonlinear partial differential governing equations of motion are established based on the third-order shear deformation theory, von Karman large deformation theory and Hamilton principle. Two-degree-of-freedom nonlinear ordinary differential equations of motion are obtained by using Galerkin method. The method of multiple scales is applied to obtain the averaged equations under the case of the primary parametric resonance-1/2 subharmonic resonance and 1:2 internal resonance. Numerical simulations are performed to portray the amplitude-frequency response and amplitude-force response curves, bifurcations and chaotic dynamics of the pretwisted rotating cantilever rectangular plate by discussing the influences of the aerodynamic force and rotating speed perturbation. The bifurcation diagrams, maximum Lyapunov exponents, phase portraits, waveforms and Poincare maps are utilized to illustrate the complex nonlinear vibrations of the pretwisted rotating cantilever rectangular plate.
Nonlinear vibrations and internal resonance of pretwisted rotating cantilever rectangular plate with varying cross-section and aerodynamic force
https://orcid.org/0000-0003-1971-7530
Highlights Nonlinear dynamics and internal resonance are studied for pretwisted rotating plate. Governing equations of motion are established for pretwisted rotating cantilever plate. Method of multiple scales is applied to obtain averaged equations. Pretwisted rotating blade exhibits hardening and softening nonlinear behaviors. Periodic, quasi-periodic and chaotic vibrations exist.
Abstract This paper investigates the complex nonlinear vibrations and internal resonance of the rotating blade subjected to the aerodynamic force, which is simplified to a pretwisted rotating cantilever rectangular plate with the varying cross-section and varying rotating speed. Considering the effects of the cross-section warping, pretwisted and presetting angles, the nonlinear partial differential governing equations of motion are established based on the third-order shear deformation theory, von Karman large deformation theory and Hamilton principle. Two-degree-of-freedom nonlinear ordinary differential equations of motion are obtained by using Galerkin method. The method of multiple scales is applied to obtain the averaged equations under the case of the primary parametric resonance-1/2 subharmonic resonance and 1:2 internal resonance. Numerical simulations are performed to portray the amplitude-frequency response and amplitude-force response curves, bifurcations and chaotic dynamics of the pretwisted rotating cantilever rectangular plate by discussing the influences of the aerodynamic force and rotating speed perturbation. The bifurcation diagrams, maximum Lyapunov exponents, phase portraits, waveforms and Poincare maps are utilized to illustrate the complex nonlinear vibrations of the pretwisted rotating cantilever rectangular plate.
Nonlinear vibrations and internal resonance of pretwisted rotating cantilever rectangular plate with varying cross-section and aerodynamic force
https://orcid.org/0000-0003-1971-7530
Highlights Nonlinear dynamics and internal resonance are studied for pretwisted rotating plate. Governing equations of motion are established for pretwisted rotating cantilever plate. Method of multiple scales is applied to obtain averaged equations. Pretwisted rotating blade exhibits hardening and softening nonlinear behaviors. Periodic, quasi-periodic and chaotic vibrations exist.
Abstract This paper investigates the complex nonlinear vibrations and internal resonance of the rotating blade subjected to the aerodynamic force, which is simplified to a pretwisted rotating cantilever rectangular plate with the varying cross-section and varying rotating speed. Considering the effects of the cross-section warping, pretwisted and presetting angles, the nonlinear partial differential governing equations of motion are established based on the third-order shear deformation theory, von Karman large deformation theory and Hamilton principle. Two-degree-of-freedom nonlinear ordinary differential equations of motion are obtained by using Galerkin method. The method of multiple scales is applied to obtain the averaged equations under the case of the primary parametric resonance-1/2 subharmonic resonance and 1:2 internal resonance. Numerical simulations are performed to portray the amplitude-frequency response and amplitude-force response curves, bifurcations and chaotic dynamics of the pretwisted rotating cantilever rectangular plate by discussing the influences of the aerodynamic force and rotating speed perturbation. The bifurcation diagrams, maximum Lyapunov exponents, phase portraits, waveforms and Poincare maps are utilized to illustrate the complex nonlinear vibrations of the pretwisted rotating cantilever rectangular plate.
Nonlinear vibrations and internal resonance of pretwisted rotating cantilever rectangular plate with varying cross-section and aerodynamic force
Zhang, Y.F. (author) / Niu, Y. (author) / Zhang, W. (author)
Engineering Structures ; 225
2020-08-22
Article (Journal)
Electronic Resource
English
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