Nonlinear vibrations and internal resonance of pretwisted rotating cantilever rectangular plate with varying cross-section and aerodynamic force

2020 ◽  
Vol 225 ◽  
pp. 111259
Author(s):  
Y.F. Zhang ◽  
Y. Niu ◽  
W. Zhang
Keyword(s):  
Rectangular Plate ◽  
Cross Section ◽  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Aerodynamic Force ◽  
Cantilever Rectangular Plate

Nonlinear Vibrations in a 2-Dimensional Protein Cluster Model with Linear Bonds

2000 ◽  
Vol 214 (1) ◽  
Author(s):  
E.G. Shidlovskaya ◽  
L. Schimansky-Geier ◽  
Yu.M. Romanovsky
Keyword(s):  
Active Site ◽  
Internal Resonance ◽  
Cluster Model ◽  
Active Sites ◽  
Nonlinear Vibrations ◽  
Nonlinear Phenomena ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Two Dimensional Model

A two dimensional model for the substrate inside a pocket of an active site of an enzyme is presented and investigated as a vibrational system. The parameters of the system are evaluated for α-chymotrypsin. In the case of internal resonance it is analytically and numerically shown that the energy concentrated on a certain degree of freedom might be several times larger than in the non-resonant case. Additionally, the system is driven by harmonic excitations and again energy due to nonlinear phenomena is redistributed inhomogeneously. These results may be of importance for the determination of the rates of catalytic events of substrates bound in pockets of active sites.

Internal Resonance and Nonlinear Vibrations of Eccentric Rotating Composite Laminated Circular Cylindrical Shell

2019 ◽  
Author(s):  
Tao Liu ◽  
Wei Zhang ◽  
Yan Zheng ◽  
Yufei Zhang
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Shear Deformation Theory ◽  
Internal Resonances

Abstract This paper is focused on the internal resonances and nonlinear vibrations of an eccentric rotating composite laminated circular cylindrical shell subjected to the lateral excitation and the parametric excitation. Based on Love thin shear deformation theory, the nonlinear partial differential equations of motion for the eccentric rotating composite laminated circular cylindrical shell are established by Hamilton’s principle, which are derived into a set of coupled nonlinear ordinary differential equations by the Galerkin discretization. The excitation conditions of the internal resonance is found through the Campbell diagram, and the effects of eccentricity ratio and geometric papameters on the internal resonance of the eccentric rotating system are studied. Then, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equations in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. Finally, we study the nonlinear vibrations of the eccentric rotating composite laminated circular cylindrical shell systems.

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