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Multiple-scale analysis

About: Multiple-scale analysis is a research topic. Over the lifetime, 1360 publications have been published within this topic receiving 27530 citations.


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TL;DR: In this article, the authors used an extended Melnikov method in the resonant case to investigate the Shilnikov type multi-pulse homoclinic bifurcations and chaotic dynamics of the high-dimensional nonlinear system for a laminated composite piezoelectric rectangular plate.
Abstract: This paper investigates the multi-pulse global bifurcations and chaotic dynamics of the high-dimension nonlinear system for a laminated composite piezoelectric rectangular plate by using an extended Melnikov method in the resonant case. Using the von Karman type equations, Reddy’s third-order shear deformation plate theory and Hamilton’s principle, the equations of motion are derived for the laminated composite piezoelectric rectangular plate with combined parametric excitations and transverse excitation. Applying the method of multiple scales and Galerkin’s approach to the partial differential governing equation, the four-dimensional averaged equation is obtained for the case of 1:2 internal resonance and primary parametric resonance. From the averaged equations obtained, the theory of normal form is used to derive the explicit expressions of normal form with a double zero and a pair of pure imaginary eigenvalues. Based on the explicit expressions of normal form, the extended Melnikov method is used for the first time to investigate the Shilnikov type multi-pulse homoclinic bifurcations and chaotic dynamics of the laminated composite piezoelectric rectangular plate. The necessary conditions of the existence for the Shilnikov type multi-pulse chaotic dynamics of the laminated composite piezoelectric rectangular plate are analytically obtained. Numerical simulations also illustrate that the Shilnikov type multi-pulse chaotic motions can also occur in the laminated composite piezoelectric rectangular plate. Overall, both theoretical and numerical studies demonstrate that the chaos in the Smale horseshoe sense exists for the laminated composite piezoelectric rectangular plate.

22 citations

Journal ArticleDOI
TL;DR: In this paper, the stability of a rotor system, which is comprised of a simply supported nonlinear spinning shaft with multi-rigid disk, near to the major critical speeds is investigated.
Abstract: In this study the stability of a rotor system, which is comprised of a simply supported nonlinear spinning shaft with multi-rigid disk, near to the major critical speeds is investigated. The nonlinearity is due to the stretching and large amplitude. The influence of rotary inertia and gyroscopic effects are included, however, shear deformation is ignored. To analyze the nonlinear equations of motion, the method of multiple scales is applied to the ordinary differential equations of motion. The influences of different parameter such as number of disks, disk mass moment of inertia, rotational speed, external damping, and position of disks on the forward and backward linear frequencies, steady state response, stability and bifurcations of the rotor system are investigated. It is seen that in the higher rotational speeds, the backward frequency is increasing with an increase of number of disks, and in the lower rotational speeds, the backward frequency is decreasing with an increase of number of disks. By increasing number of disks, bifurcations occur in the lower speeds therefore, the instability occurrence for large number of disk is at speeds lower than that regarding to the low number of disks. By an increase of disk mass moment of inertia, the amplitude and the hardening effect decrease.

21 citations

Journal ArticleDOI
TL;DR: In this paper, a viscoelastic beam obeying a fractional differentiation constitutive law is considered and the governing equation is derived from the visco-elastic material model.
Abstract: This paper deals with a viscoelastic beam obeying a fractional differentiation constitutive law. The governing equation is derived from the viscoelastic material model. The equation of motion is solved by using the method of multiple scales. Additionally, principal parametric resonances are investigated in detail. The stability boundaries are also analytically determined from the solvability condition. It is concluded that the order and the coefficient of the fractional derivative have significant effect on the natural frequency and the amplitude of vibrations.

21 citations

Journal ArticleDOI
A. H. Nayfeh1
TL;DR: In this article, an investigation of the interaction of primary resonances and combination resonances of the additive and difference types in single-degree-of-freedom systems with quadratic and cubic nonlinearities is presented.

21 citations

Journal ArticleDOI
TL;DR: In this article, the forced vibration of functionally graded (FG) Timoshenko microbeams under thermal effects and parametric excitation is studied using von Karman nonlinear theory, Hamilton's principle and the modified couple stress theory.

21 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202320
202237
202150
202042
201972
201851