scispace - formally typeset
Search or ask a question
Topic

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.


Papers
More filters
Journal ArticleDOI
TL;DR: This work considers applications to dynamic pitchfork bifurcation, pattern formation below the threshold of stability, and transient dynamics of stochastic PDEs near this deterministic bifurancations.
Abstract: For systems of partial differential equations (PDEs) with locally cubic nonlinearities, which are perturbed by additive noise, we describe the essential dynamics for small solutions. If the system is near a change of stability, then a natural separation of time-scales occurs and the amplitudes of the dominant modes are given on a long time-scale by a stochastic ordinary differential equation. We consider applications to dynamic pitchfork bifurcation, pattern formation below the threshold of stability, and transient dynamics of stochastic PDEs near this deterministic bifurcations.

23 citations

Journal ArticleDOI
TL;DR: In this article, the transverse vibrations of an axially accelerating Euler-Bernoulli beam resting on simple supports are investigated, and the effect of nonlinear terms on natural frequency is calculated for different parameters.
Abstract: The transverse vibrations of an axially accelerating Euler―Bernoulli beam resting on simple supports are investigated The supports are at the ends, and there is a support in between The axial velocity is a sinusoidal function of time varying about a constant mean speed Since the supports are immovable, the beam neutral axis is stretched during the motion, and hence, nonlinear terms are introduced to the equations of motion Approximate analytical solutions are obtained using the method of multiple scales Natural frequencies are obtained for different locations of the support other than end supports The effect of nonlinear terms on natural frequency is calculated for different parameters Principal parametric resonance occurs when the velocity fluctuation frequency is equal to approximately twice of natural frequency By performing stability analysis of solutions, approximate stable and unstable regions were identified Effects of axial velocity and location of intermediate support on the stability regions have been investigated

23 citations

Proceedings ArticleDOI
01 Jan 2011
TL;DR: In this paper, the authors developed a partial differential equation that governs the in-plane motion of a wind turbine blade subject to gravitational loading and which accommodates for aerodynamic loading using the extended Hamilton principle.
Abstract: The partial differential equation that governs the in-plane motion of a wind turbine blade subject to gravitational loading and which accommodates for aerodynamic loading is developed using the extended Hamilton principle. This partial differential equation includes nonlinear terms due to nonlinear curvature and nonlinear foreshortening, as well as parametric and direct excitation at the frequency of rotation. The equation is reduced using an assumed cantilevered beam mode to produce a single second-order ordinary differential equation (ODE) as an approximation for the case of constant rotation rate. Embedded in this ODE are terms of a nonlinear forced Mathieu equation. The forced Mathieu equation is analyzed for resonances by using the method of multiple scales. Superharmonic and subharmonic resonances occur. The effect of various parameters on the response of the system is demonstrated using the amplitude-frequency curve. A superharmonic resonance persists for the linear system as well.Copyright © 2011 by ASME

23 citations

Journal ArticleDOI
TL;DR: In this paper, an analytical model is presented for nonlinear vibration analysis of variable thickness, thin isotropic and functionally graded rectangular micro-plate containing a partial crack located within the centre line of the plate.

23 citations

Journal ArticleDOI
TL;DR: In this paper, the vibration of a dielectric elastomer balloon (DEB) using the method of multiple scales (MMS) was investigated, and the results showed that the MMS is in good agreement with the Runge-Kutta numerical method.
Abstract: Dielectric elastomers (DEs) are soft electromechanical devices, which operate under a high voltage. The majority of methods for calculating the nonlinear vibration of DEs are the numerical ones. However, the analytical methods may also be capable to achieve the reliable general and specific solutions for DEs. This paper investigates the vibration of a dielectric elastomer balloon (DEB) using the method of multiple scales (MMS). The equations of motion are derived by the method of Euler-Lagrange. Using the Taylor expansion , the governing equation of motion is transformed into a general form, then the MMS is applied to solve the problem. Two cases of voltage are considered; in the first one, the balloon is under a static voltage while in the second one the balloon is under a sinusoidal voltage . When the voltage is static, the time-history responses and the phase diagrams are depicted using the MMS and the Runge-Kutta numerical integration to verify the accuracy of the proposed method. For the sinusoidal voltage, the effect of jump phenomenon and variations of pressure and electrical potential difference (Voltage) on the frequency-response curves are studied. The results show that the MMS is in a good agreement with the Runge-Kutta numerical method. Moreover, with the presentation of various values of the pressure and the electrical potential difference, the softening behavior and the jump phenomenon are observed in the frequency response curves .

23 citations


Network Information
Related Topics (5)
Nonlinear system
208.1K papers, 4M citations
82% related
Boundary value problem
145.3K papers, 2.7M citations
80% related
Partial differential equation
70.8K papers, 1.6M citations
79% related
Reynolds number
68.4K papers, 1.6M citations
79% related
Differential equation
88K papers, 2M citations
78% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202320
202237
202150
202042
201972
201851