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.
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TL;DR: In this article, a passage through resonance in a catenary-vertical cable system with periodic external excitation is analyzed, and a simplified model of the system with proportional damping is proposed by using a combined perturbation and numerical technique.
46 citations
TL;DR: In this article, the effect of large amplitude on the dissipative nature as well as on the natural frequency of viscoelastic laminated plates is investigated. But the authors focus on the nonlinear and hereditary type governing equations.
45 citations
TL;DR: In this article, the Hamilton's principle was used to discretize the partial differential governing equation to a two-degree-of-freedom nonlinear system under combined parametric and external excitations.
45 citations
TL;DR: In this paper, a partial-differential equation governing the transverse vibration of an axially moving beam is derived from the Newton's second law, under the assumption that the tension of beam can be replaced by the averaged tension over the beam.
45 citations
TL;DR: In this paper, a forced Mathieu equation with cubic nonlinearity was used to model the response of a wind turbine blade in steady rotation to cyclic transverse loading due to wind shear, tower shadowing and gravity, and cyclic gravitational axial loading at the same fundamental frequency.
Abstract: A horizontal axis wind turbine blade in steady rotation endures cyclic transverse loading due to wind shear, tower shadowing and gravity, and a cyclic gravitational axial loading at the same fundamental frequency. These direct and parametric excitations motivate the consideration of a forced Mathieu equation with cubic nonlinearity to model its dynamic behavior. This 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. Order-two superharmonic resonance persists for the linear system. While the order-two subharmonic response level is dependent on the ratio of parametric excitation and damping, nonlinearity is essential for the order-two subharmonic resonance. Order-three resonances are present in the system as well and they are similar to those of the Duffing equation.
45 citations