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 published on a yearly basis
Papers
More filters
TL;DR: In this article, the nonlinear harmonic response of a cantilever hard-coating plate which is made of a layer of anisotropic hardcoating material and isotropic metal substrate is investigated based on the theory of high-order shear deformation of plate.
Abstract: The nonlinear harmonic response of a cantilever hard-coating plate which is made of a layer of anisotropic hard-coating material and isotropic metal substrate is investigated based on the theory of high-order shear deformation of plate. Firstly, based on the theories of von Karman and Reddy’s three-order shear deformation, the nonlinear dynamic equations of hard-coating plate are built by Hamilton variation principle. Secondly, to obtain nonlinear governing equation of hard-coating plate under transverse load, these equations are discretized in Galerkin method. The system averaged equations with 1:3 internal resonances are obtained by the method of multiple scales, and the multi-periodic responses behavior of cantilever hard-coating plate under transverse loading could be presented. Finally, the vibration response experiment of hard-coating plate is conducted, and the multi-periodic responses are also present for the hard-coating plate with three-to-one internal resonance. Besides, through the vibration response experiment of uncoated titanium alloy plate, the damping characteristic of hard coating is further analyzed.
20 citations
TL;DR: In this paper, the influence of high asymmetries in the variation of in-plane lead-lag stiffness of one blade on the ground resonance phenomenon in helicopters is analyzed by using Floquet's theory and the boundaries of instabilities predicted.
20 citations
TL;DR: In this paper, a rotor active magnetic bearing (AMB) system subjected to a periodically time-varying stiffness with quadratic and cubic nonlinearities under multi-parametric excitations is studied and solved.
20 citations
TL;DR: In this paper, conditions for the quenching or enhancement of a parametric resonance by the addition of a subharmonic resonance of order one-half were derived for a single-degree-of-freedom system with quadratic and cubic nonlinearities.
20 citations
TL;DR: In this paper, the free nonlinear vibration behavior of a cracked cantilever beam is investigated both theoretically and experimentally, and it is shown that the correction term that is added to the main part of the response reflects the effect of breathing crack on the vibration response.
Abstract: In this paper the free nonlinear vibration behavior of a cracked cantilever beam is investigated both theoretically and experimentally. For simplicity, the dynamic behavior of a cracked beam vibrating at its first mode is simulated using a simple single degree of freedom lumped parameter system. The time varying stiffness is modeled using a harmonic function. The governing equation of motion is solved by a perturbation method - the method of Multiple Scales. Results show that the correction term that is added to the main part of the response reflects the effect of breathing crack on the vibration response. Moreover, this part of response consists of the superharmonic components of the spectrum which is due to the system's intrinsic nonlinearity. Using this method an analytical relation is established between the system characteristics and the crack parameters in one hand and the nonlinear characteristics of system response on the other hand. Results have been validated by the experimental tests and a numerical method.
20 citations