Showing papers on "Multiple-scale analysis published in 1984"
TL;DR: In this article, the amplitude of the primary is replaced by an effective amplitude that depends on the amplitudes and relative phases of the two components of the excitation, and the expression for the effective amplitude is used to determine the amplitude and phase of a superharmonic excitation of order two or three needed to quench the primary response.
33 citations
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
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 article, a pair of semi-linear partial differential equations governing the slow variation in the fundamental and the third harmonic amplitudes of a quasi-monochromatic finite-amplitude Bleustein-Gulyaev (BG) wave on a crystal belonging to either the 6 mm or the 4 mm symmetry class is derived by using an extension of the method of multiple scales.
13 citations
TL;DR: In this article, the flexural vibration of a simply supported beam along with a body with a pendulum moving slowly at constant velocity is investigated. And an approximate expression for the deflection of the beam is obtained in the nonresonant case and the maximum deflection is estimated in the internal resonant case.
Abstract: This report deals with flexural vibration of a simply supported beam, along which a body with a pendulum moves slowly at constant velocity The governing equations of the whole system, which are simultaneous nonlinear ordinary differential equations with slowly varying coefficients, are asymtotically solved by using the method of multiple scales As the main result, an approximate expression for the deflection of the beam is obtained in the nonresonant case and the maximum deflection is estimated in the internal resonant case Furthermore the predicted deflections of the beam are confirmed experimentally
2 citations
TL;DR: In this paper, a method of multiple scales is employed to derive a solution for high frequency range and for finite values of the amplitude parameter, which agrees fairly well with the available numerical results in the limit of zero frequency.
1 citations
14 May 1984
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.
Abstract: The interaction of fundamental parametric resonances with subharmonic resonances of order one-half in a single-degree-of-freedom system with quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to derive two first-order ordinary differential equations that describe the modulation of the amplitude and the phase of the response with the non-linearity and both resonances. These equations are used to determine the steady state solutions and their stability. Conditions are derived for the quenching or enhancement of a parametric resonance by the addition of a subharmonic resonance of order one-half. The degree of quenching or enhancement depends on the relative amplitudes and phases of the excitations. The analytical results are verified by numerically integrating the original governing differential equation.