contributor author | Ramakrishnan, Venkatanarayanan | |
contributor author | Feeny, Brian F. | |
date accessioned | 2023-08-16T18:12:49Z | |
date available | 2023-08-16T18:12:49Z | |
date copyright | 3/2/2023 12:00:00 AM | |
date issued | 2023 | |
identifier issn | 1048-9002 | |
identifier other | vib_145_3_031011.pdf | |
identifier uri | http://yetl.yabesh.ir/yetl1/handle/yetl/4291633 | |
description abstract | The present study deals with the response of a damped Mathieu equation with hard constant external loading. A second-order perturbation analysis using the method of multiple scales (MMS) unfolds resonances and stability. Non-resonant and low-frequency quasi-static responses are examined. Under constant loading, primary resonances are captured with a first-order analysis, but are accurately described with the second-order analysis. The response magnitude is of order ϵ0, where ϵ is the small bookkeeping parameter, but can become arbitrarily large due to a small denominator as the Mathieu system approaches the primary instability wedge. A superharmonic resonance of order two is unfolded with the second-order MMS. The magnitude of this response is of order ϵ and grows with the strength of parametric excitation squared. An nth-order multiple scales analysis under hard constant loading will indicate conditions of superharmonic resonances of order n. Subharmonic resonances do not produce a non-zero steady-state harmonic, but have the instability property known to the regular Mathieu equation. Analytical expressions for predicting the magnitude of responses are presented and compared with numerical results for a specific set of system parameters. In all cases, the second-order analysis accommodates slow time-scale effects, which enable responses of order ϵ or ϵ0. The behavior of this system could be relevant to applications such as large wind-turbine blades and parametric amplifiers. | |
publisher | The American Society of Mechanical Engineers (ASME) | |
title | Responses of a Strongly Forced Mathieu Equation—Part 2: Constant Loading | |
type | Journal Paper | |
journal volume | 145 | |
journal issue | 3 | |
journal title | Journal of Vibration and Acoustics | |
identifier doi | 10.1115/1.4056907 | |
journal fristpage | 31011-1 | |
journal lastpage | 31011-9 | |
page | 9 | |
tree | Journal of Vibration and Acoustics:;2023:;volume( 145 ):;issue: 003 | |
contenttype | Fulltext | |