A linear differential equation with a time-periodic damping coefficient: stability diagram and an application |
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Authors: | Hartono A.H.P. van der Burgh |
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Affiliation: | (1) Department of Applied Mathematical Analysis, Faculty of Information Technology and Systems, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;(2) Universitas Negeri Yogyakarta, Indonesia |
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Abstract: | In this paper the second-order differential equation with time-dependent damping coefficientx + cos (2t) x + x = 0,will be studied. In particular the coexistence of periodic solutions corresponding with the vanishing of domains of instability is investigated. The coexistence of -periodic solutions occurs for ![lambda](/content/u35780j724645621/xxlarge955.gif) 4n2 where n is integer. This implies that the instability area which is emanating from =4n2 in the – stability diagram disappears. In applications, this equation can be considered as a model equation for the study of rain-wind-induced vibrations of a special oscillator.on leave as a PhD reseacher at Delft University of Technology, The Netherlands |
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Keywords: | coexistence rain-wind-induced vibrations stability diagram time-periodic damping coefficient |
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