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A linear differential equation with a time-periodic damping coefficient: stability diagram and an application

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Abstract

In this paper the second-order differential equation with time-dependent damping coefficient

x + ∈ cos (2t) x + λx = 0,

will be studied. In particular the coexistence of periodic solutions corresponding with the vanishing of domains of instability is investigated. The coexistence of π-periodic solutions occurs for λ≈4n 2 where n is integer. This implies that the instability area which is emanating from λ=4n 2 in the λ−ε 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.

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Authors and Affiliations

  1. Department of Applied Mathematical Analysis, Faculty of Information Technology and Systems, Delft University of Technology, Mekelweg 4, 2628 CD, Delft, The Netherlands

    Hartono (Lecturer in Jurusan Matematika) & A.H.P. van der Burgh

  2. Universitas Negeri Yogyakarta, Indonesia

    Hartono (Lecturer in Jurusan Matematika)

Authors
  1. Hartono
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  2. A.H.P. van der Burgh
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on leave as a PhD reseacher at Delft University of Technology, The Netherlands

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Hartono, van der Burgh, A. A linear differential equation with a time-periodic damping coefficient: stability diagram and an application. Journal of Engineering Mathematics 49, 99–112 (2004). https://doi.org/10.1023/B:ENGI.0000017475.20596.cb

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  • DOI: https://doi.org/10.1023/B:ENGI.0000017475.20596.cb

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