Stability of Axially Moving Materials

Abstract

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Membrane flutter induced by radiation of surface gravity waves on a uniform flow

“…Recent works on membrane flutter are motivated by such diverse applications as stability of membrane roofs in civil engineering (Sygulski 2007), flutter of travelling paper webs (Banichuk et al 2010(Banichuk et al , 2019, aerodynamics of sails and membrane wings of natural flyers (Newman & Paidoussis 1991;Tiomkin & Raveh 2017), as well as the design of piezoaeroelastic systems for energy harvesting (Mavroyiakoumou & Alben 2020).…”

Free vibrations of axially moving strings: Energy estimates and boundary observability

“…Theorem 1. Under the Assumptions ( 1) and ( 5), the solution of problem (WP) is given by the series (3) where the coefficients c n ∈ C are given by any of the two following formulas:…”

“…and use (23) for the first 40 frequencies, that is, |n| ≤ 40 in the series sum (3). See Figures 4 and 5.…”

“…(1) If v ≥ 1, then the problem is ill-posed; see, for instance, Ram and Caldwell [1]. The wave equation formulated above is a simple model to represent several mechanical systems such as plastic films, magnetic tapes, elevator cables, textile and fiber winding; see, for example, previous works [2][3][4]. This model can be dated back to Skutch [5], its simplicity is only apparent, and we should mention that the method of separation of variables cannot be applied to this problem.…”

Closed form solution in buckling optimization problem of twisted rod

“…Generally speaking, for non-conservative problems the dynamic approach for stability investigation must be applied (Kim, Choi, 2011), (Kirillov, 2013) (Banichuk et al, 2020). However, Euler's static approach is proved to be valid for the considered boundary value problem with conditions of fixed axes of rotation, Cases 1 and 2 (Ziegler, 1977, §5.4, Table 5.1, Section 1.2, page 127).…”