This paper considers nonlinear aerodynamic loading on an elastic beam travelling in an air-filled tube along the axial direction to derive a wave equation for flexural motions of the beam. A study of this problem is motivated by an interest of fluid-structure interactions related to dynamics of magnetically levitated trains travelling in a long tunnel at high speed (a Mach number 0.4 or even higher). Because the trains have no mechanical supports but auxiliary guiding wheels, they are prone to destabilization by aerodynamic loading. Destabilization will give rise not only to vibrations of vehicles but also to wave propagation along the train, since trains are usually very long compared with their lateral dimension. Asymptotic analysis is carried out to derive a nonlinear wave equation for flexural motions of an elastic beam of circular cross-section travelling along the centre-axis of an air-filled, circular tube placed coaxially. Both the beam and tube are assumed to be long enough for end-effects to be ignored and the aerodynamic loading on the lateral surface of the beam is considered. Assuming a compressible inviscid fluid, the velocity potential of the air is sought systematically in the form of power series in terms of the ratios of the tube radius to a wavelength and of a typical deflection to the radius. Evaluating the pressure force acting on the lateral surface of the beam, the aerodynamic loading including the effects of finite deflection as well as of air's compressibility and axial curvature of the beam are obtained. Although the nonlinearity arises from the kinematical condition on the beam surface, it may be attributed to the presence of the tube wall. With the aerodynamic loading thus obtained, a nonlinear wave equation is derived, whereas linear theory is assumed for the flexural motions of the beam. Some discussions are given on the results.
Derivation of nonlinear wave equation for flexural motions of an elastic beam travelling an air-filled tube
Ableitung der nichtlinearen Wellengleichung für die Biegeschwingungen eines axial in einem Rohr bewegten elastischen Balkens
Journal of Fluids and Structures ; 16 , 5 ; 597-612
2002
16 Seiten, 3 Bilder, 8 Quellen
Article (Journal)
English
Aerodynamik , Balken , Biegeschwingung , Druckwelle , elastische Welle , Hochgeschwindigkeitszug , Krümmungsradius , Magnetschwebebahn , mathematisches Modell , nichtlineare Differenzialgleichung , Potenzial (Mathematik) , Potenzialströmung , Potenzreihe , Rohr , Schwingungsanregung , Seitenkraft , Transversalwelle , Tunnel , Wellenausbreitung , Wellengleichung
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