Modal Characteristics Analysis on Rotating Flexible Beam Considering the Effect from Rotation
This paper deals with modal frequencies of rotating flexible beam. To investigate effects on the modal frequencies from rotation, the mathematical models are derived by using three descriptions on deformation: the conventional approach, the quadratic appr
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Abstract This paper deals with modal frequencies of rotating flexible beam. To investigate effects on the modal frequencies from rotation, the mathematical models are derived by using three descriptions on deformation: the conventional approach, the quadratic approach, and a synthetical approach. The theoretical solutions of modal frequencies based on the three methods are used to compare and draw some summaries.
Keywords Flexible beam Dynamic modeling Modal characteristics Rotation
1 Introduction Because of light weight, small inertia, high operating speed, and low energy consumption, flexible beam has many promising applications such as helicopter propellers, flexible robot, etc. However, flexible beam also has its shortages one of which is vibration. There are a lot of studies on modeling and vibration control of flexible manipulators [1]. So far, there are three classifications on description of elastic deformation for flexible beam during modeling. The common and most widely used method is the conventional linear deformation method [2]. In the past decades, some papers discussed the quadratic deformation approach, such as Abe investigation on trajectory planning based on dynamic model, which adopted the quadratic method to describe the elastic deformation of flexible beam [3]. In 2005, a synthetical method had been proposed to derive the dynamic model of flexible robots by Lee [4]. In 2011, the synthetical method was extended to two-link flexible manipulator by Yin H. Yin (&) W. Xu J. Xu F. Huang School of Mechanical and Electronic Engineering, Wuhan University of Technology, 122 Luoshi Road, Wuhan, Hubei, People’s Republic of China e-mail: [email protected]
J. J. (Jong Hyuk) Park et al. (eds.), Multimedia and Ubiquitous Engineering, Lecture Notes in Electrical Engineering 240, DOI: 10.1007/978-94-007-6738-6_84, Ó Springer Science+Business Media Dordrecht(Outside the USA) 2013
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et al. where the synthetical method was deemed to be a better approach for flexible manipulator at high speed than conventional method [5]. Above three approaches are used to derived dynamic model of a rotating flexible beam and solve the modal frequencies in consideration of the effect from rotation in this report. In recent years, some researchers have investigated the effects on modal characteristic from rotation of flexible beam. Mei proposed differential transform method (DTM) to analyze the modal shape functions of a centrifugally stiffened Timoshenko beam, where author concluded as the modal shape functions were affected by rotation [6]. Gunda addressed a rational interpolation functions to analyze rotating beam and concluded that the shape functions were not only functions of positions but also functions of rotational speed [7]. Additionally, Kaya et al. studied the modal frequencies of rotating cantilever Bernoulli–Euler beam by using DTM, where the modal frequencies increase with angular velocity [8]. However, these published modal analyses on rotating flexible beam would focus
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