JOURNAL OF SOUND AND VIBRATION Journal of Sound and Vibration 297 (2006) 880–894 Modal analysis of cantilever plates undergoing accelerated in-plane motion Hong Seok Lim, Hong Hee Yoo à School of Mechanical Engineering, Hanyang University, 17 Haengdang-Dong Sungdong-Gu, Seoul 133-791, South Korea Received 20 July 2005; received in revised form 19 April 2006; accepted 2 May 2006 Available online 30 June 2006 Abstract A modeling method for the modal analysis of cantilever plates undergoing accelerated in-plane motion is presented in this paper. Von Karman strain measures are employed to derive the in-plane and the lateral equations of motion. In-plane strain measures of the accelerated plates are obtained from the in-plane equations and substituted into the lateral equations to obtain the linear equations for modal analysis. The resulting equations are transformed into dimensionless forms in which dimensionless parameters are identified. The effects of dimensionless parameter variations on the modal characteristics of the accelerated plates are investigated through numerical studies. r 2006 Elsevier Ltd. All rights reserved. 1. Introduction Flexible cantilever plate-like structures undergoing translational rigid body motion can be found in practical engineering examples such as aircraft wings and rocket fins. For the design of these structures, their modal characteristics are frequently obtained under the assumptions that the structures are stationary. Even if the structures undergo translational motions with constant velocity, their modal characteristics remain the same as those of the stationary structures. However, the structures often undergo accelerated motions that could result in significant variations of their modal characteristics. For instance, when an aircraft or a rocket takes off, their wings or fins undergo accelerated motion. Such an accelerated motion induces in-plane strains (due to inertia force) for the plate-like structures that effectively cause the variations of their modal characteristics. Since the take-off stage is critically important for the successful flight of the aircraft or the rocket, the modal characteristics of the plate-like structures (such as wings and fins) undergoing accelerated in- plane motions need to be estimated accurately and efficiently. The modal characteristics of plates were previously studied by many researchers (see, for instance, Ref. [1]). The in-plane motion has also been studied by 3D analysis (see, for instance, Refs. [2–4]). However, study on the modal characteristics of a flexible structure undergoing rigid body motion originates from the famous paper written by Southwell and Gough [5]. Basing on this pioneering study, many researchers provided early analytical grounds on the subject (see, for instance, Refs. [6,7]). Since ARTICLE IN PRESS www.elsevier.com/locate/jsvi 0022-460X/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsv.2006.05.004 à Corresponding author. Tel.: +82 2 2220 0446; fax: +82 2 2293 5070. E-mail addresses: beyondlimits@hanmail.net (H.S. Lim), hhyoo@hanyang.ac.kr (H.H. Yoo).