Journal of the Chinese Institute of Engineers, Vol. 31, No. 2, pp. 279-290 (2008) 279 TIME-DOMAIN ROTATIONAL ANGLE IDENTIFICATION OF A BEAM STRUCTURE UTILIZING THE DYNAMIC TRANSVERSE DEFLECTION SIGNAL Syh-Tsang Jenq*, Chih-Hang Chao, Yih-Nen Jeng and En-Cheng Liu ABSTRACT The real time signal identification of rotation angle for a beam structure is stud- ied in this work. A laser displacement sensor traced transverse displacement signal was used to identify the rotation angle of a beam. An orthogonal polynomial ap- proach was used to expand the transverse displacement signal into orthogonal func- tions and their associated coefficients. These coefficients were used to identify the orthogonally expanded coefficients associated with the rotation angles of the beam structure. The rotation angle response of the beam can finally be synthesized and checked against the finite element code predicted result. We also conducted impact hammer tests on the root of a metallic cantilever beam. Both the loading history and the transverse displacement history at a specific location on the beam specimen were recorded. Similar to the numerical synthesis process, the test determined a displace- ment signal can also be used to identify the rotation angle of the beam. Through numerical and experimental verification, the currently proposed analysis seems to be able to identify the dynamic rotation angle response of the beam structure closely, when the prescribed transverse displacement input signal of the beam is given. Key Words: rotation angle identification, structure health monitoring, beam, real time signals. *Corresponding author. (Tel: 886-6-2757575 ext. 63665; Fax: 886-6-2083641; Email: stjenq@mail.ncku.edu.tw) The authors are with Department of Aeronautics & Astronautics, National Cheng Kung University, Tainan, 70101, Taiwan, R.O.C. and C. H. Chao is currently at Foxconn Technology Group, Taipei, Taiwan, R.O.C. I. BACKGROUND AND BRIEF DESCRIPTIONS OF THE PRESENT STUDY This work is concerned with the development of a real-time rotation angle identification technique for a simple beam structure based on a sensor detected dynamic transverse displacement signal. The identi- fied rotation angle and the traced transverse displace- ments signal can be used to evaluate the health of the beam structure studied if an appropriate damage pre- diction analysis is performed (Jenq et al., 2002; Chao et al ., 2004; Hanagud and Luo, 1997). The currently reported identification method enables us to find the rotation angle response of a beam using the measured transverse signal only. We can also use the measured rotation angle to determine the dynamic transverse displacement of the beam. It seems that the method under examination could reduce costs when we per- form structural monitoring. The present problem is both numerically and ex- perimentally studied in order to report on the adequacy and accuracy of the method proposed. Based on the theory of structural analysis, we can use a substructuring process to model a structure as an assemblage of fi- nite elements, such as beam and shear panel elements. This method can yield smaller substructural stiffness matrices involving only the degree of freedom related to boundaries, and this reduces the total solution cost for structures. When we work on analyzing a large structure or doing detailed modeling of a relatively small structure, it is convenient to group various types of finite elements together and handle these groups as separate substructures. Although the present problem is concerned with a simple beam structure only, it