Journal of Thermal Stresses, 33: 79–96, 2010 Copyright © Taylor & Francis Group, LLC ISSN: 0149-5739 print/1521-074X online DOI: 10.1080/01495730903409235 FREE VIBRATION OF THERMALLY PRE/POST-BUCKLED CIRCULAR THIN PLATES EMBEDDED WITH SHAPE MEMORY ALLOY FIBERS Shi-Rong Li 12 , Wen-Shan Yu 2 , and R. C. Batra 3 1 School of Civil Science and Engineering, Yangzhou University, Yangzhou, Jiangsu, China 2 Department of Engineering Mechanics, Lanzhou University of Technology, Lanzhou, Gansu, China 3 Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA Axisymmetric deformations of a uniformly heated pre-buckled and post-buckled thin circular plate reinforced with shape memory alloy (SMA) fibers placed in the radial direction only are studied. Effects of von Kármán’s nonlinearities are incorporated in the problem formulation. The matrix is assumed to be linear thermoelastic and the thermo-mechanical response of the SMA is modeled by one-dimensional constitutive relation. By assuming that plate’s deflections can be additively decomposed into three parts, namely radial displacements of a pre-buckled plate, radial and lateral displacements during post-buckling deformations, and infinitesimal radial and lateral displacements during vibration of a post-buckled plate, boundary-value problems for determining these displacements for plate edges either simply supported or clamped have been formulated. The coupled nonlinear differential equations have been numerically solved by the shooting method that has been verified by good agreement between the presently computed results with those available in the literature. The dependence of the first three frequencies upon the temperature rise, for both pre-buckled and post- buckled plates, has been delineated. Characteristic curves relating the frequency with the temperature rise for different values of the volume fraction and the pre-strain in the SMA fibers are exhibited. It is found that reinforcement of an aluminum plate with SMA fibers changes plate’s natural frequencies and enhances its resistance to buckling due to temperature rise. Keywords: Circular plate; Natural frequencies; Pre-buckling and post-buckling; Shape memory alloy; Shooting method Received 8 January 2009; accepted 16 May 2009. SRLs and WSYs work was supported by the National Natural Science Foundation of China grant numbers 10872083 and 10602021, and the Fund of the Ministry of Education of China for Supervisors of Doctorate Students (200807310002). RCB’s work was partially funded by the U.S. Office of Naval Research grants N00014-06-1-0567 and N00014-06-1-0913 to Virginia Polytechnic Institute and State University. The authors gratefully acknowledge these financial supports. Views expressed in the paper are those of authors and neither of the funding agencies nor of their institutions. Address correspondence to Shi-Rong Li, School of Civil Science and Engineering, Yangzhou 79 University, Yangzhou, Jiangsu 225009, China. E-mail: list2000@yahoo.com.cn