{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T05:09:11Z","timestamp":1773464951643,"version":"3.50.1"},"reference-count":32,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2011,6]]},"abstract":"<jats:p> An analysis on the nonlinear forced vibration of thermally loaded FGM plate with two simply supported opposite and two free edges subjected to the in-plane and transversal excitations is presented. The material properties of the FGM plates are assumed to be temperature dependent and change continuously throughout the thickness of the plate, according to the volume fraction of the constituent materials based on the power law function. The temperature is assumed to be constant in the plane and varied only in the thickness direction of the plate. The plate is modeled by using the Von Karman hypothesis and the equations of motion are obtained by using an energy approach. It is our aim to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the FGM rectangular plates with two simply supported opposite and two free edges. The equations of motion can be reduced into a two-degree-of-freedom nonlinear system of transverse motion under combined thermal and external excitations by using the Galerkin's method. By the numerical method, the nonlinear dynamical equations are analyzed to find the nonlinear responses of the FGM plate with two simply supported opposite and two free edges. Under certain conditions the periodic motions and the chaotic motions of the FGM plate are found. The bifurcation diagram demonstrates that for a certain geometric and material properties the chaotic responses of the plate exist as the transverse excitation changes. Moreover, numerical simulations also illustrate that the deflections of the nonlinear dynamic of the FGM rectangular plate are larger than that of the periodic motions. <\/jats:p>","DOI":"10.1142\/s0218127411029409","type":"journal-article","created":{"date-parts":[[2011,3,31]],"date-time":"2011-03-31T06:20:32Z","timestamp":1301552432000},"page":"1737-1753","source":"Crossref","is-referenced-by-count":9,"title":["PERIODIC AND CHAOTIC MOTIONS OF FGM THIN PLATE WITH TWO SIMPLY SUPPORTED OPPOSITE AND TWO FREE EDGES"],"prefix":"10.1142","volume":"21","author":[{"given":"Y. X.","family":"HAO","sequence":"first","affiliation":[{"name":"College of Mechanical Engineering, Beijing Information Science and Technology University, Beijing 100192, P. R. China"}]},{"given":"W.","family":"ZHANG","sequence":"additional","affiliation":[{"name":"College of Mechanical Engineering, Beijing University of Technology, Beijing 100042, P. R. China"}]},{"given":"J.","family":"YANG","sequence":"additional","affiliation":[{"name":"School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, P. O. Box 71, Bundoora, VIC 3083, Australia"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijsolstr.2005.05.025"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7683(94)00267-Z"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1993.1133"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.compstruct.2004.03.022"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.1999.2525"},{"key":"rf6","first-page":"41","volume":"18","author":"Chi S. H.","journal-title":"J. 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