{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:27Z","timestamp":1740134547988,"version":"3.37.3"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11172125","20133218110025"],"award-info":[{"award-number":["11172125","20133218110025"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Research Foundation for the Doctoral Program of Higher Education of China","award":["11172125","20133218110025"],"award-info":[{"award-number":["11172125","20133218110025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Stability and bifurcation behaviors for a model of simply supported functionally graded materials rectangular plate subjected to the transversal and in-plane excitations are studied by means of combination of analytical and numerical methods. The resonant case considered here is 1\u2009:\u20091 internal resonances and primary parametric resonance. Two types of degenerated equilibrium points are studied in detail, which are characterized by a double zero and two negative eigenvalues, and a double zero and a pair of pure imaginary eigenvalues. For each case, the stability regions of the initial equilibrium solution and the critical bifurcation curves are obtained in terms of the system parameters which may lead to Hopf bifurcation and 2D torus. With both analytical and numerical methods, bifurcation behaviors on damping parameters and detuning parameters are studied, respectively. A time integration scheme is used to find the numerical solutions for these bifurcation cases, and numerical results agree with the analytic predictions.<\/jats:p>","DOI":"10.1155\/2014\/414903","type":"journal-article","created":{"date-parts":[[2014,5,26]],"date-time":"2014-05-26T17:03:20Z","timestamp":1401123800000},"page":"1-11","source":"Crossref","is-referenced-by-count":1,"title":["Stability and Bifurcation for a Simply Supported Functionally Graded Material Plate with One-to-One Internal Resonance"],"prefix":"10.1155","volume":"2014","author":[{"given":"Dongmei","family":"Zhang","sequence":"first","affiliation":[{"name":"Department of Mechanics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"},{"name":"School of Science, Linyi University, Shandong 276005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fangqi","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","series-title":"Functionally Gradient Materials","first-page":"3","volume-title":"The concept of FGM","volume":"34","year":"1993"},{"year":"1990","key":"2"},{"issue":"33","key":"3","doi-asserted-by":"crossref","first-page":"4457","DOI":"10.1016\/S0020-7683(97)00253-9","volume":"35","year":"1998","journal-title":"International Journal of Solids and Structures"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-460X(77)90521-1"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/0020-7462(91)90052-U"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-7462(00)00023-8"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2004.11.028"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s11431-009-0051-2"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/BF00053690"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406014836"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008304701252"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1006\/jsvi.2000.3386"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s11012-011-9491-4"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1109\/9.358"},{"issue":"2","key":"15","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0307-904X(88)90011-X","volume":"12","year":"1988","journal-title":"Applied Mathematical Modelling"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1023\/A:1017993026651"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsv.2007.11.033"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.apm.2013.01.031"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/414903.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/414903.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/414903.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T09:52:00Z","timestamp":1498125120000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/414903\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":18,"alternative-id":["414903","414903"],"URL":"https:\/\/doi.org\/10.1155\/2014\/414903","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}