caa a22 4500 445361573 CHVBK 20180317142916.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s11071-011-0049-8 doi (NATIONALLICENCE)springer-10.1007/s11071-011-0049-8 Nonlinear vibrations of FGM rectangular plates in thermal environments [Elektronische Daten] [F. Alijani, F. Bakhtiari-Nejad, M. Amabili] Geometrically nonlinear vibrations of FGM rectangular plates in thermal environments are investigated via multi-modal energy approach. Both nonlinear first-order shear deformation theory and von Karman theory are used to model simply supported FGM plates with movable edges. Using Lagrange equations of motion, the energy functional is reduced to a system of infinite nonlinear ordinary differential equations with quadratic and cubic nonlinearities. A pseudo-arclength continuation and collocation scheme is used and it is revealed that, in order to obtain the accurate natural frequency in thermal environments, an analysis based on the full nonlinear model is unavoidable since the plate loses its original flat configuration due to thermal loads. The effect of temperature variations as well as volume fraction exponent is discussed and it is illustrated that thermally deformed FGM plates have stronger hardening behaviour; on the other hand, the effect of volume fraction exponent is not significant, but modal interactions may rise in thermally deformed FGM plates that could not be seen in their undeformed isotropic counterparts. Moreover, a bifurcation analysis is carried out using Gear's backward differentiation formula (BDF); bifurcation diagrams of Poincaré maps and maximum Lyapunov exponents are obtained in order to detect and classify bifurcations and complex nonlinear dynamics. Springer Science+Business Media B.V., 2011 Geometrically nonlinear vibrations nationallicence Plates nationallicence FGM nationallicence Bifurcations nationallicence Lyapunov exponents nationallicence Chaos nationallicence Alijani F. Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave, 15914, Tehran, Iran aut Bakhtiari-Nejad F. Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave, 15914, Tehran, Iran aut Amabili M. Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, H3A 2K6, Montreal, Canada aut Nonlinear Dynamics Springer Netherlands 66/3(2011-11-01), 251-270 0924-090X 66:3<251 2011 66 11071 https://doi.org/10.1007/s11071-011-0049-8 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-011-0049-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alijani F. Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave, 15914, Tehran, Iran aut NATIONALLICENCE 700 1- Bakhtiari-Nejad F. Department of Mechanical Engineering, Amirkabir University of Technology, Hafez Ave, 15914, Tehran, Iran aut NATIONALLICENCE 700 1- Amabili M. Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, H3A 2K6, Montreal, Canada aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/3(2011-11-01), 251-270 0924-090X 66:3<251 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer