caa a22 4500 44581179X CHVBK 20180317145214.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00419-011-0528-x doi (NATIONALLICENCE)springer-10.1007/s00419-011-0528-x A dynamical model for nonlinear viscoelastic corrugated circular plates with shallow sinusoidal corrugations [Elektronische Daten] [Yong-Gang Wang, Xiao-Meng Li, Dan Li, Xin-Zhi Wang] An integrated mathematic model and an efficient algorithm on the dynamical behavior of homogeneous viscoelastic corrugated circular plates with shallow sinusoidal corrugations are suggested. Based on the nonlinear bending theory of thin shallow shells, a set of integro-partial differential equations governing the motion of the plates is established from extended Hamilton's principle. The material behavior is given in terms of the Boltzmann superposition principle. The variational method is applied following an assumed spatial mode to simplify the governing equations to a nonlinear integro-differential variation of the Duffing equation in the temporal domain, which is further reduced to an autonomic system with four coupled first-order ordinary differential equation by introducing an auxiliary variable. These measurements make the numerical simulation performs easily. The classical tools of nonlinear dynamics, such as Poincaré map, phase portrait, Lyapunov exponent, and bifurcation diagrams, are illustrated. The influences of geometric and physical parameters of the plate on its dynamic characteristics are examined. The present mathematic model can easily be used to the similar problems related to other dynamical system for viscoelastic thin plates and shallow shells. Springer-Verlag, 2011 Viscoelastic corrugated circular plate nationallicence Sinusoidal corrugations nationallicence Boltzmann superposition principle nationallicence Nonlinearly dynamical system nationallicence Wang Yong-Gang Department of Applied Mechanics, China Agricultural University, 100083, Beijing, People's Republic of China aut Li Xiao-Meng Department of Applied Mechanics, China Agricultural University, 100083, Beijing, People's Republic of China aut Li Dan Department of Applied Mechanics, China Agricultural University, 100083, Beijing, People's Republic of China aut Wang Xin-Zhi School of Science, Lanzhou University of Technology, 730050, Lanzhou, People's Republic of China aut Archive of Applied Mechanics Springer-Verlag 81/12(2011-12-01), 1925-1933 0939-1533 81:12<1925 2011 81 419 https://doi.org/10.1007/s00419-011-0528-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-011-0528-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Wang Yong-Gang Department of Applied Mechanics, China Agricultural University, 100083, Beijing, People's Republic of China aut NATIONALLICENCE 700 1- Li Xiao-Meng Department of Applied Mechanics, China Agricultural University, 100083, Beijing, People's Republic of China aut NATIONALLICENCE 700 1- Li Dan Department of Applied Mechanics, China Agricultural University, 100083, Beijing, People's Republic of China aut NATIONALLICENCE 700 1- Wang Xin-Zhi School of Science, Lanzhou University of Technology, 730050, Lanzhou, People's Republic of China aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/12(2011-12-01), 1925-1933 0939-1533 81:12<1925 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer