Nonlinear axisymmetric response of closed spherical shells to a radial harmonic excitation

DOI10.1016/0020-7462(90)90013-YzbMath0729.73114MaRDI QIDQ807143

Raouf A. Raouf, Ali Hasan Nayfeh

Publication date: 1990

Published in: International Journal of Non-Linear Mechanics (Search for Journal in Brave)

zbMATH Keywords

stabilitychaoslimit cyclesevolutionnumerical schemeexternal harmonic excitationphasesamplitudesmodulationshooting techniquepitchforkjumpFloquet analysissymmetry-breakingsupercriticalNewton-Raphson procedureaxisymmetric dynamic responsecascade of period-doubling bifurcationscyclic-fold bifurcationfixed-point solutionsfour first-order nonlinear equationsinteracting modesmethod of multiple-time scalesnatural frequencies of a flexural modenumerical-perturbation approachsaturation phenomenasubcritical Hopf bifurcations

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Vibrations in dynamical problems in solid mechanics (74H45) Bifurcation and buckling (74G60) Optimization of other properties in solid mechanics (74P10) Numerical interpolation (65D05) Membranes (74K15)

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CHAOTIC VIBRATIONS OF CLOSED CYLINDRICAL SHELLS IN A TEMPERATURE FIELD

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