COBEM99

S9 Fenômenos Não-Lineares e Caóticos em Engenharia

Title:

NON-LINEAR OSCILLATIONS OF CYLINDRICAL SHELLS UNDER PERIODIC COMPRESSIVE FORCES

Summary :

ABSTRACT: IT IS OF GREAT TECHNICAL IMPORTANCE TO CLARIFY THE DYNAMIC STABILITY OF CIRCULAR CYLINDRICAL SHELLS SUBJECTED TO PERIODIC FORCES. HENCE, A NUMBER OF STUDIES HAVE BEEN MADE ON THIS SUBJECT. HOWEVER, DUE TO ITS COMPLEX NON-LINEAR BEHAVIOR UNDER DYNAMIC LOADS, THE DYNAMICS OF THESE SHELLS ARE NOT COMPLETELY UNDERSTOOD. IN FACT, ONLY RECENTLY, DUE MAINLY TO THE PROGRESSES IN THE FIELD OF NON-LINEAR DYNAMICS IN RECENT YEARS, THE GLOBAL BEHAVIOR OF THESE SHELLS UNDER DYNAMIC LOADS BEGAN TO BE UNDERSTOOD. FOR EXAMPLE, PHENOMENA SUCH AS SUBHARMONIC AND SUPERHARMONIC OSCILLATIONS, PERIOD-MULTIPLYING BIFURCATIONS, MODAL INTERACTION, JUMPS DUE TO NONLINEAR RESONANCES AND MULTIPLE POTENTIAL WELLS AND CHAOTIC MOTIONS ONLY NOW CAN BE EXPLAINED. THE COMPLEX DYNAMICS OF CYLINDRICAL SHELLS UNDER COMPRESSIVE FORCES IS DUE TO THE PRESENCE OF QUADRATIC NON-LINEARITIES EMERGING FROM STRONG MODAL COUPLING. IN THE PRESENT PAPER A LOW DIMENSIONAL MODEL IS USED TO STUDY THE NONLINEAR OSCILLATIONS AND INSTABILITIES OF THE SHELL. FOR THIS, THE DONNELL SHALLOW SHELL EQUATIONS, MODIFIED WITH THE TRANSVERSE INERTIA FORCE, ARE USED TOGETHER WITH THE GALERKIN METHOD TO DERIVE A SET OF COUPLED ORDINARY DIFFERENTIAL EQUATIONS OF MOTION WHICH ARE, IN TURN, SOLVED BY THE RUNGE-KUTTA METHOD. IN ORDER TO STUDY THE NON-LINEAR BEHAVIOR OF THE SHELL, SEVERAL NUMERICAL STRATEGIES WERE USED TO OBTAIN POINCARÉ MAPS, STABLE AND UNSTABLE FIXED POINTS, BIFURCATION DIAGRAMS AND BASINS OF ATTRACTION. SPECIAL ATTENTION IS GIVEN TO THE DETERMINATION OF THE STABILITY BOUNDARIES IN CONTROL SPACE AND TO THE IDENTIFICATION OF THE BIFURCATION PHENOMENA ASSOCIATED WITH THESE BOUNDARIES. THE RESULTS OBTAINED THROUGH THIS NUMERICAL INVESTIGATION CLARIFY THE CONDITIONS WHICH CONTROL WHETHER OR NOT ESCAPE FROM THE PRE-BUCKLING POTENTIAL WELL TAKES PLACE. THIS MAY HELP IN ESTABLISHING PROPER DESIGN CRITERIA FOR THESE SHELLS UNDER DYNAMIC LOADS, A TOPIC PRACTICALLY UNEXPLORED IN LITERATURE. KEYWORDS: SHELLS, DYNAMIC BUCKLING, MODAL INTERACTION

Author :

del Prado, Z. J.G.N.
Gonçalves, P. B.

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