COBEM99

S9 Fenômenos Não-Lineares e Caóticos em Engenharia

Title:

CHAOTIC OSCILATIONS OF COLUMNS UNDER PERIODIC AXIAL LOADS

Summary :

ABSTRACT: THE AIM OF THE PRESENT WORK IS TO DEVELOP A FORMULATION AND SOME STRATEGIES FOR THE INSTABILITY ANALYSIS OF SLENDER COLUMNS UNDER AN AXIAL HARMONIC FORCE. THE COLUMN UNDER THIS TYPE OF AXIAL LOAD MAY EXPERIENCE LARGE LATERAL VIBRATIONS, DEPENDING ON THE FORCE PARAMETERS. THIS PHENOMENON IS KNOWN AS PARAMETRIC INSTABILITY. AN EXCITATION IS SAID TO BE PARAMETRIC IF IT APPEARS AS TIME-DEPENDENT - OFTEN PERIODIC - COEFFICIENTS IN THE EQUATIONS GOVERNING THE MOTION OF THE SYSTEM, AND NOT AS AN INHOMOGENEOUS TERM. THE COLUMN IS DESCRIBED BY NAVIER CLASSICAL FORMULATION. THE PRESENT WORK CONSIDER THE COLUMN WITH ONE OR THREE DEGREES OF FREEDOM WITH OR WITHOUT NONLINEARITIES. THE EQUATIONS GOVERNING THE MOTION ARE OBTAINED BY THE RITZ METHOD. THE LINEAR EQUATION (MATHIEU EQUATION) AND THE DUFFING EQUATION WITH SMALL DAMPING ARE SOLVED NUMERICALLY AND BY PERTURBATION TECHNIQUES REVEALING THE POSSIBILITY OF DESTABILIZING THE STATIC EQUILIBRIUM POSITION IN CERTAIN REGIONS OF THE CONTROL SPACE. THIS ENABLES ONE TO OBTAIN TIME RESPONSE, PHASE SPACE PROJECTIONS, POINCARÉ SECTIONS AND BIFURCATION DIAGRAMS. THE NUMERICAL RESULTS SHOW THAT THE COLUMN WITH NONLINEARITIES AND LOADED BY A PERIODIC LONGITUDINAL FORCE CAN PRESENT VARIOUS SOLUTIONS WITH THE SAME PERIOD AS THE FORCING AND SUBHARMONIC E SUPERHARMONIC OSCILLATIONS, AS WELL AS CHAOTIC MOTIONS. KEY WORDS: PARAMETRIC INSTABILITY, BUCKLING, MATHIEU EQUATION, DUFFING EQUATION, COLUMN

Author :

Gonçalves, Paulo Batista
Oliveira, Salete de Souza

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