Stability analysis of an axially accelerating string

被引:177
作者
Pakdemirli, M [1 ]
Ulsoy, AG [1 ]
机构
[1] CELAL BAYAR UNIV,DEPT ENGN MECH,TR-45040 MANISA,TURKEY
关键词
D O I
10.1006/jsvi.1996.0935
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
The dynamic response of an axially accelerating string is investigated. The time dependent velocity is assumed to vary harmonically about a constant mean velocity. Approximate analytical solutions are sought using two different approaches. In the first approach, the equations are discretized first and then the method of multiple scales is applied to the resulting equations. In the second approach, the method of multiple scales is applied directly to the partial differential system. Principal parametric resonances and combination resonances are investigated in detail. Stability boundaries are determined analytically. It is found that instabilities occur when the frequency of velocity fluctuations is close to two times the natural frequency of the constant velocity system or when the frequency is close to the sum of any two natural frequencies. When the velocity variation frequency is close to zero or to the difference of two natural frequencies, however, no instabilities are detected up to the first order of perturbation. Numerical results are presented for a band-saw and a threadline problem. (C) 1997 Academic Press Limited.
引用
收藏
页码:815 / 832
页数:18
相关论文
共 27 条
[1]   VIBRATION LOCALIZATION IN BAND WHEEL SYSTEMS - THEORY AND EXPERIMENT [J].
ALJAWI, AAN ;
ULSOY, AG ;
PIERRE, C .
JOURNAL OF SOUND AND VIBRATION, 1995, 179 (02) :289-312
[2]   VIBRATION LOCALIZATION IN DUAL-SPAN, AXIALLY MOVING BEAMS .2. PERTURBATION ANALYSIS [J].
ALJAWI, AAN ;
PIERRE, C ;
ULSOY, AG .
JOURNAL OF SOUND AND VIBRATION, 1995, 179 (02) :267-287
[3]   VIBRATION LOCALIZATION IN DUAL-SPAN, AXIALLY MOVING BEAMS .1. FORMULATION AND RESULTS [J].
ALJAWI, AAN ;
PIERRE, C ;
ULSOY, AG .
JOURNAL OF SOUND AND VIBRATION, 1995, 179 (02) :243-266
[4]  
Hsu C. S., 1963, J APPLIED MECHANICS, V30, P367, DOI DOI 10.1115/1.3636563
[5]   NEW METHOD OF SOLUTION OF EIGENVALUE PROBLEM FOR GYROSCOPIC SYSTEMS [J].
MEIROVIT.L .
AIAA JOURNAL, 1974, 12 (10) :1337-1342
[6]   MODAL ANALYSIS FOR RESPONSE OF LINEAR GYROSCOPIC SYSTEMS [J].
MEIROVITCH, L .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 1975, 42 (02) :446-450
[7]   THE WAVE EQUATION IN A MEDIUM IN MOTION [J].
MIRANKER, WL .
IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1960, 4 (01) :36-42
[8]  
MOCKENSTURM EM, IN PRESS T AASME J V
[9]  
MOTE CD, 1975, T ASME J DYNAMIC SYS, P96
[10]  
Nayfeh A. H., 2008, Nonlinear Oscillations