0
Research Papers

Moving-Inertial-Loads-Induced Dynamic Instability for Slender Beams Considering Parametric Resonances

[+] Author and Article Information
Zhi Sun

State Key Laboratory for Disaster Reduction
on Civil Engineering,
Siping Road 1239,
Shanghai 200092, China
e-mail: sunzhi1@tongji.edu.cn

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 6, 2014; final manuscript received August 25, 2015; published online November 19, 2015. Assoc. Editor: Jeffrey F. Rhoads.

J. Vib. Acoust 138(1), 011014 (Nov 19, 2015) (9 pages) Paper No: VIB-14-1427; doi: 10.1115/1.4031518 History: Received November 06, 2014; Revised August 25, 2015

This paper investigates the moving-inertial-loads-induced dynamic instability limit for transverse bending vibration of slender beams considering both simple and combination parametric resonances under disturbances on multiple modal coordinates. The vibration system is described in the modal domain using ordinary differential equations with periodic parameters. Straightforward expansion is conducted to analyze the possible resonance regions. The impulsive parametric excitation method is employed to compute the monodromy matrices. System dynamic stability is evaluated and the transition curves are computed. Numerical studies on single-span clamped–clamped and clamped–hinged beams considering the first two modes are conducted. The computed dynamic instability maps verify the analytically derived resonance occurrence conditions and present the following observations. The initial disturbances on multiple modes will induce variation of the parametric resonance instability region and create new resonance tongues. Among all resonance tongues, principal simple and sum combination resonance tongues are the most important. For the mitigation of combination resonances, damping measures are required to be applied on all related modes.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

A clamped–clamped Euler–Bernoulli beam carrying moving inertial loads: (a) elevation view and (b) top view

Grahic Jump Location
Fig. 2

The triphase plot of ‖Λ‖inf for the clamped–clamped beam with one on-beam inertial load considering the first mode

Grahic Jump Location
Fig. 3

The (a) triphase and (b) plane projection plots of ‖Λ‖inf for the clamped–clamped beam with one on-beam inertial load considering the first two modes

Grahic Jump Location
Fig. 4

Dynamic instability transition curves of clamped–clamped beam with one on-beam inertial load considering the first two beam vibration modes

Grahic Jump Location
Fig. 5

Modal responses of the beam with ε=0.2, β=2.8 under (a) unit initial disturbance on u1 and (b) unit initial disturbance on u2

Grahic Jump Location
Fig. 6

Dynamic instability transition curves of the clamped–clamped beam with ξ1=0%, ξ2=5% carrying one on-beam inertial load considering the first two modes

Grahic Jump Location
Fig. 7

Dynamic instability transition curves of the clamped–clamped beam with no damping and ξ1=ξ2=2% carrying one on-beam inertial load considering the first two modes

Grahic Jump Location
Fig. 8

Dynamic instability transition curves of the clamped–clamped beam carrying one, three, and five on-beam inertial loads considering the first two modes

Grahic Jump Location
Fig. 9

A single-span clamped–hinged Euler–Bernoulli beam carrying moving inertial loads: (a) elevation view and (b) top view

Grahic Jump Location
Fig. 10

The triphase plot of ‖Λ‖inf distribution on ε-β plane for the clamped–hinged beam with one on-beam inertial load considering the first two modes

Grahic Jump Location
Fig. 12

Dynamic instability transition curves of the clamped–hinged beam carrying one on-beam moving inertial load with modal damping considering the first two modes

Grahic Jump Location
Fig. 11

Dynamic instability transition curves of the clamped–hinged beam with one on-beam moving inertial load considering the first two modes

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In