0
Research Papers

Nonlinear Periodic Response of Composite Curved Beam Subjected to Symmetric and Antisymmetric Mode Excitation

[+] Author and Article Information
S. M. Ibrahim, B. P. Patel

Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, India

Y. Nath1

Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, Indianathyogendra@hotmail.com

1

Corresponding author.

J. Comput. Nonlinear Dynam 5(2), 021009 (Feb 19, 2010) (11 pages) doi:10.1115/1.4000825 History: Received March 15, 2009; Revised October 03, 2009; Published February 19, 2010; Online February 19, 2010

The periodic response of cross-ply composite curved beams subjected to harmonic excitation with frequency in the neighborhood of symmetric and antisymmetric linear free vibration modes is investigated. The analysis is carried out using higher-order shear deformation theory based finite element method (FEM). The governing equations are integrated using Newmark’s time marching coupled with shooting technique and arc-length continuation. Shooting method is used to solve the second-order differential equations of motion directly without converting them to the first-order differential equations. This approach is computationally efficient as the banded nature of equations is retained. A detailed study revealed that the response of antisymmetrically excited beams has contribution of higher antisymmetric as well as symmetric modes whereas the response of symmetrically excited beams has the significant participation of the higher symmetric modes except for the excitation in the neighborhood of first symmetric mode. The beam excited in the neighborhood of first symmetric mode has an additional branch corresponding to significant participation of first antisymmetric mode due to two-to-one internal resonance. Furthermore, for the beams excited in the neighborhood of higher modes, the peak response amplitude becomes less than that of the beam excited in the neighborhood of first mode but vibration behavior is drastically different due to the presence of subharmonics and higher harmonics. Two-to-one internal resonance between second antisymmetric mode and first symmetric mode is predicted for the first time.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Geometry and coordinate system of a curved beam

Grahic Jump Location
Figure 2

Element details showing the degrees-of-freedom at three nodes

Grahic Jump Location
Figure 3

First seven free vibration modes of immovable simply supported two-layered (00/900) cross-ply curved beam

Grahic Jump Location
Figure 4

Nonlinear steady-state response amplitude versus forcing frequency curves for immovable simply supported two-layered cross-ply (00/900) curved beam subjected to excitation in the neighborhood of first symmetric mode

Grahic Jump Location
Figure 5

Time history, frequency spectrum, and displacement variation along length corresponding to the points marked in Fig. 4 for curved beam excited in the neighborhood of first symmetric mode

Grahic Jump Location
Figure 6

Exact response and its comparison with response constructed using first two, four, and ten modal participations

Grahic Jump Location
Figure 7

Nonlinear steady-state response amplitude versus forcing frequency curves for immovable simply supported two-layered cross-ply (00/900) curved beam subjected to excitation in the neighborhood of first antisymmetric mode

Grahic Jump Location
Figure 8

Time history, frequency spectrum and displacement variation along length corresponding to the points marked in Fig. 7 for curved beam excited in the neighborhood of first antisymmetric mode

Grahic Jump Location
Figure 9

Nonlinear steady-state response amplitude versus forcing frequency curves for immovable simply supported seven-layered cross-ply (00/900/00/900/00/900/00) curved beam subjected to excitation in the neighborhood of first antisymmetric mode (ωm=745.60 rad/s)

Grahic Jump Location
Figure 10

Nonlinear steady-state response amplitude versus forcing frequency curves for immovable simply supported two-layered cross-ply (00/900) curved beam subjected to excitation in the neighborhood of second symmetric mode

Grahic Jump Location
Figure 11

Time history, frequency spectrum, and displacement variation along length corresponding to the points marked in Fig. 1 for curved beam excited in the neighborhood of second symmetric mode

Grahic Jump Location
Figure 12

Nonlinear steady-state response amplitude versus forcing frequency curves for immovable simply supported two-layered cross-ply (00/900) curved beam subjected to excitation in the neighborhood of second antisymmetric mode

Grahic Jump Location
Figure 13

Time history, frequency spectrum and displacement variation along length corresponding to the points marked in Fig. 1 for curved beam excited in the neighborhood of second antisymmetric mode

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.

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