The equations of motion governing the three-dimensional finite-amplitude response of a plate in arbitrary space motion are derived and shown to lead to dynamic coupling between the transverse and in-plane displacement. A general method of solution for such problems is demonstrated in an example involving a simply supported rectangular plate spinning about an axis parallel to an edge and nutating through a small angle. The method involves an asymptotic expansion using the derivative expansion version of the method of multiple time scales, in conjunction with the Galerkin method. A critical spin rate leading to the loss of stability in divergence is determined. Then, a numerical example of resonant excitation of one principal coordinate demonstrates that the nonlinear response resembling the one obtained from linear theory may lose stability in favor of a second response in which several principal coordinates are mutually excited. Consideration of the interaction between in-plane and transverse displacements is shown to be crucial to the prediction of this “unusual” response.
Skip Nav Destination
Article navigation
March 1979
Research Papers
Resonant Excitation of a Spinning, Nutating Plate
J. W. Klahs, Jr.,
J. W. Klahs, Jr.
Structural Dynamics Research Corporation, Cincinnati, Ohio
Search for other works by this author on:
J. H. Ginsberg
J. H. Ginsberg
School of Mechanical Engineering, Purdue University, West Lafayette, Ind. 47907
Search for other works by this author on:
J. W. Klahs, Jr.
Structural Dynamics Research Corporation, Cincinnati, Ohio
J. H. Ginsberg
School of Mechanical Engineering, Purdue University, West Lafayette, Ind. 47907
J. Appl. Mech. Mar 1979, 46(1): 132-138 (7 pages)
Published Online: March 1, 1979
Article history
Received:
April 1, 1978
Online:
July 12, 2010
Citation
Klahs, J. W., Jr., and Ginsberg, J. H. (March 1, 1979). "Resonant Excitation of a Spinning, Nutating Plate." ASME. J. Appl. Mech. March 1979; 46(1): 132–138. https://doi.org/10.1115/1.3424484
Download citation file:
Get Email Alerts
Cited By
Related Articles
Stochastic Stability of Coupled Oscillators in Resonance: A Perturbation Approach
J. Appl. Mech (November,2004)
Comparison of the Two Formulations of w-u-v and w-F in Nonlinear Plate Analysis
J. Appl. Mech (July,2002)
Dynamic Stability of Disks With Periodically Varying Spin Rates Subjected to Stationary In-Plane Edge Loads
J. Appl. Mech (July,2004)
Vibrations and Stability of an Axially Moving Rectangular Composite Plate
J. Appl. Mech (January,2011)
Related Proceedings Papers
Related Chapters
A Utility Perspective of Wind Energy
Wind Turbine Technology: Fundamental Concepts in Wind Turbine Engineering, Second Edition
Fluidelastic Instability of Tube Bundles in Single-Phase Flow
Flow-Induced Vibration Handbook for Nuclear and Process Equipment
Smart Semi-Active Control of Floor-Isolated Structures
Intelligent Engineering Systems Through Artificial Neural Networks, Volume 17