0
TECHNICAL PAPERS

Solution of the Moving Mass Problem Using Complex Eigenfunction Expansions

[+] Author and Article Information
K.-Y. Lee, A. A. Renshaw

Department of Mechanical Engineering, Columbia University, Mail Code 4703, New York, NY 10027

J. Appl. Mech 67(4), 823-827 (Mar 12, 2000) (5 pages) doi:10.1115/1.1325010 History: Received September 15, 1999; Revised March 12, 2000
Copyright © 2000 by ASME
Your Session has timed out. Please sign back in to continue.

References

Wickert,  J. A., and Mote,  C. D., 1991, “Response and Discretization Methods for Axially Moving Materials,” Appl. Mech. Rev., 44, pp. S279–S284.
Hryniv,  R. O., Lancaster,  P., and Renshaw,  A. A., 1999, “A Stability Criterion for Parameter Dependent Gyroscopic Systems,” ASME J. Appl. Mech., 66, pp. 660–664.
Renshaw,  A. A., 1997, “Modal Decoupling of Systems Described by Three Linear Operators,” ASME J. Appl. Mech., 64, pp. 238–240.
Wickert,  J. A., and Mote,  C. D., 1990, “Classical Vibration Analysis of Axially Moving Continua,” ASME J. Appl. Mech., 57, pp. 738–744.
Olsson,  M., 1991, “On the Fundamental Moving Load Problem,” J. Sound Vib., 145, pp. 299–307.
Sadiku,  S., and Leipholz,  H. H. E., 1987, “On the Dynamics of Elastic Systems With Moving Concentrated Masses,” Ing.-Arch., 57, pp. 223–242.
Lee,  U., 1996, “Revisiting the Moving Mass Problem: Onset of Separation Between the Mass and Beam,” ASME J. Vibr. Acoust., 118, pp. 516–521.
Nelson,  H. D., and Conover,  R. A., 1971, “Dynamic Stability of a Beam Carrying Moving Masses,” ASME J. Appl. Mech., 93, pp. 1003–1006.
Pesterev,  A. V., and Bergman,  L. A., 1998, “Response of a Nonconservative Continuous System to a Moving Concentrated Load,” ASME J. Appl. Mech., 65, pp. 436–444.
Shen,  I. Y., 1993, “Response of a Stationary, Damped, Circular Plate Under a Rotating Slider Bearing System,” ASME J. Vibr. Acoust., 115, pp. 65–69.
Stanisic,  M. M., 1985, “On a New Theory of the Dynamic Behavior of the Structures Carrying Moving Masses,” Ing.-Arch., 55, pp. 176–185.
Wickert,  J. A., and Mote,  C. D., 1991, “Traveling Load Response of an Axially Moving String,” J. Sound Vib., 149, pp. 267–284.
Iwan,  W. D., and Moeller,  T. L., 1976, “The Stability of a Spinning Elastic Disk With a Transverse Load System,” ASME J. Appl. Mech., 43, pp. 485–490.

Figures

Grahic Jump Location
Schematic of a damped, axially moving string subject to a concentrated moving mass
Grahic Jump Location
The determinant of Mmn=〈Mun,um*〉 as a function of N, the number of trial functions used
Grahic Jump Location
Plots of SN(x) for the uniform load f=1 for N=10, 20, and 30 using the eigenfunctions of the undamped string
Grahic Jump Location
Plots of SN(x) for the uniform load f=δ(x−0.3) for N=10, 20, and 30 using the eigenfunctions of the undamped string
Grahic Jump Location
The displacement of the concentrated mass at the midpoint of the span as a function of N for Galerkin’s method using real trial functions (plus) and the proposed eigenfunction expansion technique (circle). The dashed line is the result obtained using the method of Wickert and Mote 12. c=0,v=0.25,t=2, and m=g=0.375.
Grahic Jump Location
Same as Fig. 5 except t=1,v=0.5,m=g=0.125. Galerkin’s method using real trial functions (plus) and the proposed eigenfunction expansion technique (circle). The dashed line is the result obtained using the method of Wickert and Mote 12.
Grahic Jump Location
The displacement of the concentrated mass at the midpoint of the span as a function of N for Galerkin’s method using real trial functions (plus) and the proposed eigenfunction expansion technique (circle). c=0.3,v=0.25, and m=g=0.375.
Grahic Jump Location
Same as Fig. 7 except t=1,v=0.5,m=g=0.125. Galerkin’s method using real trial functions (plus) and the proposed eigenfunction expansion technique (circle).

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