In this paper, a new series expansion for calculating the bending moment and the shear force in a proportionally damped, one-dimensional distributed parameter system due to moving loads is suggested. The number of moving forces, which may be functions of time and spatial coordinate, and their velocities are arbitrary. The derivation of the series expansion is not limited to moving forces that are a priori known, making this method also applicable to problems in which the moving forces depend on the interactions between the continuous system and the subsystems it carries, e.g., the moving oscillator problem. A main advantage of the proposed method is in the accurate and efficient evaluation of the bending moment and shear force, and in particular, the shear jumps at the locations where the moving forces are applied. Numerical results are presented to demonstrate the rapid convergence of the new series representation.
A New Method for Calculating Bending Moment and Shear Force in Moving Load Problems
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, Jan. 10, 2000; final revision, Aug. 18, 2000. Associate Editor: A. K. Mal. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
Pesterev, A. V., Tan, C. A., and Bergman, L. A. (August 18, 2000). "A New Method for Calculating Bending Moment and Shear Force in Moving Load Problems ." ASME. J. Appl. Mech. March 2001; 68(2): 252–259. https://doi.org/10.1115/1.1356028
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