Linear, nonlinear, and dynamic programming formulations are developed for the solution of the min-max response of a single-degree-of-freedom dynamic system with incompletely prescribed input functions. The problem is: Given an oscillator whose equation of motion is mx¨ + g(x, x˙) = f(t), subject to stated initial conditions, and acted upon by a forcing function, f(t), which is nonnegative, and of specified finite duration and total impulse, find the particular forces which produce the least possible maximum displacement of the oscillator, and find this bounding value. Previously, Sevin developed an analytical technique for the solution which is inherently dependent upon a linear undamped form for the restoring force g(x, x˙). In the current work, an alternate statement of the problem is presented which lends itself to tractable computational formulations involving less stringent restrictions on g(x, x˙). Results obtained by dynamic and linear programming for specified forms of g(x, x˙) are given as functions of load duration.
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March 1967
Research Papers
Computational Approaches to the Min-Max Response of Dynamic Systems With Incompletely Prescribed Input Functions
Eugene Sevin,
Eugene Sevin
Mechanics Research Division, IIT Research Institute, Chicago, Ill.
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Walter Pilkey
Walter Pilkey
Mechanics Research Division, IIT Research Institute, Chicago, Ill.
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Eugene Sevin
Mechanics Research Division, IIT Research Institute, Chicago, Ill.
Walter Pilkey
Mechanics Research Division, IIT Research Institute, Chicago, Ill.
J. Appl. Mech. Mar 1967, 34(1): 87-90 (4 pages)
Published Online: March 1, 1967
Article history
Received:
March 21, 1966
Revised:
July 5, 1966
Online:
September 14, 2011
Citation
Sevin, E., and Pilkey, W. (March 1, 1967). "Computational Approaches to the Min-Max Response of Dynamic Systems With Incompletely Prescribed Input Functions." ASME. J. Appl. Mech. March 1967; 34(1): 87–90. https://doi.org/10.1115/1.3607673
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