A Comparison of Higher-Order Difference Methods in the Solution of Beam-Vibration Problems
dc.contributor.author | Greenwood, Donald | en_US |
dc.date.accessioned | 2010-04-14T14:02:26Z | |
dc.date.available | 2010-04-14T14:02:26Z | |
dc.date.issued | 1964 | en_US |
dc.identifier.citation | Greenwood, Donald (1964). "A Comparison of Higher-Order Difference Methods in the Solution of Beam-Vibration Problems." Simulation 3(1): 33-44. <http://hdl.handle.net/2027.42/68833> | en_US |
dc.identifier.issn | 0037-5497 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/68833 | |
dc.description.abstract | Several higher-order difference methods are investi gated and compared for the problem of finding the natural frequencies of the lateral vibration of a beam. All of the methods considered are applicable to either digital or analog computers, although particu lar reference is made to the analog computer. The methods considered in most detail use the same basic central difference approximation, the variations occurring in the method of representing boundary conditions. Three higher-order approaches to the problem of boundary conditions are pre sented. They are 1) the use of one-sided differences of fourth order, 2) the use of symmetry assumptions, and 3) the passive-circuit approach. Each method is shown to have its advantages, the final choice de pending upon the particular requirements of the problem. Results are presented in the form of curves of per centage mode-frequency error vs number of cells for the various approximation methods. | en_US |
dc.format.extent | 3108 bytes | |
dc.format.extent | 1092913 bytes | |
dc.format.mimetype | text/plain | |
dc.format.mimetype | application/pdf | |
dc.publisher | Sage Publications | en_US |
dc.title | A Comparison of Higher-Order Difference Methods in the Solution of Beam-Vibration Problems | en_US |
dc.type | Article | en_US |
dc.subject.hlbtoplevel | Engineering | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Aeronautical and Astronautical Engineering University of Michigan Ann Arbor, Michigan | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/68833/2/10.1177_003754976400300110.pdf | |
dc.identifier.doi | 10.1177/003754976400300110 | en_US |
dc.identifier.source | Simulation | en_US |
dc.identifier.citedreference | R.M. Howe and V.S. Haneman, The Solution of Partial Differential Equations by Difference Methods Using the Electronic Differential Analyzer, Proc. IRE, vol. 41, pp. 1497-1508; October, 1953. | en_US |
dc.identifier.citedreference | G.D. Mc Cann and R.H. Mac Neal, Beam Vibration Analysis with the Electric Analog Computer, J. Appl. Mech., vol. 17, pp. 13-26; 1950. | en_US |
dc.identifier.citedreference | M.E. Fisher, Higher Order Differences in the Analogue Solution of Partial Differential Equations, J. ACM, vol. 3, pp. 325-347 ; October, 1956. | en_US |
dc.identifier.citedreference | M.E. Fisher, Limitations Due to Noise, Stability, and Component Tolerance on the Solution of Partial Differential Equations by Differential Analyzers, J. Electronics and Control, vol. 8, pp. 113-126; February, 1960. | en_US |
dc.identifier.citedreference | C.E. Howe and R.M. Howe, Application of Difference Techniques to the Lateral Vibration of Beams Using the Electronic Differential Analyzer, Engrg. Res. Inst., University of Michigan, Ann Arbor, Rept. No. AIR-7; February, 1954. | en_US |
dc.identifier.citedreference | R.W. Michie, Frequency Errors in Analog Computer Methods, Lockheed Aircraft Corp., Burbank, Calif., Rept. No. MAS-46; 1956. | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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