ISSN:
0029-5981
Keywords:
Engineering
;
Engineering General
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
,
Technology
Notes:
A method, called the Lehmann-Maehly method, for determining upper and lower bounds for eigenvalues, which was introduced by Bazley and Fox4 in 1964, is applied to the determination of bounds to the frequencies of elastic systems. In reviewing the fundamental theory involved, the present paper emphasizes the physical significance of the adjoint operators T and T* employed. An error in the paper by Bazley and Fox is noted and it is pointed out that with the corrected theory it is possible to use the Lehmann-Maehly method as a procedure for computing converging sequences of upper and lower bounds merely by varying a constant, the shifting constant. Thus, sequences of bounds are shown to be easily obtainable without prior knowledge of rough bounds, and the procedure for obtaining the bounds is not significantly more difficult to apply than the familiar Rayleigh-Ritz method for upper bounds. Since displacements and stresses are independently varied, the displacement functions used in the approximation procedure are only required to satisfy prescribed displacement boundary conditions while the stress functions only need satisfy the natural (stress) boundary conditions. Operators are derived for a non- uniform beam based on Timoshenko beam theory. Tables of bounds computed by the Lehmann-Maehly method and also the Rayleigh-Ritz method are given as an illustrative example.
Additional Material:
5 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/nme.1620060304
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