The transverse vibration of a rotating beam with tip mass: The method of integral equations
Author:
Louise H. Jones
Journal:
Quart. Appl. Math. 33 (1975), 193-203
DOI:
https://doi.org/10.1090/qam/99665
MathSciNet review:
QAM99665
Full-text PDF Free Access
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Abstract: An integral equation method is used to obtain improvable lower bounds for the second eigenvalue of the second-order “reduced” problem obtained from the problem described in the title by singular perturbation methods. These lower bounds are compared with results obtained directly by invariant embedding. The computational aspects of the integral equation method are stressed. The method is shown to be quite general and can be applied to a variety of boundary-value problems including those in which the eigenvalue parameter appears in the boundary conditions as well as in the differential operator.
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L. H. Jones, Integral equation methods for non-linear eigenvalue problems, Doctoral dissertation, University of Delaware, Newark, Delaware, 1970
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A. V. LaGinestra, On convergence and evaluation of the traces for the problem $Lu = N\lambda u,U - (u,\lambda ) = 0$; Doctoral dissertation, Rensselaer Polytechnic Institute, Troy, New York, 1967
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T. S. Y. Fou, Transverse vibration of a rotating beam with tip mass, computation of integral equation, Masters thesis, University of Delaware, Newark, Delaware, 1973
W. E. Boyce and G. H. Handelman, Vibrations of rotating beams with tip mass, Angew. Math. Phys. 12, 369–392 (1972)
L. H. Jones and B. E. Goodwin, The transverse vibrations of a pipe containing flowing fluid: methods of integral equations, Quart. Appl. Math. 29, 363–374 (1971)
B. E. Goodwin, On the realization of the eigenvalues of integral equations whose kernels are entire or meromorphic in the eigenvalue parameter, J. SIAM Appl. Math. 14, 65–85 (1966)
G. H. Handelman, W. E. Boyce, and H. Cohen, Vibrations of a uniform rotating beam with tip mass, in Proc. Third U. S. Natl. Congress of Appl. Mech., Providence, Rhode Island, 175–180 (1958)
F. G. Tricomi, Integral equations, Pure and Appl. Math. 5, Interscience, New York, 1957
M. R. Spiegel, The summation of series involving roots of transcendental equations and related applications. J. Appl. Phys. 24, 1103–1106 (1953)
L. H. Jones, Integral equation methods for non-linear eigenvalue problems, Doctoral dissertation, University of Delaware, Newark, Delaware, 1970
H. Brysk, Determinantal solution of the Fredholm equation with Green’s function kernel, J. Math. Physics 4, 1536–1538 (1963)
A. V. LaGinestra, On convergence and evaluation of the traces for the problem $Lu = N\lambda u,U - (u,\lambda ) = 0$; Doctoral dissertation, Rensselaer Polytechnic Institute, Troy, New York, 1967
M. R. Scott, L. F. Shampine, and G. M. Wing, Invariant imbedding and the calculation of eigenvalues for Sturm-Liouville systems, Computing 4, 10–23 (1969)
T. S. Y. Fou, Transverse vibration of a rotating beam with tip mass, computation of integral equation, Masters thesis, University of Delaware, Newark, Delaware, 1973
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Article copyright:
© Copyright 1975
American Mathematical Society
