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• W2131155888 abstract "International Journal for Numerical Methods in EngineeringVolume 18, Issue 9 p. 1271-1295 Article On the reliability of the linear oscillator and systems of coupled oscillators† L. A. Bergman, L. A. Bergman Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, Illinois, U.S.A.Search for more papers by this authorJ. C. Heinrich, J. C. Heinrich Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, U.S.A.Search for more papers by this author L. A. Bergman, L. A. Bergman Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, Illinois, U.S.A.Search for more papers by this authorJ. C. Heinrich, J. C. Heinrich Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, Arizona, U.S.A.Search for more papers by this author First published: September 1982 https://doi.org/10.1002/nme.1620180902Citations: 44 † Dedicated to Professor O. C. Zienkiewicz on the occasion of his sixtieth birthday. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL References 1 Y. K. Lin, Probabilistic Theory of Structural Dynamics, McGraw-Hill, New York, 1967. 2 J.-N. Yang and M. Shinozuka, ‘First passage time problem’, J. Acoust. Soc. Am., 47, 393– 394 (1970). 3 S. H. Crandall, ‘First corssing probabilities of the linear oscillator’, J. Sound Vib., 12, 285– 299 (1970). 4 S. H. Crandall, K. L. Chandiramani and R. G. Cook, ‘Some first-passage problems in random vibration’, J. Appl. Mech., 33, 532– 538 (1966). 5 O. C. Zienkiewicz, The Finite Element Method, 3rd edn, McGraw-Hill, London, 1977. 6 J. C. Heinrich, P. S. Huyakorn, O. C. Zienkiewicz and A. R. Mitchell, ‘An “Upwind” finite element scheme for two-dimensional convective-transport equation’, Int. J. num. Meth. Engng, 11, 131– 143 (1977). 7 J. C. Heinrich and O. C. Zienkiewicz, ‘ The finite element method and “Upwinding” techniques in the numerical solution of convection dominated flow problems’, in Finite Element Methods for Convection Dominated Flows, ASME AMD, vol. 34, 1979, pp. 105– 136. 8 L. A. Bergman, ‘ Moments of time to first passage of the linear oscillator’, Doctoral thesis, Dept. of Civil Engineering, Case Western Reserve Univ., Cleveland, Ohio (1979). 9 L. A. Bergman and J. C. Heinrich, ‘Solution of the Pontriagin-Vitt equation for the moments of time to first passage of the randomly accelerated particle by the finite element method’, Int. J. num. Meth. Engng, 14, 1408– 1412 (1980). 10 L. A. Bergman and J. C. Heinrich, ‘On the moments of time to first passage of the linear oscillator’, Earthquake Eng. Struct. Dynam. (to appear). 11 L. A. Bergman and J. C. Heinrich, ‘Petrov-Galerkin finite element solution for the first passage probability and moments of first passage time of the randomly accelerated free particle’, Comp. Meth. Appl. Mech. Eng. (to appear). 12 P. Hood, ‘Frontal solution program for unsymmetric matrices’, Int. J. num. Meth. Engng, 10, 379– 399 (1976). 13 D. C. Dowson and A. Wragg, ‘ Maximum entropy distributions having prescribed first and second moments’, I.E.E.E. Trans. Information Theory, 689– 693 (September, 1973). 14 G. E. Myers, ‘ Numerically-induced oscillation and stability characteristics of finite-element solutions to two-dimensional heat-conduction transients’, Univ. of Wisconsin Engineering Experiment Station, Report No. 43 (August, 1977). 15 B. Sahay and W. Lennox, ‘Moments of the first-passage time for a narrow-band process’, J. Sound Vibr., 32(4), 449– 458 (1974). 16 L. Meirovitch, Analytical Methods in Vibrations, Macmillan, London (1967). 17 R. H. Toland and C. Y. Yang, ‘Random walk model for first passage probability’, A.S.C.E.J. Eng. Mech. Div. 97, 791– 807 (1971). 18 J. N. Franklin and E. R. Rodemich, ‘Numerical analysis of an elliptic-parabolic partial differential equation’, SIAM J. Num. Anal., 5 (1968). 19 J. C. Heinrich, ‘ On Bubnov-Galerkin, Petrov-Galerkin and added balancing dissipation’, Dept. of Aerospace and Mechanical Engineering Report, Univ. of Arizona, Tucson (1980). 20 J. N. Yang and M. Shinozuka, ‘On the first excursion probability in stationary narrow-band random vibration’, J. Appl. Mech., 38, 1017– 1022 (1971). 21 J. N. Yang and M. Shinozuka, ‘On the first excursion probability in stationary narrow-band random vibration II’, J. Appl. Mech., 39, 733– 738 (1972). 22 J. B. Roberts, ‘First passage time for the envelope of a randomly excited linear oscillator’, J. Sound Vib., 46, 1– 14 (1976). 23 J. B. Roberts, ‘ Probability of first passage failure for lightly damped oscillators’, IUTAM Symp. on Stochastic Problems in Dynamics, Univ. of Southampton, July 19– 23 (1976). Citing Literature Volume18, Issue9September 1982Pages 1271-1295 ReferencesRelatedInformation" @default.
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