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  • 1
    Electronic Resource
    Electronic Resource
    Three-dimensional vibration of cylindrical shell panels – solution by continuum and discrete approaches (2000)
    Springer
    Computational mechanics 26 (2000), S. 208-221 
    Details
    ISSN: 1432-0924
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract  This paper presents a three-dimensional elasticity solution to the free vibration problem of thick cylindrical shell panels of rectangular planform. The natural frequencies and corresponding mode shapes were obtained for thick cylindrical shell panels and detailed parametric investigations were carried out. Comparisons were also made with corresponding finite element simulation results. To validate the accuracy of the results as well as the stability of the present methodology, comprehensive convergence studies were also carried out. Further comparisons of present results were made with existing experimental and numerical results (classical, first-order and higher-order shell theories) available in open literature and the validity and range of applicability of the various shell theories examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004660000168
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems (1993)
    Springer
    Nonlinear dynamics 4 (1993), S. 357-372 
    Details
    ISSN: 1573-269X
    Keywords: Backward Kolmogorov equation ; Duffing oscillator ; finite elements ; first passage problem ; Fokker-Planck equation ; linear oscillator ; nonlinear vibration ; probability distribution ; random vibration ; stochastic processes ; Van der Pol oscillator
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The finite element method is applied to the solution of the transient Fokker-Planck equation for several often cited nonlinear stochastic systems accurately giving, for the first time, the joint probability density function of the response for a given initial distribution. The method accommodates nonlinearity in both stiffness and damping as well as both additive and multiplicative excitation, although only the former is considered herein. In contrast to the usual approach of directly solving the backward Kolmogorov equation, when appropriate boundary conditions are prescribed, the probability density function associated with the first passage problem can be directly obtained. Standard numerical methods are employed, and results are shown to be highly accurate. Several systems are examined, including linear, Duffing, and Van der Pol oscillators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00120671
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Solution of the Pontriagin-Vitt equation for the moments of time to first passage of the randomly accelerated particle by the finite element method (1980)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 15 (1980), S. 1408-1412 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Pontriagin-Vitt equation governing the mean of the time of first passage of a randomly accelerated particles has been studied extensively by Franklin and Rodemich.1 In their paper is presented the analytic solution for the two-sided barrier problem and solutions by several finite difference procedures.This note demonstrates solution of the problem by a Petrov-Galerkin finite element method using upstream weighting functions,2 shown to give rapidly convergent results. In addition, the equation is generalized to include higher statistical moments, and solutions for the first few ordinary moments are reported.
    Additional Material: 2 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620150913
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  • 4
    Electronic Resource
    Electronic Resource
    On the reliability of the linear oscillator and systems of coupled oscillatorsDedicated to Professor O. C. Zienkiewicz on the occasion of his sixtieth birthday. (1982)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 18 (1982), S. 1271-1295 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 20 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620180902
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