Transient Nonlinear Vibration of Randomly Excited Cylindrical Shallow Panels in Non Aging Viscous Medium

Journal of Solid Mechanics

مقاله 12، دوره 9، شماره 2، شهریور 2017، صفحه 384-395   

نوع مقاله: Research Paper

نویسنده

A Asnafi^*

Hydro-Aeronautical Research Center, Shiraz University, Shiraz, Iran

چکیده

In this paper, the nonlinear transient vibration of a cylindrical shallow panel under lateral white noise excitation is studied. The panel is in contact with a non aging viscoelastic medium. Since the external load is a time varying random wide band process, deterministic and conventional approaches cannot be used. Instead, the evolution of the probability density function of the response is investigated. To compute the density function, the famous Monte Carlo simulation is employed while its correctness for this specific application is validated with another work in literature. The governing equation is rewritten to a non dimensional format; so that the results can be applied to a wide range of panels. Specifically, the transient behavior is investigated with respect to the quasi slenderness ratio and the non dimensional mean value of lateral load. As expected, both the simple damped oscillation and unstable jumping phenomenon are seen relative to the values of prescribed parameters. Finally, the joint probability density function of the response is drawn that give someone an idea about the quality of the response in the phase plane. 

کلیدواژه‌ها

Circular panels؛ Shallow shells, Monte carlo simulation؛ Random vibration؛ Non aging materials

مراجع

Amabili M., Paıdoussis P., 2003, Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction, Applied Mechanics Reviews 56(4): 349-381.
[2] Paı¨doussis MP., 2003, Fluid-Structure Interactions: Slender Structures and Axial Flow, Elsevier/Academic Press, London, UK.
[3] Kubenko V.D., Koval’chuk P.S., 1998, Nonlinear problems of the vibration of thin shells review, International Applied Mechanics 34: 703-728.
[4] Mei C., Abdel-Motagaly K., Chen R., 1999, Review of nonlinear panel flutter at supersonic and hypersonic speeds, Applied Mechanics Reviews 52(10): 321-332.
[5] Abrate S., 2007, Transient response of beams, plates, and shells to impulsive loads, In ASME 2007 International Mechanical Engineering Congress and Exposition 9: 107-116.
[6] Bodaghi M., Shakeri M., 2012, An analytical approach for free vibration and transient response of functionally graded piezoelectric cylindrical panels subjected to impulsive loads, Composite Structures 94(5): 1721-1735.
[7] Şenyer M., Kazanci Z., 2012, Nonlinear dynamic analysis of a laminated hybrid composite plate subjected to time-dependent external pulses, Acta Mechanica Solida Sinica 25(6): 586-597.
[8] Lutes L. D., 1997, Stochastic Analysis of Structural and Mechanical Vibrations, Prentice Hall.
[9] Mahadevan S., 1997, Monte Carlo simulation, Mechanical Engineering New York and Basel-Marcel Dekker.
[10] Risken H., 1984, Fokker-Planck Equation , Springer Berlin Heidelberg.
[11] Bolotin V. V. E., 2013, Random Vibrations of Elastic Systems , Springer Science & Business Media.
[12] Zhu W.Q., 1996, Recent developments and applications of the stochastic averaging method in random vibration, Applied Mechanics Reviews 49(10S): S72-S80.
[13] Roberts J. B., Spanos P. D., 2003, Random Vibration and Statistical Linearization, Courier Corporation.
[14] Wang D., 2007, Numerical and Experimental Studies of Self-Centering Post-Tensioned Steel Frames, ProQuest.
[15] Ilki A., Fardis M. N., 2013, Seismic Evaluation and Rehabilitation of Structures, Springer.
[16] Zhu H. T., Er G. K., Iu V. P., Kou K. P., 2011, Probabilistic solution of nonlinear oscillators excited by combined Gaussian and Poisson white noises, Journal of sound and vibration 330(12): 2900-2909.
[17] Asnafi A., 2014, Analytic bifurcation investigation of cylindrical shallow shells under lateral stochastic excitation, Modares Mechanical Engineering 14(5): 77-84.
[18] Potapov V. D., 1999, Stability of Stochastic Elastic and Viscoelastic Systems, Wiley.
[19] Chen L. Q., Zhang N. H., Zu J. W., 2003, The regular and chaotic vibrations of an axially moving viscoelastic string based on fourth order Galerkin truncation, Journal of Sound and Vibration 261(4): 764-773.
[20] Haddad Y. M., 1995, Viscoelasticity of Engineering Materials, Chapman & Hall, 2-6 Boundary Row, London, UK.
[21] Drozdov A. D., 1998, Viscoelastic Structures: Mechanics of Growth and Aging, Academic Press.
[22] Janno J., 2003, Determination of degenerate relaxation functions in three-dimensional viscoelasticity, Proceedings of the Estonian Academy of Sciences, Physics and Mathematics 52(2): 171-185.
[23] Banks H. T., Hu S., Kenz Z. R., 2011, A brief review of elasticity and viscoelasticity for solids, Advances in Applied Mathematics and Mechanics 3(1): 1-51.
[24] Eierle B., Schikora K., 1999, Computational viscoelasticity of aging materials, In European Conference on Computational Mechanics (ECCM), München, Germany.
[25] Lin Y. K., Cai G. Q., 2004, Probabilistic Structural Dynamics: Advanced Theory and Applications, Mcgraw-Hill Professional Publishing.
[26] Papoulis A., Pillai S. U., 2002, Probability, Random Variables, and Stochastic Processes, Tata McGraw-Hill Education.
[27] Ahn A., Haugh M., 2014, Linear Programming and the Control of Diffusion Processes , Informs Journal on Computing 27: 646-657.
[28] Haugh M., 2004, Generating Random Variables and Stochastic Processes, Lecture Notes, Monte Carlo Simulation, IEOR E4703.