ARTICLE
Influence of the damping effect on the dynamic response of a plate
 
More details
Hide details
1
Lodz University of Technology, Department of Strength of Materials, Łódź, Poland
Publish date: 2019-01-20
Submission date: 2018-07-30
Acceptance date: 2018-10-23
 
Journal of Theoretical and Applied Mechanics 2019;57(1):263–272
KEYWORDS
ABSTRACT
The subject of the research is analysis of the influence of the damping effect on the dynamic response of a plate. During the tests, the areas of dynamic stability and instability for the plate with and without damping are compared. Besides, exact analysis of the nature of the solution by applying criteria such as phase portraits, Poincar´e maps, FFT analysis, the largest Lyapunov exponents are carried out and found.
 
REFERENCES (32)
1.
Alijani F., Amabili M., Karagiozis K., Bakhtiari-Nejad F., 2011a, Nonlinear vibrations of functionally graded doubly curved shallow shells, Journal of Sound and Vibration, 330, 7, 1432-1454.
 
2.
Alijani F., Bakhtiari-Nejad F., Amabili M., 2011b, Nonlinear vibrations of FGM rectangular plates in thermal environments, Nonlinear Dynamics, 66, 3, 251-270.
 
3.
Ari-Gur J., Simonetta S.R., 1997, Dynamic pulse buckling of rectangular composite plates, Composites Part B: Engineering, 28, 3, 301-308.
 
4.
Bazant Z.P., Cedolin L., 2010, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories, World Scientific Bolotin V., 1962, Dynamic Stability of Elastic Systems, Vol. 1.
 
5.
Borkowski L., 2017, Numerical analysis of dynamic stability of an isotropic plate by applying tools used in dynamics, [In:] Dynamical Systems in Theoretical Perspective, J. Awrejcewicz (Edit.), Springer.
 
6.
Budiansky B., Roth R.S., 1962, Axisymmetric dynamic buckling of clamped shallow spherical shells, NASA TND1510, 597-606.
 
7.
Collatz L., 2012, The Numerical Treatment of Differential Equations, Springer Science and Business Media.
 
8.
Cooley J.W., Tukey J.W., 1965, An algorithm for the machine calculation of complex Fourier series, Mathematics of Computation, 19, 90, 297-301.
 
9.
Fortuna Z., Macukow B., Wasowski J., 2005, Metody numeryczne, WNT, Warszawa, ISBN 83-204-3075-5.
 
10.
Gilat R., Aboudi J., 2000, Parametric stability of non-linearly elastic composite plates by Lyapunov exponents, Journal of Sound and Vibration, 235, 4, 627-637.
 
11.
Hsu Y.C., Forman R.G., 1975, Elastic-plastic analysis of an infinite sheet having a circular hole under pressure, Journal of Applied Mechanics, 42, 2, 347-352.
 
12.
Hutchinson J.W., Budiansky B., 1966, Dynamic buckling estimates, AIAA Journal, 4, 3, 525-530.
 
13.
Kleiber M., Kotula W., Saran M., 1987, Numerical analysis of dynamic quasi-bifurcation, Engineering Computations, 4, 1, 48-52.
 
14.
Kolakowski Z., 2007, Some aspects of dynamic interactive buckling of composite columns, Thin-Walled Structures, 45, 10, 866-871.
 
15.
Kolakowski Z., Kubiak T., 2007, Interactive dynamic buckling of orthotropic thin-walled channels subjected to in-plane pulse loading, Composite Structures, 81, 2, 222-232.
 
16.
Kolakowski Z., Teter A., 2013, Influence of inherent material damping on the dynamic buckling of composite columns with open cross-sections,Mechanics and Mechanical Engineering, 17, 1, 59-69.
 
17.
Kowal-Michalska K., 2010, About some important parameters in dynamic buckling analysis of plated structures subjected to pulse loading, Mechanics and Mechanical Engineering, 14, 2, 269-279.
 
18.
Kubiak T., 2007, Criteria of dynamic buckling estimation of thin-walled structures, Thin-Walled Structures, 45, 10, 888-892.
 
19.
Kubiak T., Kolakowski Z., Kowal-Michalska K., Mania R., Swiniarski J., 2010, Dynamic response of conical and spherical shell structures subjected to blast pressure, Proceedings of SSDS’Rio.
 
20.
Mania R., Kowal-Michalska K., 2007, Behaviour of composite columns of closed cross-section under in-plane compressive pulse loading, Thin-Walled Structures, 45, 10, 902-905.
 
21.
Michlin S.G., Smolnicki C.L., 1970, Approximate Methods for the Solution of Integral and Differential Equations, PWN, Warsaw.
 
22.
Moorthy J., Reddy J.N., Plaut R.H., 1990, Parametric instability of laminated composite plates with transverse shear deformation, International Journal of Solids and Structures, 26, 7, 801-811.
 
23.
Petry D., Fahlbusch G., 2000, Dynamic buckling of thin isotropic plates subjected to in-plane impact, Thin-Walled Structures, 38, 3, 267-283.
 
24.
Raftoyiannis I.G., Kounadis A.N., 2000, Dynamic buckling of 2-DOF systems with mode interaction under step loading, International Journal of Non-Linear Mechanics, 35, 3, 531-542.
 
25.
Shariyat M., 2007, Thermal buckling analysis of rectangular composite plates with temperaturedependent properties based on a layerwise theory, Thin-Walled Structures, 45, 4, 439-452.
 
26.
Touati D., Cederbaum G., 1995, Influence of large deflections on the dynamic stability of nonlinear viscoelastic plates, Acta Mechanica, 113, 1-4, 215-231.
 
27.
Volmir A.S., 1972, Nonlinear Dynamics Plates and Shells, Moscow, Science Wang Y.G., Song H.F., Li D., Wang J., 2010, Bifurcations and chaos in a periodic time-varying temperature-excited bimetallic shallow shell of revolution, Archive of Applied Mechanics, 80, 7, 815-828.
 
28.
Wu G.Y., Shih Y.S., 2006, Analysis of dynamic instability for arbitrarily laminated skew plates, Journal of Sound and Vibration, 292, 1, 315-340.
 
29.
Yeh Y.L., Lai H.Y., 2002, Chaotic and bifurcation dynamics for a simply supported rectangular plate of thermo-mechanical coupling in large deflection, Chaos, Solitons and Fractals, 13, 7, 1493-1506.
 
30.
Yuda H., Zhiqiang Z., 2011, Bifurcation and chaos of thin circular functionally graded plate in thermal environment, Chaos, Solitons and Fractals, 44, 9, 739-750.
 
31.
Zhang T., Liu T.G., Zhao Y., Luo J.Z., 2004, Nonlinear dynamic buckling of stiffened plates under in-plane impact load, Journal of Zhejiang University – Science A, 5, 5, 609-617.
 
32.
Zizicas G.A., 1952, Dynamic buckling of thin plates, Transactions ASME, 74, 7, 1257-1268.
 
eISSN:2543-6309
ISSN:1429-2955