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This paper deals with implementation of the generalized-exact method for solving the problems of vibrations of the cylindrical sandwich shell with damping. The essential procedures of this paper are based on a set of generalized principles of the analytical method. The primary operation is the variables separation in the homogeneous system of partial differential equations describing free vibrations of this shell. The effect of this separation is a single homogeneous ordinary differential equation concerning the complex modal function with respect to the time-variable, and a homogeneous system of the ordinary differential equations concerning the complex modes with respect to the spatial variable. The following basic procedure is imposition of the assumed boundary conditions on the solution of the system of the ordinary differential equations, i.e. formulation of the boundary-value problem. The results of the solution of the boundary-value problem are two infinite complex sequences, i.e. eigen-frequencies and eigenvectors of eigenfunctions corresponding to the eigenfrequencies and satisfying the fundamental principle of orthogonality. The above-mentioned results are then used in other procedures. The penultimate procedures refer to solving the free vibrations problem. The essence of these procedures is determination of the integration constants appearing in the modal function by means of a generalized formula with respect to the initial conditions. The last, also significant procedures relate to solving the forced vibrations by means of a certain set of generalized formulae assigned to the analytical method.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
113--128
Opis fizyczny
Bibliogr. 28 poz., rys.
Twórcy
autor
- Kazimierz Wielki University in Bydgoszcz, Faculty of Mathematics, Physics and Technology, Institute of Technology, Chodkiewicza 30, 85-064 Bydgoszcz, Poland, kasiac@ukw.edu.pl
Bibliografia
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- 3. N.D. PANKRATOVA, B. NIKOLAEV, E. ŚWITOŃSKI, Non-axisymmetrical deformation of flexible rotational shells in classical and improved statement, Journal of Engineering Mechanics, 3, 2, 89-96, Brno 1996.
- 4. W. SZCZEŚNIAK, The selection of problems of beams and shells subjected to inertial moving load, Building Engineering, Pub. of the Warsaw Univ. of Tech., 132, Warsaw 1994.
- 5. M. GURGOZE, Alternative formulations of the characteristic equation of a Bernoulli-Euler beam to which several viscously damped spring-mass system are attached in span, Journal of Sound and Vibration, 223, 666-677, 1999.
- 6. S. KUKLA, Application of Green functions in frequency analysis of Timoshenko beams with oscillators, Journal of Sound and Vibration, 205, 355-363, 1997.
- 7. G. KIRCHHOFF, Über des Gleichgewicht und die Bewegung einer elastischen Scheibe, Journal für die Reine und Angewandte Math., 40, 1, 55-88, 1850.
- 8. S.P. TIMOSHENKO, WOJNOWSKY-KRYGIER, Theory of Plates and Shell, Arkady, New York, Toronto, London 1959.
- 9. C. WOŹNIAK, Foundations of dynamics of deformable bodies, PWN, Warsaw 1969.
- 10. M.W.D. WHITE, G.R. HEPLER, Vibration modes and frequencies of Timoshenko beams with attached rigid bodies, Journal and Applied Mechanics, 62, 193-199, 1995.
- 11. J. CABAŃSKI, An exact method for the free vibration analysis of Timoshenko-Kelvin beams with oscillators, Journal of Sound Vibration, 253, 669-685, 2002.
- 12. J. CABAŃSKI, Generalized exact method of free and forced oscillations in the non-conservative physical system, Journal Technical Physics, 41, 4, 471-481, 2000.
- 13. L. CREMER, M. HECKEL, E. UNGAR, Structural Vibrations and Sound Radiation at Audio Frequencies, Structure-Borne Sound, Springer-Verlag, Berlin 1988.
- 14. W. KURNIK, A. TYLIKOWSKI, Mechanics of Laminated Elements, Publ. Warsaw Univ. of Tech., Warsaw 1997.
- 15. D. NASHIF, D. JOHNES, J. HENDERSON, Vibration damping, Journal Vibration Acoustic, Mir, Moscow 1988.
- 16. W. NOWACKI, The Building Dynamics, Arkady, Warsaw 1972.
- 17. Cz. RYMARZ, Mechanics of continua, PWN, Warsaw 1993.
- 18. H. ABRAMOWICH, Natural frequencies of Timoshenko beams under compressive axial loads, Journal of Sound and Vibration, 157, 183-189, 1992.
- 19. R. BOGACZ, T. KRZYŻYŃSKI, K. POPP, Influence of shear deformation and rotatory inertia on the solutions of the generalized Mathews problem, Festschrift für Angewandte Mathematik und Mechanik, 73, 1, 5-13, 1993.
- 20. DI TARANTO, J.R. McGRAW, Vibratory bending of damped laminated plates, Journal Engineering for Industry, Transactions of American Society of Mechanical Engineers, 91, 1081-1090, 1969.
- 21. G. JEMIELITA, On the shear coefficients, Theoretical Found, in Civil Engng., Faculty of Civil Engng., Warsaw Univ. of Tech., 6, 115-122, Warsaw 1998.
- 22. W. SZCZEŚNIAK, The problems from dynamics of the plates, The publishing house of the Warsaw Univ. of Tech., Warsaw 2000.
- 23. R.A. TARANTO, J.R. McGRAW, Vibratory bending of damped laminated plates, Trans. ASME, Journal Eng. Industry, 91, 1081-1090, 1969.
- 24. J. NIZIOL, J. SNAMINA, Free vibration of the discrete-continuous system with damping, Journal Theoretical and Applied Mechanics, 28, 1-2, 149-160, 1990.
- 25. F. TSE, I. MORSE, R. HINKLE, Mechanical Vibrations, Theory and Applications, Allyn &: Bacon, Boston 1978.
- 26. K. CABAŃSKA-PŁACZKIEWICZ, Dynamics analysis of sandwich cylindrical shell, International Journal of Strength of Materials, National Academy of Sciences of Ukraine, Institute of Problems of Strength, 4, 346, 119-127, Kiev 2000.
- 27. K. CABAŃSKA-PŁACZKIEWICZ, Vibrations of a complex systems with damping under dynamic loading, International Journal of Strength of Material, National Academy of Sciences of Ukraine, Institute of Problems of Strength, 2, 356, 82-101, Kiev 2002.
- 28. K. CABAŃSKA-PŁACZKIEWICZ, Vibrations of the three-layered shell with damping, Engineering Transactions, 54, 4, 329-351, 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0033-0031