Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
New closed form solutions for harmonic vibrations of infinite Kirchhoff plates subjected to a constant harmonic ring load, a constant harmonic circular load and an alternating harmonic circular load are derived. Two different approaches are used to define the closed form solutions. The first approach uses the integration of the harmonic point force and the addition theorem for Bessel functions, while the second approach applies the Hankel transform to solve the inhomogeneous partial differential equation of the Kirchhoff plate theory. The new closed form particular solutions can especially be used in Trefftz like methods and extend their field of application.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
949—961
Opis fizyczny
Bibliogr. 20 poz., rys.
Twórcy
autor
- Graz University of Technology, Institute of Mechanics, Graz, Austria
autor
- Graz University of Technology, Institute of Mechanics, Graz, Austria
Bibliografia
- 1. Abramowitz M., Stegun I., 1972, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, New York, Dover Publications
- 2. Bathe K., 2006, Finite Element Procedures, New Jersey, Prentice Hall
- 3. Chandrashekhara K., 2001, Theory of Plates, Hyderabad, Universities Press
- 4. Cremer L., Heckl M., Petersson B., 2005, Structure-Born Sound, Berlin, Springer Verlag
- 5. Debnath L., Bhatta D., 2014, Integral Transforms and Their Applications, Boca Raton, CRC Press
- 6. Filippi P.J.T., 2010, Vibrations and Acoustic Radiation of Thin Structures: Physical Basis, Theoretical Analysis and Numerical Methods, Hoboken, Wiley
- 7. Junger M.C., Feit D., 1986, Sound, Structures, and their Interaction, Massachusetts, MIT Press
- 8. Kirchhoff B., 1850, Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe, Journal f¨ur die reine und angewandte Mathematik, 40, 51-88
- 9. Klanner M., Ellermann K., 2015, Wave Based Method for the steady-state vibrations of thick plates, Journal of Sound and Vibration, 345, 146-161
- 10. Korenev B., 2002, Bessel Functions and their Applications, London, Taylor & Francis
- 11. Lin Q.-G., 2014, Infinite integrals involving Bessel functions by an improved approach of contour integration and the residue theorem, The Ramanujan Journal, 35, 3, 443-466
- 12. Magnus W., Oberhettinger F., Soni R., 1966, Formulas and Theorems for the Special Functions of Mathematical Physics, Berlin, Springer Verlag
- 13. Martincek G., 1994, Dynamics of Pavement Structures, London, Taylor & Francis
- 14. Mitrinović D., Keckić J., 1984, The Cauchy Method of Residues, Dordrecht, D. Reidel Publishing Company
- 15. Rao S. 2007, Vibration of Continuous Systems, New Jersey, Wiley
- 16. Riou H., Ladeveze P., Kovalevsky L., 2013, The variational theory of complex rays: An answer to the resolution of mid-frequency 3D engineering problems, Journal of Sound and Vibration, 332, 1947-1960
- 17. Rouch P., Ladeveze P., 2003, The variational theory of complex rays: A predictive tool for medium-frequency vibrations, Computer Methods in Applied Mechanics and Engineering, 192, 28/30, 3301-3315
- 18. Trefftz E., 1926, Ein Gegenstuck zum Ritzschen Verfahren, Proceedings of the 2nd International Congress of Applied Mechanics, Zurich, Orell Fussli Verlag, 131-137
- 19. Vanmaele C., Vandepitte D., Desmet W., 2007, An efficient wave based prediction technique for plate bending vibrations, Computer Methods in Applied Mechanics and Engineering, 196, 3178- 3189
- 20. Watson G., 1944, A Treatise on the Theory of Bessel Functions, London, Cambridge University Press
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c5a2d560-a747-48a4-8db6-2776a0ec2cd3
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