Vibration analysis of irregularly shaped plates by the spline-based differential quadrature method

• Autorzy: Krowiak A.
• Konferencja: Jubilee Symposium Vibrations In Physical Systems (25 ; 15-19.05.2012 ; Będlewo koło Poznania ; Polska)
• Języki publikacji: EN

Abstrakty

EN

The paper deals with the free vibration analysis of irregularly shaped plates using differential quadrature method (DQM). In the paper some effective approaches to deal with the problem of mapping irregular area into regular one are presented. These approaches are used in conjunction with a branch of the DQM based on spline interpolation to solve the free vibration problem of thin, isotropic plates. The use of this type of interpolation in the DQM ensures the stability of the method. As the results, the convergent tests of the natural frequencies are presented and compared with the results from conventional DQM.

Słowa kluczowe

EN

differential quadrature; irregularly shaped plates; blending functions; free vibration

PL

kwadratury różniczkowe; płyta o nieregularnym kształcie; funkcja mieszana; drgania swobodne

• Wydawca: Poznan University of Technology. Institute of Applied Mechanics
• Czasopismo: Vibrations in Physical Systems
• Rocznik: 2012
• Tom: Vol. 25
• Strony: 241--246
• Opis fizyczny: Bibliogr. 9 poz., rys., 1 wykr.

Twórcy

autor

Krowiak A.

• Cracow University of Technology, Institute of Computing Science, Al. Jana Pawła II 37, 31-864 Kraków, Poland

Bibliografia

• 1. A. Krowiak, Symbolic computing in spline-based differential 1. quadrature method, Commun. Numer. Meth. Engng, 22 (2006) 1097-1107.
• 2. R. Bellman, J. Casti, Differential quadrature and long term integration, Journal of Mathematical Analysis and Application, 34 (1971) 235–238.
• 3. C.W. Bert, M. Malik, The differential quadrature method for irregular domains and application to plate vibration, Int. J. Mech. Sci., 38 (1996) 589 – 606.
• 4. W.J. Gordon, C.A. Hall, Transfinite Element Methods: Blending Function Interpolation over Arbitrary Curved Element Domains, Numer. Math., 21 (1973) 109 – 129.
• 5. M. Malik, C.W. Bert, Vibration analysis of plates with curvilinear quadrilateral planforms by DQM using blending functions, J. Sound Vib., 230 (2000) 949 – 954.
• 6. C. Shu, H. Du, Free vibration analysis of curvilinear quadrilateral plates by the differential quadrature method, J. Comp. Phys., 163 (2000) 452 – 466.
• 7. C. Shu, Differential quadrature and its application in engineering, Springer-Verlag, London 2000.
• 8. A. Krowiak, The convergence and stability of the spline-based differential quadrature method applied to the vibration analysis of rectangular plates with free corners, Vibration in Physical Systems, 22 (2006) 197 – 202.
• 9. A. Krowiak, Modified spline-based differential quadrature method applied to vibration analysis of truncated conical shells, Engineering Computations, in press.