Modelling the vibrations of multi-span beams and plates through adaptive global piecewise-smooth functions (A-GPSFS)
- 15 Downloads
Multi-span beams and plates which are freely vibrating are analysed through suitable adaptive sets of global piecewise-smooth functions (or A-GPSFs). Such approximating functions were introduced in Messina (Int J Mech Sci 90:179–189, 2015) as an extension of an original work published in Messina (J Sound Vib 256(1):103–129, 2002), where GPSFs were in turn used in order to model physical quantities through the thickness of structural elements. Herein these functions are used on the middle plane of the structural elements to model free vibrations of thin multi-span beams and plates, thus showing the capability of the same functions to include previous classical formulations in several circumstances of engineering interest. Depending on the internal constraints in beams and plates, the A-GPSFs could require further supplementary conditions. As such functional sets are not immediately available, explicit subroutines are illustrated. The efficiency and capability of the proposed models result from the comparison between calculated eigen-parameters and those of other models presented in open literature.
Unable to display preview. Download preview PDF.
- 6.Timoshenko, S.P.: History of Strength of Materials. Dover publications, New York (1953)Google Scholar
- 11.Bickford, W.B.: A consistent higher order beam theory. Dev. Theor. Appl. Mech. 11, 137–150 (1982)Google Scholar
- 16.Wang, C.M., Xiang, Y., Wang, C.Y.: Buckling and vibration of plates with an internal line-hinge via the Ritz method. In: Proceedings of First Asian–Pacific Congress on Computational Mechanics, Sydney, pp. 1663–1672 (2001)Google Scholar
- 18.Hu, Haichang: Variational Principles of Theory of Elasticity with Applications. Science Press and Gordon and Breach, Beijing (1984)Google Scholar
- 19.Whitney, M.J.: Structural Analysis of Laminated Anisotropic Plates. Technomic, Lancaster (1987)Google Scholar
- 20.MATHEMATICA Ver. 10.3.0.0, Wolfram Research Inc. 1988–2015Google Scholar
- 21.MATLAB 126.96.36.199613 (R2015a), The Mathworks Inc. 1984–2015Google Scholar
- 22.Sansone, G.: Moderna teoria delle funzioni di variabile reale III ed. Parte II (Sviluppi in serie di funzioni ortogonali). Nicola Zanichelli Editore, Bologna (1952). (In Italian) Google Scholar
- 24.Gentile, A., Messina, A.: Detection of cracks by only measured mode shapes in damaged conditions. In: Proceedings of the 3rd International Conference on Identification in Engineering systems, Swansea, pp. 208–220 (2002)Google Scholar