A discrete-continuous method of mechanical system modelling

• Autorzy: Hein R.
• Języki publikacji: EN

Abstrakty

EN

The paper describes a discrete-continuous method of dynamic system modelling. The presented approach is hybrid in its nature, as it combines the advantages of spatial discretization methods with those of continuous system modelling methods. In the proposed method, a three-dimensional system is discretised in two directions only, with the third direction remaining continuous. The thus obtained discrete-continuous model is described by a set of coupled partial differential equations, derived using the rigid finite element method (RFEM). For this purpose, firstly the general differential equations are written. Then these equations are converted into difference equations. The derived equations, expressed in matrix form, allow to create a global matrix for the whole system. They are solved using the distributed transfer function method. The proposed approach is illustrated with the examples of a simple beam fixed at both ends and a simply supported plate.

Słowa kluczowe

EN

modelling; mechanical system; dynamic systems; vibrations; hybrid modelling methods

• Wydawca: Gdańsk University of Technology, Faculty of Ocean Engineering & Ship Technology
• Czasopismo: Polish Maritime Research
• Rocznik: 2017
• Tom: S 1
• Strony: 97--107
• Opis fizyczny: Bibliogr. 18 poz., rys., tab.

Twórcy

autor

Hein R.

• Gdansk University of Technology Narutowicza 11/12, 80-233 Gdansk Poland

Bibliografia

• 1. Hein R., Orlikowski C.: Hybrid reduced model of rotor, The Archive of Mechanical Engineering, Vol. LX, No 3, pp. 319-333, 2013.
• 2. Hein R., Orlikowski C.: Optimum control of gyroscopic systems, Solid State Phenomena, Vol. 164, pp. 121-126, 2013.
• 3. Kaliński K. J., Galewski M. A.: A modified method of vibration surveillance by using the optimal control at energy performance index. Mechanical Systems and Signal Processing 58-59 (2015) 41-52.
• 4. Kaliński K. J., Galewski M. A.: Chatter vibration surveillance by the optimal-linear spindle speed control. Mechanical Systems and Signal Processing Volume 25, Issue 1, January 2011, Pages 383–399.
• 5. Kruszewski J., Gawroński W., Wittbrodt E., Najbar F., Grabowski S.: Metoda sztywnych elementów skończonych [Rigid finite element method], Arkady, Warszawa 1975.
• 6. Kujawa M., Szymczak C.: Numerical and experimental investigation of rotational stiffness of zed-purlins connection with sandwich panels// THIN-WALLED STRUCTURES. -Vol. 75, (2014), s.43-52.
• 7. Lipiński K.: Modeling and control of a redundantly actuated variable mass 3RRR planar manipulator controlled by a model-based feedforward and a model-based-proportional-derivative feedforward–feedback controller. Mechatronics 37 (2016), 42-53.
• 8. Orlikowski C., Hein R.: A simplified model of 3-D pipe system conveying flowing liquid, Solid State Phenomena, Vol. 198, pp. 621-626, 2013.
• 9. Orlikowski C., Hein R.: Modelling of geared multi-rotor system, Solid State Phenomena, Vol. 198, pp. 669-674, 2013.
• 10. Orlikowski C., Hein R.: Modelling and analysis of beam/ bar structure by application of bond graphs. Journal of Theoretical and Applied Mechanics, Vol. 49, No. 4, 2011.
• 11. Orlikowski C., Hein R.: Modal reduction and analysis of gyroscopic systems, Solid State Phenomena, Vol. 164, pp. 189-194, 2010.
• 12. Park D.-H., Yang B.: Distributed transfer function analysis of multi-body prismatic elastic solids, Int. J. of Structural stability and dynamics, Vol. 1, No. 1, pp. 83-104, 2001.
• 13. Wittbrodt E., Adamiec-Wójcik I., Wojciech S.: Dynamics of Flexible Multibody Systems. Rigid Finite Element Method. Foundations of Engineering Mechanics. Springer, Germany 2006. Pp. 225 (ISBN 3-540-32351-1, SPIN 11593553).
• 14. Wittbrodt E., Szczotka M., Maczyński A., Wojciech S.: Rigid finite element method in analysis of dynamics of offshore structures. Ocean Engineering & Oceanography 1. Springer-Verlag Berlin Heidelberg, 2013. Pp. 252 (ISBN 978-3-642-29885-1, ISSN 2194-6396).
• 15. Yang B., Tan C.A.: Transfer functions of one-dimensional distributed parameter systems, ASME Journal of Applied Mechanics, Vol. 59, December, pp. 1009 – 1014 , 1992.
• 16. Yang B.: Distributed transfer function analysis of complex distributed parameter systems, ASME Journal of Applied Mechanics, Vol. 61, pp. 84 – 92, 1994.
• 17. Yang B., Zhou J.: Semi-analytical solution of 2-D elasticity problems by the strip distributed transfer function method, Int. J. Solids Structures, Vol. 33, No. 27, pp. 3983-4005,1996.
• 18. Zhou J., Feng Z.: Transient response analysis of onedimensional distributed parameter systems, Int. J. of Solids and structures, Vol. 36, pp. 2807-2824, 1999.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017)