Skip to main content
SpringerLink
Log in
Book cover

IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics pp 239–252Cite as

Analysis of Dynamic Variable Mass and Variable Parameter Systems Applying Semi-analytic Time-Integration

  • Conference paper
  • First Online:

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 34))

Abstract

For open dynamic systems with moving boundaries the derivation of the equations of motion and the computation of the solution for the vibrations is discussed. The mechanical model has to consider the variable mass by the flow of mass through the boundary of the applied control volume and the variable parameter of the system in the derivation of the equations of motion. An efficient semi-analytic time-integration algorithm is introduced, analysed with respect to the numerical behaviour and applied to compute the solution of the non-symmetric and non-linear equations of motion. As an example a defined winding process in a Steckel mill is considered and the computed results of some characteristic forces and displacements are shown for given operation conditions.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Irschik, H., Holl, H.J.: The equations of Lagrange written for a non-material volume. Acta Mech. 153(3–4), 231–248 (2002)

    Article  Google Scholar 

  2. Ziegler, F.: Mechanics of Solids and Fluids. Springer, New York (1991)

    Book  Google Scholar 

  3. Irschik, H., Holl, H.J.: Mechanics of variable-mass systems - Part 1: balance of mass and linear momentum. Appl. Mech. Rev. 57(2), 145–160 (2004)

    Article  Google Scholar 

  4. Cveticanin, L.: Dynamics of Bodies with Time-Variable Mass. Springer, Berlin (2016)

    Book  Google Scholar 

  5. Pesce, C.P.: The application of Lagrange equations to mechanical systems with mass explicitly dependent on position. J. Appl. Mech. 70, 751–756 (2003)

    Article  Google Scholar 

  6. Casetta, L., Pesce, C.P.: The generalized Hamiltons principle for a non-material volume. Acta Mech. 224(4), 919–924 (2013)

    Article  MathSciNet  Google Scholar 

  7. Casetta, L., Irschik, H., Pesce, C.P.: A generalization of Noether’s theorem for a non-material volume. Z. Angew. Math. Mech. 96(6), 696–706 (2016)

    Article  MathSciNet  Google Scholar 

  8. Casetta, L.: Theorem on a new conservation law for the dynamics of a position-dependent mass particle. Acta Mech. 228(1), 351–355 (2017)

    Article  MathSciNet  Google Scholar 

  9. Cveticanin, L.: Principle of generalized velocities in dynamics of planar separation of a rigid body. Acta Mech. 226, 2511–2525 (2015)

    Article  MathSciNet  Google Scholar 

  10. Jiang, W.-A., Xia, L.-L.: Symmetry and conserved quantities for non-material volumes. Acta Mech. 229, 1773–1781 (2018)

    Article  MathSciNet  Google Scholar 

  11. Newmark, N.M.: A method of computation for structural dynamics. J. Eng. Mech. Div. 85, 67–94 (1959)

    Google Scholar 

  12. Chung, J., Hulbert, G.M.: A time integration algorithms for structural dynamics with improved numerical dissipations: the generalized-method. J. Appl. Mech. 60, 371–375 (1993)

    Article  MathSciNet  Google Scholar 

  13. Hilber, H.M., Hughes, T.J.R., Taylor, R.L.: Improved numerical dissipation for time integration algorithms in structural dynamics. Earthq. Eng. Struct. Dyn. 5, 283–292 (1977)

    Article  Google Scholar 

  14. Fung, T.C.: Higher-order accurate time-step-integration algorithms by post-integration techniques. Int. J. Numer. Methods Eng. 53, 1175–1193 (2002)

    Article  MathSciNet  Google Scholar 

  15. Fung, T.C.: Stability and accuracy of differential quadrature method in solving dynamic problems. Comput. Methods Appl. Mech. Eng. 191, 1311–1331 (2002)

    Article  MathSciNet  Google Scholar 

  16. Schindler, T., Rezaei, S., Kursawe, J., Acary, V.: Half-explicit timestepping schemes on velocity level based on time-discontinuous Galerkin methods. Comput. Methods Appl. Mech. Eng. 290, 250–276 (2015)

    Article  MathSciNet  Google Scholar 

  17. Soares, D.: A simple and effective single-step time marching technique based on adaptive time integrators. Comput. Methods Appl. Mech. Eng. 283, 1138–1166 (2017)

    Article  Google Scholar 

  18. Hairer, E., Wanner, G.: Solving Ordinary Differential Equations I: Nonstiff Problems. Springer Series in Computational Mathematics, vol. 8, 2nd edn. Springer, Berlin (2009)

    Google Scholar 

  19. Holl, H.J.: An efficient semi-analytic time-integration method with application to non-linear rotordynamic systems. Comput. Mech. 26(4), 362–375 (2000)

    Article  Google Scholar 

  20. Holl, H.J.: A time-integration algorithm for time-varying systems with non-classical damping based on modal methods. In: Wicks, A.L. (ed.) Proceedings of the 15th IMAC Society for Experimental Mechanics, pp. 1558–1564. Springer (1997)

    Google Scholar 

  21. Holl, H.J., Belyaev, A.K., Irschik, H.: Simulation of the duffing-oscillator with time-varying mass by a BEM in time. Comput. Struct. 73, 177–186 (1999)

    Article  Google Scholar 

Download references

Acknowledgements

This work has been supported by the LCM - K2 Center within the framework of the Austrian COMET-K2 program.

Author information

Authors and Affiliations

  1. Institute of Technical Mechanics, Johannes Kepler University of Linz, Altenbergerstraße 69, 4040, Linz, Austria

    Helmut J. Holl

Authors
  1. Helmut J. Holl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Helmut J. Holl .

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand

    Stefanie Gutschmidt

  2. Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand

    James N. Hewett

  3. Department of Mechanical Engineering, University of Canterbury, Christchurch, New Zealand

    Mathieu Sellier

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Holl, H.J. (2019). Analysis of Dynamic Variable Mass and Variable Parameter Systems Applying Semi-analytic Time-Integration. In: Gutschmidt, S., Hewett, J., Sellier, M. (eds) IUTAM Symposium on Recent Advances in Moving Boundary Problems in Mechanics. IUTAM Bookseries, vol 34. Springer, Cham. https://doi.org/10.1007/978-3-030-13720-5_20

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-13720-5_20

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-13719-9

  • Online ISBN: 978-3-030-13720-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation