A numerical approach for determining the optimal position of a single damper for damping a distinct eigenfrequency of multi-body systems

Ninoslav Truhar,

Corresponding Author

Ninoslav Truhar

[email protected]

orcid.org/0000-0002-0848-8309

School of Applied Mathematics and Computer Science, University of Osijek, Osijek, Croatia

Correspondence

Ninoslav Truhar, School of Applied Mathematics and Computer Science, University of Osijek, Osijek 31000, Croatia.

Email: [email protected]

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Wolfgang E. Weber,

Wolfgang E. Weber

orcid.org/0000-0002-5914-1380

Chair of Structural Analysis, Helmut Schmidt University / University of the Federal Armed Forces Hamburg, Hamburg, Germany

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Ninoslav Truhar,

Corresponding Author

Ninoslav Truhar

[email protected]

orcid.org/0000-0002-0848-8309

School of Applied Mathematics and Computer Science, University of Osijek, Osijek, Croatia

Correspondence

Ninoslav Truhar, School of Applied Mathematics and Computer Science, University of Osijek, Osijek 31000, Croatia.

Email: [email protected]

Search for more papers by this author

Wolfgang E. Weber,

Wolfgang E. Weber

orcid.org/0000-0002-5914-1380

Chair of Structural Analysis, Helmut Schmidt University / University of the Federal Armed Forces Hamburg, Hamburg, Germany

Search for more papers by this author

First published: 21 September 2023

https://doi.org/10.1002/pamm.202300050

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Abstract

In this paper the damping optimization of a multi-body oscillator with arbitrary n degrees of freedom is considered. The main contribution is a theoretical result for the optimal position of a single damper in a structured optimization. For that purpose the optimization criterion based on the average total energy is considered. As the damping optimization by means of the chosen optimization criterion in general is not a straight-forward task, a numerical approach based on the formula of Veselić is introduced in this contribution. This approach can be used for efficiently calculating optimal damping for medium-size problems with $urn:x-wiley:16177061:media:pamm202300050:pamm202300050-math-0001$ .

REFERENCES

1Mikota, J., & Reiter, H. (2003). Development of a compact and tuneable vibration compensator for hydraulic systems. International Journal of Fluid Power, 4(1), 17–30.
10.1080/14399776.2003.10781152
Google Scholar
2Weber, W. E., Müller, P. C., & Anders, B. (2018). The remarkable structure of the mode shapes and eigenforces of a special multibody oscillator. Archive of Applied Mechanics, 88(4), 563–571.
10.1007/s00419-017-1327-9
Web of Science® Google Scholar
3Weber, W. E., Anders, B., & Müller, P. C. (2015). A proof on eigenfrequencies of a special linear vibration system. Zeitschrift für Angewandte Mathematik und Mechanik, 95(5), 519–526.
10.1002/zamm.201300058
Web of Science® Google Scholar
4Weber, W. E., Anders, B., & Zastrau, B. W. (2013). Calculating the right-eigenvectors of a special vibration chain by means of modified Laguerre polynomials. Journal of Theoretical and Applied Mechanics, 43(4), 17–28.
10.2478/jtam-2013-0030
Google Scholar
5Weber, W., Anders, B., & Zastrau, B. W. (2008). Some damping characteristics of a chain structured vibration system. Proceedings in Applied Mathematics and Mechanics, 8(1), 10391–10392.
10.1002/pamm.200810391
Google Scholar
6Weber, W. E., & Zastrau, B. W. (2018). Model order reduction of Mikota's vibration chain including damping effects by means of proper orthogonal decomposition. Journal of Theoretical and Applied Mechanics, 56(2), 511–521.
10.15632/jtam-pl.56.2.511
Web of Science® Google Scholar
7Müller, P. C., & Weber, W. E. (2021). Modal analysis and insights into damping phenomena of a special vibration chain. Archive of Applied Mechanics, 91(5), 2179–2187.
10.1007/s00419-020-01876-z
Web of Science® Google Scholar
8Araújo, A. L., Martins, P., Soares, C. M. M., Soares, C. A. M., & Herskovits, J. (2009). Damping optimization of viscoelastic laminated sandwich composite structures. Structural and Multidisciplinary Optimization, 39, 569.
10.1007/s00158-009-0390-4
Web of Science® Google Scholar
9Rottmann, M., Roloff, T., Rauter, N., Rittmeier, L., Sinapius, M., & Weber, W. E. (2023). A numerical study on planar gradient acoustic impedance matching for guided ultrasonic wave detection. Journal of Vibration and Control, 0(0), 1–14. https://doi.org/10.1177/10775463221149764
10.1177/10775463221149764
Google Scholar
10Weber, W., Rauter, N., Lammering, R., & Welker, K. (2022). Räumliche Auflösung des Schadenszustandes aus mechanischer und mathematischer Sicht. In D. Schulz, A. Fay, W. Matiaske, & M. Schulz (Eds.), dtec.bw-beiträge der helmut-schmidt-universität / universität der bundeswehr hamburg (Vol. 1, pp. 281–286).
Google Scholar
11Benner, P., Tomljanović, Z., & Truhar, N. (2011). Dimension reduction for damping optimization in linear vibrating systems. Zeitschrift für Angewandte Mathematik und Mechanik, 91(3), 179–191.
10.1002/zamm.201000077
Web of Science® Google Scholar
12Tomljanović, Z., Beattie, C., & Gugercin, S. (2018). Damping optimization of parameter dependent mechanical systems by rational interpolation. Advances in Computational Mathematics, 44, 1797–1820.
10.1007/s10444-018-9605-9
Web of Science® Google Scholar
13Veselić, K. (1990). On linear vibrational systems with one dimensional damping II. Integral Equations and Operator Theory, 13, 883–897.
10.1007/BF01198923
Web of Science® Google Scholar
14Gürgöze, M., & Müller, P. (1992). Optimal positioning of dampers in multi-body systems. Journal of Sound and Vibration, 158, 517–530.
10.1016/0022-460X(92)90422-T
Web of Science® Google Scholar
15Brabender, K. (1998). Optimale Dämpfung von linearen Schwingungssystemen [PhD thesis]. Fernuniversität Hagen, Hagen.
Google Scholar
16Truhar, N., & Veselić, K. (2009). An efficient method for estimating the optimal dampers' viscosity for linear vibrating systems using Lyapunov equation. SIAM Journal on Matrix Analysis and Applications, 31(1), 18–39.
10.1137/070683052
Web of Science® Google Scholar