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Keywords: rheological-dynamical analogy theory, viscous damping ratio, equivalent damping coefficient, iterative procedure.

Summary

There are two widely used methods of solving the vibrations of multi-degree-of-freedom structures in the time domain: modal superposition and direct integration. The problem with both of these methods is defining damping coefficients as they are commonly adopted as constant empirical input variables for the whole discretised structure.

This paper considers two types of damping for viscoelastoplastic single degree-of-freedom rheological dynamical analogy (RDA) systems: viscous damping in the case of linear analysis, defined as stiffness and, or proportional mass, and in the case of nonlinear analysis, hysteretic damping caused by inelastic deformations of the damper. A steel bar has been modelled and used as a prototype in RDA research for years and its parameters have been proven experimentally [1,2,3]. Viscous damping plays a major role in linear analysis. However, it is of minor importance in nonlinear analysis because of low values. Hysteretic damping is one of the most important parameters in nonlinear analysis. The RDA hysteretic damping coefficient is a function of the damper geometry, the viscoplastic creep coefficient and the shape of the cyclic variation. None of these factors which affect dampers are included in empirical proposals.

The RDA modelling technique reduces material nonlinear problems to linear dynamic problems, which allows for the possibility of using the modal analysis. Therefore, this paper proposes a modification which can be simply integrated in the extant modal analysis algorithms and refers to the procedure of calculating damping coefficients for the various parts of a discretised structure. As demonstrated in the case of two degree-of-freedom systems, the distribution of external load masses applied to a structure by means of the ratio between the load masses and the mass of those parts acting as dampers affects directly the damping ratio of those parts, and indirectly the other parts of the structure. Before using the iterative procedure to coordinate the different states of dynamic equilibrium in a discretised structure which has undergone different viscoelastoplastic deformations in its different parts, it is necessary to obtain the eigenvalues of the RDA model. According to the principle of analogy, the eigenvalues are calculated for a discretised structure relieved of external loads, which represent the eigenvalues for the structure in the condition of critical deformation.

The RDA theory of vibrations of multi-degree-of freedom structures is applied to the design of viscoelastoplastic dampers (bars) under tension, compression and bending.

References

1: Milašinovic D.D., "Rheological-dynamical analogy: modeling of fatigue behavior", Int. J. Solids Structures, 40(1), 181-217, 2003. doi:10.1016/S0020-7683(02)00518-8
2: Milašinovic D.D., "Rheological-dynamical analogy: viscoelastoplastic behavior of metallic bars", Int. J. Solids Structures, 41(16-17), 4599-4634, 2004. doi:10.1016/j.ijsolstr.2004.02.061
3: Milašinovic D.D., "Rheological-dynamical analogy: Prediction of damping parameters of hysteresis damper", Int. J. Solids Structures, 44(22-23), 7143-7166, 2007. doi:10.1016/j.ijsolstr.2007.04.001

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 88 PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and M. Papadrakakis Paper 192 Rheological-Dynamical Theory of Vibrations of Multi-Degree-of-Freedom Structures: Design of Viscoelastoplastic Dampers D.D. Milašinovic¹ and A. Borkovic² ¹Faculty of Civil Engineering, University of Novi Sad, Subotica, Serbia ²Faculty of Architecture and Civil Engineering, University of Banjaluka, Bosnia and Herzegovina doi:10.4203/ccp.88.192 purchase the full-text of this paper Full Bibliographic Reference for this paper , "Rheological-Dynamical Theory of Vibrations of Multi-Degree-of-Freedom Structures: Design of Viscoelastoplastic Dampers", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 192, 2008. doi:10.4203/ccp.88.192 Keywords: rheological-dynamical analogy theory, viscous damping ratio, equivalent damping coefficient, iterative procedure. Summary There are two widely used methods of solving the vibrations of multi-degree-of-freedom structures in the time domain: modal superposition and direct integration. The problem with both of these methods is defining damping coefficients as they are commonly adopted as constant empirical input variables for the whole discretised structure. This paper considers two types of damping for viscoelastoplastic single degree-of-freedom rheological dynamical analogy (RDA) systems: viscous damping in the case of linear analysis, defined as stiffness and, or proportional mass, and in the case of nonlinear analysis, hysteretic damping caused by inelastic deformations of the damper. A steel bar has been modelled and used as a prototype in RDA research for years and its parameters have been proven experimentally [1,2,3]. Viscous damping plays a major role in linear analysis. However, it is of minor importance in nonlinear analysis because of low values. Hysteretic damping is one of the most important parameters in nonlinear analysis. The RDA hysteretic damping coefficient is a function of the damper geometry, the viscoplastic creep coefficient and the shape of the cyclic variation. None of these factors which affect dampers are included in empirical proposals. The RDA modelling technique reduces material nonlinear problems to linear dynamic problems, which allows for the possibility of using the modal analysis. Therefore, this paper proposes a modification which can be simply integrated in the extant modal analysis algorithms and refers to the procedure of calculating damping coefficients for the various parts of a discretised structure. As demonstrated in the case of two degree-of-freedom systems, the distribution of external load masses applied to a structure by means of the ratio between the load masses and the mass of those parts acting as dampers affects directly the damping ratio of those parts, and indirectly the other parts of the structure. Before using the iterative procedure to coordinate the different states of dynamic equilibrium in a discretised structure which has undergone different viscoelastoplastic deformations in its different parts, it is necessary to obtain the eigenvalues of the RDA model. According to the principle of analogy, the eigenvalues are calculated for a discretised structure relieved of external loads, which represent the eigenvalues for the structure in the condition of critical deformation. The RDA theory of vibrations of multi-degree-of freedom structures is applied to the design of viscoelastoplastic dampers (bars) under tension, compression and bending. References 1 Milašinovic D.D., "Rheological-dynamical analogy: modeling of fatigue behavior", Int. J. Solids Structures, 40(1), 181-217, 2003. doi:10.1016/S0020-7683(02)00518-8 2 Milašinovic D.D., "Rheological-dynamical analogy: viscoelastoplastic behavior of metallic bars", Int. J. Solids Structures, 41(16-17), 4599-4634, 2004. doi:10.1016/j.ijsolstr.2004.02.061 3 Milašinovic D.D., "Rheological-dynamical analogy: Prediction of damping parameters of hysteresis damper", Int. J. Solids Structures, 44(22-23), 7143-7166, 2007. doi:10.1016/j.ijsolstr.2007.04.001 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £145 +P&P)
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