Dynamic properties of structures with dampers modelled using fractional order derivatives
Affiliation(s)
Institute of Structural Engineering Poznan University of Technology 60-965 Poznań, Poland.
Institute of Structural Engineering Poznan University of Technology 60-965 Poznań, Poland.
ABSTRACT
The focus of this paper is on determination of the dynamic parameters of structural systems with viscoelastic (VE) dampers described by Maxwell rheological models. Such parameters could be obtained after solving the appropriately defined nonlinear eigenvalue problem for frames with VE dampers. The solution to the nonlinear eigenvalue problem is obtained by equating to zero the determinant of the considered system of equations. Apart from complex conjugate eigenvalues, the real ones occurred when dampers that are described by the classic Maxwell model, are also determined.
The focus of this paper is on determination of the dynamic parameters of structural systems with viscoelastic (VE) dampers described by Maxwell rheological models. Such parameters could be obtained after solving the appropriately defined nonlinear eigenvalue problem for frames with VE dampers. The solution to the nonlinear eigenvalue problem is obtained by equating to zero the determinant of the considered system of equations. Apart from complex conjugate eigenvalues, the real ones occurred when dampers that are described by the classic Maxwell model, are also determined.
Cite this paper
nullPawlak, Z. and Lewandowski, R. (2012) Dynamic properties of structures with dampers modelled using fractional order derivatives. Open Journal of Applied Sciences, 2, 138-142. doi: 10.4236/ojapps.2012.24B033.
nullPawlak, Z. and Lewandowski, R. (2012) Dynamic properties of structures with dampers modelled using fractional order derivatives. Open Journal of Applied Sciences, 2, 138-142. doi: 10.4236/ojapps.2012.24B033.
References
[1] S. W. Park, Analytical modelling of viscoelastic dampers for structural and vibration control. International Journal of Solids and Structures, 38, 8065–8092, 2001. [2] C. Christopoulos, A. Filiatrault, Principles of Passive Supplemental Damping and Seismic Isolation. IUSS Press, Pavia, Italy, 2006. [3] I. Takewaki, Building control with passive dampers, Optimal performance-based design for earthquakes. Wiley and Sons (Asia), Singapore, 2009. [4] R. L. Bagley, P. J. Torvik, Fractional calculus – a different approach to the analysis of viscoelastically damped structures. AIAA Journal, 27, 1412–1417, 1998. [5] T. Chang, M. P. Singh, Seismic analysis of structures with a fractional derivative model of viscoelastic dampers. Earthquake Engineering and Engineering Vibration, 1, 251-260, 2002. [6] I. Podlubny, Fractional Differential Equations. Academic Press, 1999. [7] R. Lewandowski, A. Bartkowiak, H. Maciejewski, Dynamic analysis of frames with viscoelastic dampers: a comparison of dampers models, Structural Engineering and Mechanics, 41, 113-137, 2012. [8] R. Lewandowski, Z. Pawlak, Dynamic Analysis of Frames with Viscoelastic Dampers Modelled by Rheological Models with Fractional Derivatives. Journal of Sound and Vibration, 330, 923-936, 2011. [9] R. Lewandowski, Z. Pawlak, Description of dynamic behavior of frame structures with fractional viscoelastic dampers, 6th ICCSM International Congress of Croatian Society of Mechanics, September 30 – October 2, 2009, Dubrovnik, Croatia.
[1] S. W. Park, Analytical modelling of viscoelastic dampers for structural and vibration control. International Journal of Solids and Structures, 38, 8065–8092, 2001. [2] C. Christopoulos, A. Filiatrault, Principles of Passive Supplemental Damping and Seismic Isolation. IUSS Press, Pavia, Italy, 2006. [3] I. Takewaki, Building control with passive dampers, Optimal performance-based design for earthquakes. Wiley and Sons (Asia), Singapore, 2009. [4] R. L. Bagley, P. J. Torvik, Fractional calculus – a different approach to the analysis of viscoelastically damped structures. AIAA Journal, 27, 1412–1417, 1998. [5] T. Chang, M. P. Singh, Seismic analysis of structures with a fractional derivative model of viscoelastic dampers. Earthquake Engineering and Engineering Vibration, 1, 251-260, 2002. [6] I. Podlubny, Fractional Differential Equations. Academic Press, 1999. [7] R. Lewandowski, A. Bartkowiak, H. Maciejewski, Dynamic analysis of frames with viscoelastic dampers: a comparison of dampers models, Structural Engineering and Mechanics, 41, 113-137, 2012. [8] R. Lewandowski, Z. Pawlak, Dynamic Analysis of Frames with Viscoelastic Dampers Modelled by Rheological Models with Fractional Derivatives. Journal of Sound and Vibration, 330, 923-936, 2011. [9] R. Lewandowski, Z. Pawlak, Description of dynamic behavior of frame structures with fractional viscoelastic dampers, 6th ICCSM International Congress of Croatian Society of Mechanics, September 30 – October 2, 2009, Dubrovnik, Croatia.