Non-Proportionality Indices and Error Constraint in Modal Analysis of Viscously Damped Linear Structures
Source abstract
Abstract
Use of modal procedures in systems with non-proportional damping (such as structures with added viscous damping systems) results in response errors, shown in this study to depend on dissimilar and often conflicting conditions for different variables and stories; thus, it is not possible to propose simple rules based on structural or damping properties to limit the error in a global way. However, four existing indices (originally proposed to measure damping non-proportionality) present a positive correlation with the extreme errors in modal procedures for all variables and stories. Thus, limiting the index value is a sufficient condition to keep the error in all variables within a given threshold. For practical application, limit values for these indices are tabulated as a function of error and can be used as an acceptance criterion for the validity of modal procedures.
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Research context
OpenAlex topics: Structural Health Monitoring Techniques · Seismic Performance and Analysis · Structural Engineering and Vibration Analysis
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Affiliations
Departamento de Estructuras y Física de la Edificación, Escuela Técnica Superior de Arquitectura, Universidad Politécnica de Madrid, Av. Juan de Herrera, 4, 28040 Madrid, Spain
References (45)
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1. Soong, T., and Dargush, G.F. (1997). Passive Energy Dissipation Systems in Structural Engineering, Wiley. [1st ed.].10.1201/9781439834350.ch27 ↗
2. Christopoulos, C., and Filiatrault, A. (2006). Principles of Passive Supplemental Damping and Seismic Isolation, Iuss Press.
3. Energy dissipation systems for seismic applications: Current practice and recent developments10.1061/(ASCE)0733-9445(2008)134:1(3) ↗
4. Constantinou, M.C., and Symans, M.D. (1992). Experimental and Analytical Investigation of Seismic Response of Structures with Supplemental Fluid Viscous Dampers, National Center for Earthquake Engineering Research.
5. Seleemah, A.A., and Constantinou, M.C. (1997). Investigation of Seismic Response of Buildings with Linear and Nonlinear Fluid Viscous Dampers, National Center for Earthquake Engineering Research.
6. Classical normal modes in damped linear dynamic systems10.1115/1.3627262 ↗
7. Federal Emergency Management Agency (1997). FEMA 273: NEHRP Guidelines for the Seismic Rehabilitation of Buildings.
8. American Society of Civil Engineers (ASCE), A.S.O.C. (2017). Minimum Design Loads and Associated Criteria for Buildings and Other Structures, American Society of Civil Engineers (ASCE).
9. Labbé, P. (2018, January 18–21). Outlines of the revision of the Eurocode 8, part 1-generic clauses. Proceedings of the 16th European Conference on Earthquake Engineering, Thessaloniki, Greece.
10. Coordinates which uncouple the equations of motion of damped linear dynamic systems10.1115/1.4011828 ↗
11. Modal analysis of non-classically damped linear systems10.1002/eqe.4290140205 ↗
12. Hanson, R.D., and Soong, T.T. (2001). Seismic Design with Supplemental Energy Dissipation Devices, Earthquake Engineering Research Institute.
13. Ramirez, O.M., Constantinou, M.C., Kircher, C.A., Whittaker, A., Johnson, M., Gomez, J.D., and Chrysostomou, C.Z. (2001). Development and Evaluation of Simplified Procedures of Analysis and Design for Structures with Passive Energy Dissipation Systems, Multidisciplinary Center for Earthquake Engineering Research, University of Buffalo. Technical Report No. MCEER-00–0010, Revision 1.
14. Clough, R.W., and Penzien, J. (2013). Dynamics of Structures, Computers and Structures. [3rd ed.].
15. Passive Control Systems for Seismic Damage Mitigation10.1061/(ASCE)0733-9445(1998)124:5(501) ↗
16. Performance Spectra Based Method for the Seismic Design of Structures equipped with Passive Supplemental Damping Systems10.1002/eqe.2261 ↗
17. Chopra, A.K. (2007). Dynamics of Structures: Theory and Applications to Earthquake Engineering, Pearson Prentice Hall. [3rd ed.].
18. Classical normal modes in damped linear dynamic systems10.1115/1.3643949 ↗
19. Goodman, L.E., Rosenblueth, E., and Newmark, N.M. (1952). Aseismic Design of Elastic Structures Founded on Firm Ground, University of Illinois Engineering Experiment Station, College of Engineering, University of Illinois at Urbana-Champaign. Civil Engineering Studies SRS-026.
20. Der Kiureghian, A. (1979). On Response of Structures to Stationary Excitation, University of California, Earthquake Engineering Research Center.
21. Der Kiureghian, A. (1980). A Response Spectrum Method for Random Vibrations, University of California, Earthquake Engineering Research Center.
22. New real-value modal combination rules for non-classically damped structures10.1002/eqe.394 ↗
23. Improved response-spectrum analysis of base-isolated buildings: A substructure-based response spectrum method10.1016/j.engstruct.2018.02.037 ↗
24. Design strategies of viscous dampers for seismic protection of building structures: A review10.1016/j.soildyn.2018.12.024 ↗
25. Conde, J. (2020). Seismic Response of Structures Equipped with Passive Energy Dissipation Systems Using Simplified Methods Based on Equivalent Effective Properties. [Ph.D. Thesis, Universidad Politécnica de Madrid (UPM)].
26. Liang, Z., and Lee, G.C. (2001). Damping of Structures: Part 1-Theory of Complex Damping, National Center for Earthquake Engineering Research, University of Buffalo.
27. A graphic explanation of undamped and damped mode shapes and its application10.1016/0022-460X(89)90691-3 ↗
28. Errors in response calculations for non-classically damped structures10.1002/eqe.4290050404 ↗
29. Quantification of the extent of non-proportional viscous damping in discrete vibratory systems10.1016/S0022-460X(86)80134-1 ↗
30. A modal superposition pseudo-force method for dynamic analysis of structural systems with non-proportional damping10.1002/eqe.4290200402 ↗
31. An index of damping non-proportionality for discrete vibrating systems10.1006/jsvi.1994.1554 ↗
32. Estimates of errors in the frequency response of non-classically damped systems10.1006/jsvi.1995.0304 ↗
33. Mode shapes during asynchronous motion and non-proportionality indices10.1006/jsvi.1997.1070 ↗
34. Quantification of non-proportionality of damping in discrete vibratory systems10.1016/S0045-7949(99)00230-8 ↗
35. Evaluation of damping non-proportionality using identified modal information10.1006/mssp.2000.1326 ↗
36. A measure of non-proportional damping10.1006/mssp.1999.1280 ↗
37. Optimal complex modes and an index of damping non-proportionality10.1016/S0888-3270(03)00048-7 ↗
38. Examination of the validity of proportional damping approximations with two further numerical indices10.1016/0022-460X(86)90274-9 ↗
39. Conde, J., and Bernabeu, A. (2021). Influence of Maxwell Stiffness in Damage Control and Analysis of Structures with Added Viscous Dampers. Appl. Sci., 11.10.3390/app11073089 ↗
40. Internet site for European strong-motion data
41. (2021, February 09). ESD, European Strong-Motion Database. Available online: http://www.isesd.hi.is/ESD_Local/frameset.htm.
42. European Committee for Standardization (2004). En-1998-1: 2004. Eurocode 8: Design of Structures for Earthquake Resistance. Part 1: General Rules, Seismic Actions and Rules for Buildings, CEN.
43. Calculation of response spectra from strong-motion earthquake records10.1785/BSSA0590020909 ↗
44. Determining equivalent linear parameters for use in a capacity spectrum method of analysis10.1061/(ASCE)0733-9445(2006)132:1(59) ↗
45. Generic frame model for simulation of earthquake responses of steel moment frames10.1002/eqe.148 ↗