Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative Stiffness
The present article deals with the mathematical investigation of a negative-stiffness ideal system that can be used in seismic isolation of civil engineering structures. Negative-stiffness systems can be used in the seismic isolation of structures, because in the case of a strong earthquake, they do...
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| Format: | Article |
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MDPI AG
2022-08-01
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| Series: | Buildings |
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| Online Access: | https://www.mdpi.com/2075-5309/12/8/1214 |
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| author | Nikoleta Chatzikonstantinou Triantafyllos K. Makarios Asimina Athanatopoulou |
| author_facet | Nikoleta Chatzikonstantinou Triantafyllos K. Makarios Asimina Athanatopoulou |
| author_sort | Nikoleta Chatzikonstantinou |
| collection | DOAJ |
| description | The present article deals with the mathematical investigation of a negative-stiffness ideal system that can be used in seismic isolation of civil engineering structures. Negative-stiffness systems can be used in the seismic isolation of structures, because in the case of a strong earthquake, they do not easily allow vibrations to develop. These negative-stiffness systems can be significantly more efficient than the usual seismic isolation systems, as they drastically reduce the vibrational amplitudes of structures, as well as eliminate the inertial seismic structure loadings. The mathematical investigation of a negative-stiffness ideal system provides documented answers about the effect of negative-stiffness systems in the seismic behavior of structures. First, the differential equation of motion of a single-degree-of-freedom oscillator (SDoF) is formulated, without classical damping, but with negative stiffness. Furthermore, the mathematical solution of the equation of motion is given, where it is proven that this solution does not describe a structure vibration. Furthermore, the seismic structure motion follows an exponential increase when the seismic ground excitation is purely sinusoidal. Finally, to calculate the real response of the negative-stiffness system, a suitable modification of the Newmark iterative numerical method is proposed. |
| first_indexed | 2024-03-09T09:59:32Z |
| format | Article |
| id | doaj.art-7e3acf08b8be4fd08d1ea0f700cd28d5 |
| institution | Directory Open Access Journal |
| issn | 2075-5309 |
| language | English |
| last_indexed | 2024-03-09T09:59:32Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Buildings |
| spelling | doaj.art-7e3acf08b8be4fd08d1ea0f700cd28d52023-12-01T23:31:47ZengMDPI AGBuildings2075-53092022-08-01128121410.3390/buildings12081214Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative StiffnessNikoleta Chatzikonstantinou0Triantafyllos K. Makarios1Asimina Athanatopoulou2Institute of Structural Analysis and Dynamics of Structure, School of Civil Engineering, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, GreeceInstitute of Structural Analysis and Dynamics of Structure, School of Civil Engineering, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, GreeceInstitute of Structural Analysis and Dynamics of Structure, School of Civil Engineering, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, GreeceThe present article deals with the mathematical investigation of a negative-stiffness ideal system that can be used in seismic isolation of civil engineering structures. Negative-stiffness systems can be used in the seismic isolation of structures, because in the case of a strong earthquake, they do not easily allow vibrations to develop. These negative-stiffness systems can be significantly more efficient than the usual seismic isolation systems, as they drastically reduce the vibrational amplitudes of structures, as well as eliminate the inertial seismic structure loadings. The mathematical investigation of a negative-stiffness ideal system provides documented answers about the effect of negative-stiffness systems in the seismic behavior of structures. First, the differential equation of motion of a single-degree-of-freedom oscillator (SDoF) is formulated, without classical damping, but with negative stiffness. Furthermore, the mathematical solution of the equation of motion is given, where it is proven that this solution does not describe a structure vibration. Furthermore, the seismic structure motion follows an exponential increase when the seismic ground excitation is purely sinusoidal. Finally, to calculate the real response of the negative-stiffness system, a suitable modification of the Newmark iterative numerical method is proposed.https://www.mdpi.com/2075-5309/12/8/1214equivalent negative potential energymodified Newmark’s methodnegative-stiffness systemnegative stiffnessseismic isolation |
| spellingShingle | Nikoleta Chatzikonstantinou Triantafyllos K. Makarios Asimina Athanatopoulou Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative Stiffness Buildings equivalent negative potential energy modified Newmark’s method negative-stiffness system negative stiffness seismic isolation |
| title | Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative Stiffness |
| title_full | Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative Stiffness |
| title_fullStr | Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative Stiffness |
| title_full_unstemmed | Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative Stiffness |
| title_short | Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative Stiffness |
| title_sort | integration method for response history analysis of single degree of freedom systems with negative stiffness |
| topic | equivalent negative potential energy modified Newmark’s method negative-stiffness system negative stiffness seismic isolation |
| url | https://www.mdpi.com/2075-5309/12/8/1214 |
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