Critical response of a single-degree-of-freedom system with bilinear hysteresis and viscous damping under triple impulse
A triple impulse is used as a mathematical model of forward-directivity inputs, which are fault-normal components of near-fault earthquake ground motions. In this paper, two types of the triple impulse input are employed. One is the triple impulse with the same time interval. The critical triple imp...
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Frontiers Media S.A.
2025-03-01
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| Series: | Frontiers in Built Environment |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fbuil.2025.1539299/full |
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| author | Kotaro Kojima Izuru Takewaki |
| author_facet | Kotaro Kojima Izuru Takewaki |
| author_sort | Kotaro Kojima |
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| description | A triple impulse is used as a mathematical model of forward-directivity inputs, which are fault-normal components of near-fault earthquake ground motions. In this paper, two types of the triple impulse input are employed. One is the triple impulse with the same time interval. The critical triple impulse of this sequence is defined as the triple impulse with the critical time intervals maximizing the displacement response, and the critical time intervals are necessary to be captured by changing the time intervals. The other is the triple impulse, with second and third impulses acting at zero-restoring force points. The elastic–plastic responses of single-degree-of-freedom (SDOF) systems with bilinear hysteresis and viscous damping under the two types of triple impulses are obtained by time-history response analysis and compared. Furthermore, approximate expressions are derived for the responses of the damped bilinear hysteretic SDOF system under the triple impulse (the latter triple impulse stated above), with impulses acting at the zero-restoring force timing. In response derivation, a quadratic function approximation of the damping force–displacement relationship and an energy balance approach are employed. The validity of the triple impulse as the model of the forward-directivity input and the accuracy of approximate expressions to the triple impulse (the latter triple impulse stated above) are checked by comparing them with responses under the equivalent three wavelets of sinusoidal waves and the Ricker wavelet. |
| format | Article |
| id | doaj-art-e7fc7895ddb14ceba8db65a8abb71f01 |
| institution | DOAJ |
| issn | 2297-3362 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Frontiers Media S.A. |
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| series | Frontiers in Built Environment |
| spelling | doaj-art-e7fc7895ddb14ceba8db65a8abb71f012025-08-20T03:02:06ZengFrontiers Media S.A.Frontiers in Built Environment2297-33622025-03-011110.3389/fbuil.2025.15392991539299Critical response of a single-degree-of-freedom system with bilinear hysteresis and viscous damping under triple impulseKotaro Kojima0Izuru Takewaki1Faculty of Design and Architecture, Kyoto Institute of Technology, Kyoto, JapanDepartment of Architecture, Kyoto Arts and Crafts University, Kyoto, JapanA triple impulse is used as a mathematical model of forward-directivity inputs, which are fault-normal components of near-fault earthquake ground motions. In this paper, two types of the triple impulse input are employed. One is the triple impulse with the same time interval. The critical triple impulse of this sequence is defined as the triple impulse with the critical time intervals maximizing the displacement response, and the critical time intervals are necessary to be captured by changing the time intervals. The other is the triple impulse, with second and third impulses acting at zero-restoring force points. The elastic–plastic responses of single-degree-of-freedom (SDOF) systems with bilinear hysteresis and viscous damping under the two types of triple impulses are obtained by time-history response analysis and compared. Furthermore, approximate expressions are derived for the responses of the damped bilinear hysteretic SDOF system under the triple impulse (the latter triple impulse stated above), with impulses acting at the zero-restoring force timing. In response derivation, a quadratic function approximation of the damping force–displacement relationship and an energy balance approach are employed. The validity of the triple impulse as the model of the forward-directivity input and the accuracy of approximate expressions to the triple impulse (the latter triple impulse stated above) are checked by comparing them with responses under the equivalent three wavelets of sinusoidal waves and the Ricker wavelet.https://www.frontiersin.org/articles/10.3389/fbuil.2025.1539299/fullcritical earthquake responsetriple impulseforward-directivity inputsingle-degree-of-freedom systembilinear hysteresisviscous damping |
| spellingShingle | Kotaro Kojima Izuru Takewaki Critical response of a single-degree-of-freedom system with bilinear hysteresis and viscous damping under triple impulse Frontiers in Built Environment critical earthquake response triple impulse forward-directivity input single-degree-of-freedom system bilinear hysteresis viscous damping |
| title | Critical response of a single-degree-of-freedom system with bilinear hysteresis and viscous damping under triple impulse |
| title_full | Critical response of a single-degree-of-freedom system with bilinear hysteresis and viscous damping under triple impulse |
| title_fullStr | Critical response of a single-degree-of-freedom system with bilinear hysteresis and viscous damping under triple impulse |
| title_full_unstemmed | Critical response of a single-degree-of-freedom system with bilinear hysteresis and viscous damping under triple impulse |
| title_short | Critical response of a single-degree-of-freedom system with bilinear hysteresis and viscous damping under triple impulse |
| title_sort | critical response of a single degree of freedom system with bilinear hysteresis and viscous damping under triple impulse |
| topic | critical earthquake response triple impulse forward-directivity input single-degree-of-freedom system bilinear hysteresis viscous damping |
| url | https://www.frontiersin.org/articles/10.3389/fbuil.2025.1539299/full |
| work_keys_str_mv | AT kotarokojima criticalresponseofasingledegreeoffreedomsystemwithbilinearhysteresisandviscousdampingundertripleimpulse AT izurutakewaki criticalresponseofasingledegreeoffreedomsystemwithbilinearhysteresisandviscousdampingundertripleimpulse |