Title: Closed-form rocking vibration of rigid block under critical and non-critical double impulse

Authors: Ryo Taniguchi; Kunihiko Nabeshima; Kotaro Kojima; Izuru Takewaki

Addresses: Department of Architecture and Architectural Engineering, Graduate School of Engineering, Kyoto University, Kyotodaigaku-Katsura, Nishikyo, Kyoto 615-8540, Japan ' Department of Architecture and Architectural Engineering, Graduate School of Engineering, Kyoto University, Kyotodaigaku-Katsura, Nishikyo, Kyoto 615-8540, Japan ' Department of Architecture and Architectural Engineering, Graduate School of Engineering, Kyoto University, Kyotodaigaku-Katsura, Nishikyo, Kyoto 615-8540, Japan ' Department of Architecture and Architectural Engineering, Graduate School of Engineering, Kyoto University, Kyotodaigaku-Katsura, Nishikyo, Kyoto 615-8540, Japan

Abstract: A closed-form expression of the rocking response of a rigid block under a double impulse with arbitrary second impulse timing is derived by introducing a linear approximation in the equations of motion. While such linear approximation was unnecessary in the derivation of the maximum response in the case under the critical timing except the derivation of the critical timing (time up to the critical second impulse), this is necessary in the non-critical timing. The closed-form expression of the maximum angle of rotation is derived for two cases, i.e. Case (a): the second impulse before the impact on the ground, Case (b): the second impulse after the impact. It is demonstrated through numerical analyses that, although most closed-form expressions have reasonable accuracy, slight differences appear for the timings of the second impulse after the impact. It is also shown that such difference becomes smaller as the aspect ratio becomes larger.

Keywords: rigid block; rocking vibration; double impulse; critical input; non-critical input.

DOI: 10.1504/IJEIE.2017.083708

International Journal of Earthquake and Impact Engineering, 2017 Vol.2 No.1, pp.32 - 45

Available online: 04 Apr 2017 *

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