Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the s...Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.展开更多
To study the damage mechanism of multi‐anchor piles in tunnel crossing landslide area under earthquake,the damping performance of multi‐anchor piles was discussed.The energy dissipation springs were used as the opti...To study the damage mechanism of multi‐anchor piles in tunnel crossing landslide area under earthquake,the damping performance of multi‐anchor piles was discussed.The energy dissipation springs were used as the optimization device of the anchor head to carry out the shaking table comparison test on the reinforced slope.The Hilbert spectrum and Hilbert marginal spectrum were proposed to analyze the seismic damage mechanism of the multi‐anchor piles,and the peak Fourier spectrum amplitude(PFSA)was used to verify the effectiveness of the method.The results show that the seismic energy is concentrated in the high‐frequency component(30-40Hz)of the Hilbert spectrum and the low‐frequency component(12-30 Hz)of the marginal spectrum.This indicates that they can be combined with the distribution law of the PFSA to identify the overall and local dynamic responses of the multi‐anchored piles,respectively.The stretchable deformation of the energy‐dissipation springs improves the coordination of the multi‐anchor piles,resulting in better pile integrity.The damage mechanism of the multi‐anchor piles is elucidated based on the energy method:local damage at the top and middle areas of the multi‐anchor piles is mainly caused by the low‐frequency component(12-30 Hz)of the marginal spectrum under the action of 0.15g and 0.20g seismic intensities.As the seismic intensity increases to 0.30g,the dynamic response of the slope is further amplified by the high‐frequency component(30-40 Hz)of the Hilbert energy spectrum,which leads to the overall damage of the multi‐anchor piles.展开更多
基金National Natural Science Foundation of China Under Grant No.50278090
文摘Under harmonic wave excitation, the dynamic response of a bilinear SDOF system can be expressed by the Hilbert spectrum. The Hilbert spectrum can be formulated by (1) the inter-wave combination mechanism between the steady response and the transient response when the system behaves linearly, or (2) the intra-wave modulation mechanism embedded in one intrinsic mode function (IMF) component when the system behaves nonlinearly. The temporal variation of the instantaneous frequency of the IMF component is consistent with the system nonlinear behavior of yielding and unloading. As a thorough study of this fundamental structural dynamics problem, this article investigates the influence of the amplitude of the harmonic wave excitation on the Hilbert spectrum and the intrinsic oscillatory mode of the dynamic response of a bilinear SDOF system.
基金Science and technology development project of China Railway Ninth Bureau Group Co.,Ltd,Grant/Award Number:DLF‐ML‐JSFW‐2021‐09Science and Technology Development Project of China Railway Research Institute Co.Ltd,Grant/Award Number:2017‐KJ008‐Z008‐XB+2 种基金Gansu Province Youth Science and Technology Fund program,China,Grant/Award Number:21JR7RA739Natural Science Foundation of Gansu Province,China,Grant/Award Number:21JR7RA738National Key R&D Program of China,Grant/Award Number:2018YFC1504901。
文摘To study the damage mechanism of multi‐anchor piles in tunnel crossing landslide area under earthquake,the damping performance of multi‐anchor piles was discussed.The energy dissipation springs were used as the optimization device of the anchor head to carry out the shaking table comparison test on the reinforced slope.The Hilbert spectrum and Hilbert marginal spectrum were proposed to analyze the seismic damage mechanism of the multi‐anchor piles,and the peak Fourier spectrum amplitude(PFSA)was used to verify the effectiveness of the method.The results show that the seismic energy is concentrated in the high‐frequency component(30-40Hz)of the Hilbert spectrum and the low‐frequency component(12-30 Hz)of the marginal spectrum.This indicates that they can be combined with the distribution law of the PFSA to identify the overall and local dynamic responses of the multi‐anchored piles,respectively.The stretchable deformation of the energy‐dissipation springs improves the coordination of the multi‐anchor piles,resulting in better pile integrity.The damage mechanism of the multi‐anchor piles is elucidated based on the energy method:local damage at the top and middle areas of the multi‐anchor piles is mainly caused by the low‐frequency component(12-30 Hz)of the marginal spectrum under the action of 0.15g and 0.20g seismic intensities.As the seismic intensity increases to 0.30g,the dynamic response of the slope is further amplified by the high‐frequency component(30-40 Hz)of the Hilbert energy spectrum,which leads to the overall damage of the multi‐anchor piles.
