摘要
块系岩体中摆型波具有非线性特征,导致难以解释其频谱特征及准共振现象机理。针对此问题,建立了考虑三次项的摆型波非线性振动模型,利用改进的L-P法与振型叠加法,求得多自由度强非线性振动的近似解析解,一定程度上解释了试验观测到块系岩体摆型波的非线性现象机理。结果表明,块体系统振动频率可表示为输入能量的高次多项式,随能量增大振动频率呈非单调变化;各谐振频率之间的比例与系统构造有关,近似满足√2的整数倍比例关系。通过建立摆型波的层次构造模型,得出准共振是摆型波在不同尺度块体之间跃迁的标志。
The pendulum waves in blocky rock masses exhibit nonlinear characteristics,making it difficult to interpret their spectral features and the mechanism of quasi-resonance phenomena.To address this issue,a nonlinear vibration model of pendulum wave that considers cubic terms is established.The approximate analytical solution of multi degree of freedom strong nonlinear vibration is obtained by using the improved L-P method and the mode superposition method.This,to a certain extent,explains the nonlinear phenomenon mechanism of pendulum wave in blocky rock mass observed in the experiments.The results show that the vibration frequency can be expressed as high order polynomials of the input energy and changes non-monotonously as the energy increases.The ratios between the resonance frequencies are related to the system structure and are approximately equal to integer multiples of √2.By establishing a hierarchical structure model for pendulum waves,it is concluded that quasi-resonance serves as an indicator of transitions between pendulum waves across different-sized blocks.
作者
徐天涵
崔海涛
邓勇
邢灏喆
李超
纪玉国
XU Tianhan;CUI Haitao;DENG Yong;XING Haozhe;LI Chao;JI Yuguo(College of National Defense Engineering,Army Engineering University of PLA,Nanjing 210007,China;Beifang Investigation,Design&Research Co.Ltd.,Tianjin 300222,China;Changjiang Institute of Survey,Planning,Design and Research Co.Ltd.,Wuhan 430010,China)
出处
《陆军工程大学学报》
2024年第5期1-10,共10页
Journal of Army Engineering University of PLA
基金
国家自然科学基金(42102331,12372378)。
关键词
摆型波
强非线性
改进L-P法
块系岩体
准共振
pendulum waves
strong nonlinear
improved L-P method
blocky rock mass
quasi-resonan
