振动压路机作业引起地基振动的解析法研究

利用Shah函数和Heaviside阶跃函数描述振动压路机在时间和空间上的间隔冲击作用，并将荷载函数代入弹性半空间的动力控制方程进行联立求解。利用三重Fourier变换推导出频率-波数域的解析解，然后反演到时间-空间域。通过数值算例，研究了振动压路机引起地基振动的衰减规律和频谱特征，并考察了压路机激振频率、名义振幅和行驶速度对地基振动特性的影响。研究表明：压路机激振频率对地基振幅影响甚微，但对地基振动频率分布产生很大影响，激振频率越大，地基振动的峰值频率数越多，峰值频率分布的频带越宽；压路机名义振幅对地基振幅影响显著，名义振幅越大，地基振幅则越大，但名义振幅对地基振动频率没有影响；随着压路机行驶速度增大，地基振幅先增大后减小，拐点出现在5 km/h附近，激振频率越大，地基振幅在低速阶段的增幅越明显。

Analytic method research on vibration of ground caused by vibratory roller operation

The Shah function and the Heaviside step function were used to describe the interval impact action of a vibratory roller in time and space, and the load function was substituted into the dynamic control equation of elastic half space for simultaneous solution. The analytical solution in frequency-wavenumber domain was derived by using the triple Fourier transform, and then the solution was obtained in time-space domain by numerical inversion. Through numerical examples, the attenuation law and frequency spectrum characteristics of ground vibration caused by vibratory roller were studied, and the influence of vibration frequency, nominal amplitude and travel speed on foundation vibration characteristics was investigated. The results show that the influence of the vibration frequency of the roller on the amplitude of the foundation was very limited, but it has a great influence on the frequency distribution of the foundation vibration;on the contrary, the nominal amplitude of the roller has a great influence on the foundation amplitude. With the increase of the nominal amplitude, the foundation amplitude increases significantly, but the nominal amplitude has no effect on the vibration frequency of ground. As the speed of the road roller increases, the foundation amplitude first increases and then decreases, and the inflection point appears near 5 km/h. The greater the vibration frequency of the roller, the greater the increase of the foundation amplitude in the low-speed stage.