基于弹性介质动力学理论，研究了圆形洞室在瞬态径向非均匀荷载下的动力响应。利用波函数展开法与Laplace变换法，并考虑圆形洞室内表面应力边界非均匀条件，得到单位脉冲荷载下圆形洞室二维空间中应力和位移场在时域内的数值解。并通过算例，分析了径向非均匀瞬态荷载下的波动特性以及剪切模量等因素对应力位移场在径向和环向上分布特征的影响。研究结果表明，随着时间推移环向应力与位移的振动响应均表现出异步性，峰值出现的位置随时间在0-π之间变化，发生极值旋转；无量纲时间 大于2时，径向应力发生明显衰减,而径向位移与环向响应在无量纲时间 大于8时，才出现明显衰减，径向应力的振动周期最小；剪切模量对洞室表面应力位移幅值有显著影响；在非均匀荷载作用下，非均匀处响应幅值明显大于其他位置，径向应力、位移响应大于环向，衰减速度也更快。
Abstract
Based on the theory of elastic medium dynamics, the dynamic response of a circular cavity under transient radial inhomogeneous load was studied.Considering the circular cavity inner surface stress boundary conditions of uneven, the numerical solution of stress and displacement of sourrounding rock was obtained in the time domain under unit impulse load by an expansion method for wave function and the Laplace transform method.The factors, such as wave characteristics of radial nonuniform transient loads and shear modulus, produce effects on the distribution of stress and displacement in radial and annular direction.The effects were analyzed through an example.The dynamic response of tangential stress and displacement were asynchronous with time, and the position of peak value changes from 0 to π over time.When the dimensionless parameter of time was greater than 2, radial stress damped obviously.When the dimensionless parameter of time was greater than 8, radial displacement and tangential response damped to 0 gradually.The vibration period of radial stress is minimal.Shear modulus has significant influence on the amplitude of cavity inner surface displacement.Under non-uniform load, the response amplitude of non-uniform location is obviously greater than that of other positions, and the response of radial stress and displacement is greater than that of ring direction, and the attenuation speed is faster.
关键词
径向非均匀 /
Laplace变换 /
圆形洞室 /
动力响应
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Key words
radial inhomogeneity /
laplace transform /
cylindrical cavity /
dynamic response
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