基于黏弹性基支薄板模型的顶板力学分析

Mechanical Analysis of Roof Based on the Thin Plate Model on Viscoelastic Foundation

老顶力学模型采用薄板模型,根据弹性力学中的最小势能原理,求得基于文克勒弹性地基薄板模型的顶板位移函数。将支撑老顶的直接顶与煤层视为黏弹性基础,基础模型为广义开尔文模型,在弹性地基薄板模型分析结果的基础上,根据"弹性-黏弹性"对应原理,通过拉普拉斯变换法得到了基于黏弹性基支四边固支薄板模型的老顶位移、应力的解析解,为分析顶板稳定性及预测老采空区的地表沉降提供一定的理论依据。

The model of the main roof was treated as the thin plate model,according to the principle of the minimum potential energy of the elasticity, the displacement of the roof based on the thin plate model laid on the Winkler foundation was obtained. The immediate roof and coal which support the main roof were regarded as viscoelastic foundation, the model of the foundation was the Generalized Kelvin-Voigt model, on the basis of the analytic results which based on the plate on the elastic foundation, according to elastic-viscoelastic theory, then the analytic solutions of the displacement and the stress of the roof based on the plate on viscoelastic foundation were got by Laplace transform method, provided theoretical basis for analyzing the stability of the roof and forecasting the subsidence of the old mine goal area.