移动荷载下路表弯沉响应分析
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摘要
利用广义Duhamel积分,对移动荷载下弹性层状体系表面弯沉响应问题进行了求解.采用积分变换的方法,求得了广义Duhamel积分式中的弯沉脉冲响应函数,并编制了相应的数值积分逆变换程序.以3层沥青路面体系为算例,计算了单个移动荷载下路表面弯沉响应规律,对于多个荷载组合,通过线性叠加的方法得到单轴单轮移动荷载下路表面弯沉响应.距离荷载经过中心较近处,当荷载驶近时弯沉持续增大,荷载驶离时,弯沉呈波动形式向零点附近衰减,速度越快衰减速度越快,经历的波动循环越少.
The surface deflection response of elastic layered system under moving load is solved by means of general Duhamel integration.The deflection pulse response function in the general Duhamel integration is got by using integral transform and the program of corresponding numerical inverse integral is worked out.Three layered asphalt pavement is provided as an example and the surface deflection response rule is computed under single moving load.The problem of multi-load can be solved by linearity superposition method and the result under single axle — single wheel load is given.Near the center of loads,the deflection value increases continuously when load comes close and the deflection decreases wavily to zero point when load goes off.When load moves faster,deflection decreases more rapidly and the number of repetition is less.
The surface deflection response of elastic layered system under moving load is solved by means of general Duhamel integration.The deflection pulse response function in the general Duhamel integration is got by using integral transform and the program of corresponding numerical inverse integral is worked out.Three layered asphalt pavement is provided as an example and the surface deflection response rule is computed under single moving load.The problem of multi-load can be solved by linearity superposition method and the result under single axle — single wheel load is given.Near the center of loads,the deflection value increases continuously when load comes close and the deflection decreases wavily to zero point when load goes off.When load moves faster,deflection decreases more rapidly and the number of repetition is less.
引文
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[2]Lianq Robert,Zeng Sanping.Efficient dynamic analysis of multilayered system during falling weight deflectometer experi-ments[J].Journal Transportation Engineering,2002,128(4):366 374.
[3]孙璐,邓学钧.运动分布荷载作用下弹性地基上无限大板瞬态响应[J].应用力学学报,1997,14(2):72 78.Sun Lu,Deng Xuejun.Transient response for infinite plate on winkler foundation by a moving distributed load[J].ChineseJournal of Applied Mechanics,1997,14(2):72 78.(in Chinese)
[4]郭大智,冯德成.层状弹性体系力学[M].哈尔滨:哈尔滨工业大学出版社,2001:141 158.
[5]马宏伟,吴斌.弹性动力学及其数值方法[M].北京:中国建材工业出版社,2000:153 170.
[6]曾三平,曹志远.多层地基的瞬态波动解[J].地震工程与工程振动,1991,11(3):33 44.Zeng Sanping,Cao Zhiyuan.Transient wave propagation in the multilayered foundations[J].Earthquake Engineering andEngineering Vibration,1991,11(3):33 44.(in Chinese)
[7]Papagiannakis A T,Raha R.Formulation for viscoelastic response of pavements under moving dynamic loading[J].Jour-nal of Transportion Engineering,1998,122(2):140 145.
[8]Durbin P.Numerial inversion of laplace transform[J].The Computer Journal,1974(17):371 376.
[9]Piessens R,Huysmans R.Automatic numerical inversion of laplace transform[J].ACM Transation on Mathematical Soft-ware,1984,10(3):348 353.
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