突变理论在岩土与结构工程中的若干应用
|
摘要
自然界中有许多现象都涉及不连续性。微积分学虽成功地解释了光滑的连续变化现象,但对于非连续问题有时就无能为力了。而突变理论是一种能够直接处理不连续性而无须联系任何特殊内在机制的数学工具。这使它特别适用于内部作用尚属未知的系统研究,并适合用于仅有的可信观察具有不连续性的情况。土工中结构突变、失稳、破坏等本身就是一种典型的突变现象。其中应用最多是尖点突变模型,因为它的临界面容易构造,且几何直观性很强。因此,论文主要以尖点突变模型为基础,对土工中突变现象及机理,如边坡失稳、地震液化、硬及软土应力-变形特性等,给予数学描述,并通过试验确定其可供应用的模型。论文主要研究内容及所取得的研究成果包括以下方面:
1.应用突变理论尖点模型研究砂土的地震液化模型
根据国内外实测液化资料、孔压的各类模型推导出在即将液化时,松土的超静孔隙水压力有突变,而密实土的超静孔隙水压力无突变这一现象,将尖点突变模型成功运用于对地震液化的判断。对Zeeman突变方程进行了重大修改。原始的突变方程是基于Zeeman突变机构得来的,这一模型目前被广泛应用。通过调整各系数可以使孔压、液化的发展更加精确地被方程所反映。通过逐步逼近的方法算出了方程中的参数,同时液化点和分叉曲线也被唯一地确定。通过对国内外液化资料的回判,可以看出此模型有较高的准确性。
2.应用突变理论尖点模型研究土的静力工作状态
(1)尖点突变模型描述静力载荷试验曲线的可行性及应用研究
静力载荷试验主要用于测定承压板下应力主要影响范围内岩土的承载力和变形特性。但其试验时间很长,加载困难,试验结果也难确定。对于较硬土地基而言,当荷载大于某一数值时,基础急剧下降,地基发生突然破坏。而软粘土和松沙地基土的变形是渐变的,没有突变现象。根据静力载荷试验曲线的特点,定性地分析了利用尖点突变模型表达载荷-沉降曲线的可行性。通过坐标变换导出平板载荷试验的载荷-沉降曲线方程在沉降量、施加荷载及承载力因子三维空间中的表达式。根据土的破坏条件,确定出相应参数并建立其尖点突变模型。利用该突变模型对已有的试验进行了预测,预测结果和试验结果吻合较好。
(2)尖点突变模型在边坡失稳中的应用研究
总结目前国内外判别边坡稳定性的方法、分析各种判别方法的优缺点及适用范围。研究尖点突变模型模拟监测时间一坡体变形速率的可行性,提出用突变模型模拟目前国内外滑坡体实际监测数据思想和方法,并建立模型。结合各滑坡体实际监测数据定性的检验了模型研究的可行性,提出了预测的思想,并通过现有的数据对监测时间一变形速率进行了初步的预测。
(3)土本构关系的描述及软粘土流动性的模型研究
利用突变理论尖点模型建立的土的本构模型,该模型既可反映软土的渐变破坏,又能拟合硬土的突变破坏,使以往按土的松软或紧硬程度的区别分别建立的各自相应的本构关系,能够统一于同一个模型中。同时,该模型在求解土初始切线弹性模量上达到了实用上要求的精度,并且对土的应力应变路径进行了定性分析。在此基础上,对土尖点模型描述应力应变路径的可行性进行定量分析。通过分析推导和比较,表明突变理论中的尖点突变模型描述土的应力应变路径,在定量和定性上都是合理的,可行的。对饱和粘性土而言,仅当剪应力小于长期强度时,土体才呈现类似理想体那样的规律;而当剪应力小于长期强度时,土在恒定剪力作用下,变形渐趋停止。本文引用尖顶突变模式,建立了γ-τ-t的数学关系式,然后带入数据检验计算结果表明,理论和实测值吻合较好。由此可见该模型是可用的。
3.对于建筑结构墙体共振振幅的突变性及细长杆突变失稳中点屈曲位移的研究
(1)细长杆突变失稳中点屈曲位移的研究
压杆失稳问题是工程中的突变问题。Euler公式基于小变形的近似方法,由于采用了曲率的近似表达式而无法求得中点屈曲位移δ。为此,本文利用突变理论原理及精确的曲率表达式建立了Euler杆在考虑几何非线性时的微分方程,通过算例揭示了压力大于分叉荷载时压力与中点屈曲位移的关系。研究结果表明,当压力达到荷载分叉点时,Euler杆不会立即丧失承载力,其承载力尚有微量的储备。研究结果与实验结果完全吻合。
(2)本文还应用自创的共振仪对于建筑结构共振振幅的突变性进行验试印证。由作者申请专利的共振仪通过改变偏心块重量W或调节变频器使起振机电机的转速ω近似于连续变化,就可以使起振机获得不同的激振力。将共振机固定在悬臂梁模型顶部中央,在可调变频的共振机上,通过调节共振机的振动频率装置给系统加载。由试验成果可见,振动过程中顶点振幅存在跳跃现象,也即随着激振力增大,系统具有振幅突变特性。
Many phenomena in nature are of uncontinuity that can not be interpreted by calculus. While catastrophe theory can deal with uncontinuity directly and it is unnecessary to relate with any special internal mechanism, which makes it especially fit for the system that internal action is unknown and can be used in the condition that believable observation is discontinuous. The structures of geo-technic engineering break and failure are typically discontinuous phenomena. So the application of catastrophe theory in geo-technic engineering is promising to solve the uncontinuity. Especially the cusp model is characterized by simplify and practicality, which has two control variables, one state variable and an attainable critical surface. Therefore, the phenomena and mechanism in soil engineering, such as slope failure, liquefaction induced by earthquake, stress-strain of hard and soft soil, are described and predicted based on the cusp catastrophe models established by experiments data. The main investigations and achievements are composed of following portions.
1. Estimation of liquefaction based on catastrophe theory
Cusp catastrophe model was applied to construct a model to simulate occurrence of soil liquefaction induced by earthquake. In the proposed model, pore water pressure was looked as a state variable and capability of site anti- liquefaction and received earthquake energy were treated as two control variables. Comparison was made between site earthquake liquefaction information and the results obtained from the proposed method. It is shown that the suggested method is convincing, reliable and practical in the engineering. At the same time, stability problem including any soil body due to critical shear strength can be simulated conveniently. The cusp catastrophe model also has interesting implications for seismic dynamic intensity analysis of soil-structure interaction system and seismic stability analysis of earth dam and slope and so on.
2. The applications of cusp model in static soil mehanics and engineering
(1)Study on application and prediction of cusp-catastrophe model in plane-plate loading test
Based on the property of loading- settlement curve obtained from static loading test, the feasibility of cusp-catastrophe theory applied to the simulation of the curve for plane plate loading test is qualitatively analyzed Through coordinate transformation, a curve equation of plane-plate loading test, which is illustrated in the space of axes settlement, load and factor of bearing capacity for soils is established. According to the failure condition defined by soil deformations, the parameters of model are determined and the model is built up. By analysis of test data, it indicated that the studied model is feasible. The cusp-catastrophe model is applied in the prediction of the relationship between load and settlement of several plane-plate loading experiments. Through comparison and verification, it is displayed that the predicted results by cusp catastrophe model are accordance with the test results in a degree.
(2)Study on cusp catastrophe mutation of slope destabilization
Identification methods of slope destabilization are summarized and theirs characteristic and application are pointed out. The feasibility of monitoring time-slope displacement is studied and the application of cusp model to actual monitored data is suggested. Combined practical data of slope the proposed model is tested, which demonstrates the feasibility. Moreover, the prediction of time-displacement rate is performed.
(3)Description of soil constitutive relationship and analysis of flowing rule for soft clay with cusp catastrophe model
Soil constitutive mode that can represent both soft soil's gradual failure and hard soil's abrupt failure is established by using cusp catastrophe theory, which makes the hard and soft's soil model unified in one model. The precision on determining initial shear modulus using the model satisfies practical requirement. Qualitative and quantitive analysis of description of stress-strain relationship for soil with cusp-catastrophe model is made. Analysis and comparison represent that the proposed model is more effective. For saturated soft clay only when the shear stress is greater than the long-term strength, the soil obeys the ideal plastic rule. But when the shear stress is smaller than the long-term strength the deformation of the soil decays gradually under a constant shear stress. A "γ-τ-t" relation with the cusp catastrophe model is proposed which agrees with the test data.
3. Get a series test data on the model with the resonant apparatus of own patent and the computation of middle displacement of Euler pole after bucking.
(1)The computation of middle displacement of Euler pole after bucking
Pole's bucking is one of break problem in engineering. When pressure is smaller than bifurcate load, exoteric disturbance will make the pole deviate initial balanceable form. Allowing for non-linearity of Euler's pole, its differential equation by a precise expression of curvature is established. A program is written to compute it. The relationship between the load, when it is larger than critical load and the displacement of mid-pole is obtained. The study shows that Euler's pole does not lose its bearing capacity when the load is added up to the critical one. Its bearing capacity will be strengthened instead. The results agree well with the test.
(2) The paper also get a series test results on the model of building structure with the resonant apparatus which the author had his own patent.The resonant apparatus adjusted its deviatonic or the inverter so as to get approximately continuously motor force while the motor roated velocityωcould change to any value in its restrict area .So did the motor force.In the dynmatic experiment, amplitude of the top had justment phenomenon.To that suddenly changed amplitude,the thesis gave a catastrophe theory idea constitution to explain the sudden changing amplitude.
1.应用突变理论尖点模型研究砂土的地震液化模型
根据国内外实测液化资料、孔压的各类模型推导出在即将液化时,松土的超静孔隙水压力有突变,而密实土的超静孔隙水压力无突变这一现象,将尖点突变模型成功运用于对地震液化的判断。对Zeeman突变方程进行了重大修改。原始的突变方程是基于Zeeman突变机构得来的,这一模型目前被广泛应用。通过调整各系数可以使孔压、液化的发展更加精确地被方程所反映。通过逐步逼近的方法算出了方程中的参数,同时液化点和分叉曲线也被唯一地确定。通过对国内外液化资料的回判,可以看出此模型有较高的准确性。
2.应用突变理论尖点模型研究土的静力工作状态
(1)尖点突变模型描述静力载荷试验曲线的可行性及应用研究
静力载荷试验主要用于测定承压板下应力主要影响范围内岩土的承载力和变形特性。但其试验时间很长,加载困难,试验结果也难确定。对于较硬土地基而言,当荷载大于某一数值时,基础急剧下降,地基发生突然破坏。而软粘土和松沙地基土的变形是渐变的,没有突变现象。根据静力载荷试验曲线的特点,定性地分析了利用尖点突变模型表达载荷-沉降曲线的可行性。通过坐标变换导出平板载荷试验的载荷-沉降曲线方程在沉降量、施加荷载及承载力因子三维空间中的表达式。根据土的破坏条件,确定出相应参数并建立其尖点突变模型。利用该突变模型对已有的试验进行了预测,预测结果和试验结果吻合较好。
(2)尖点突变模型在边坡失稳中的应用研究
总结目前国内外判别边坡稳定性的方法、分析各种判别方法的优缺点及适用范围。研究尖点突变模型模拟监测时间一坡体变形速率的可行性,提出用突变模型模拟目前国内外滑坡体实际监测数据思想和方法,并建立模型。结合各滑坡体实际监测数据定性的检验了模型研究的可行性,提出了预测的思想,并通过现有的数据对监测时间一变形速率进行了初步的预测。
(3)土本构关系的描述及软粘土流动性的模型研究
利用突变理论尖点模型建立的土的本构模型,该模型既可反映软土的渐变破坏,又能拟合硬土的突变破坏,使以往按土的松软或紧硬程度的区别分别建立的各自相应的本构关系,能够统一于同一个模型中。同时,该模型在求解土初始切线弹性模量上达到了实用上要求的精度,并且对土的应力应变路径进行了定性分析。在此基础上,对土尖点模型描述应力应变路径的可行性进行定量分析。通过分析推导和比较,表明突变理论中的尖点突变模型描述土的应力应变路径,在定量和定性上都是合理的,可行的。对饱和粘性土而言,仅当剪应力小于长期强度时,土体才呈现类似理想体那样的规律;而当剪应力小于长期强度时,土在恒定剪力作用下,变形渐趋停止。本文引用尖顶突变模式,建立了γ-τ-t的数学关系式,然后带入数据检验计算结果表明,理论和实测值吻合较好。由此可见该模型是可用的。
3.对于建筑结构墙体共振振幅的突变性及细长杆突变失稳中点屈曲位移的研究
(1)细长杆突变失稳中点屈曲位移的研究
压杆失稳问题是工程中的突变问题。Euler公式基于小变形的近似方法,由于采用了曲率的近似表达式而无法求得中点屈曲位移δ。为此,本文利用突变理论原理及精确的曲率表达式建立了Euler杆在考虑几何非线性时的微分方程,通过算例揭示了压力大于分叉荷载时压力与中点屈曲位移的关系。研究结果表明,当压力达到荷载分叉点时,Euler杆不会立即丧失承载力,其承载力尚有微量的储备。研究结果与实验结果完全吻合。
(2)本文还应用自创的共振仪对于建筑结构共振振幅的突变性进行验试印证。由作者申请专利的共振仪通过改变偏心块重量W或调节变频器使起振机电机的转速ω近似于连续变化,就可以使起振机获得不同的激振力。将共振机固定在悬臂梁模型顶部中央,在可调变频的共振机上,通过调节共振机的振动频率装置给系统加载。由试验成果可见,振动过程中顶点振幅存在跳跃现象,也即随着激振力增大,系统具有振幅突变特性。
Many phenomena in nature are of uncontinuity that can not be interpreted by calculus. While catastrophe theory can deal with uncontinuity directly and it is unnecessary to relate with any special internal mechanism, which makes it especially fit for the system that internal action is unknown and can be used in the condition that believable observation is discontinuous. The structures of geo-technic engineering break and failure are typically discontinuous phenomena. So the application of catastrophe theory in geo-technic engineering is promising to solve the uncontinuity. Especially the cusp model is characterized by simplify and practicality, which has two control variables, one state variable and an attainable critical surface. Therefore, the phenomena and mechanism in soil engineering, such as slope failure, liquefaction induced by earthquake, stress-strain of hard and soft soil, are described and predicted based on the cusp catastrophe models established by experiments data. The main investigations and achievements are composed of following portions.
1. Estimation of liquefaction based on catastrophe theory
Cusp catastrophe model was applied to construct a model to simulate occurrence of soil liquefaction induced by earthquake. In the proposed model, pore water pressure was looked as a state variable and capability of site anti- liquefaction and received earthquake energy were treated as two control variables. Comparison was made between site earthquake liquefaction information and the results obtained from the proposed method. It is shown that the suggested method is convincing, reliable and practical in the engineering. At the same time, stability problem including any soil body due to critical shear strength can be simulated conveniently. The cusp catastrophe model also has interesting implications for seismic dynamic intensity analysis of soil-structure interaction system and seismic stability analysis of earth dam and slope and so on.
2. The applications of cusp model in static soil mehanics and engineering
(1)Study on application and prediction of cusp-catastrophe model in plane-plate loading test
Based on the property of loading- settlement curve obtained from static loading test, the feasibility of cusp-catastrophe theory applied to the simulation of the curve for plane plate loading test is qualitatively analyzed Through coordinate transformation, a curve equation of plane-plate loading test, which is illustrated in the space of axes settlement, load and factor of bearing capacity for soils is established. According to the failure condition defined by soil deformations, the parameters of model are determined and the model is built up. By analysis of test data, it indicated that the studied model is feasible. The cusp-catastrophe model is applied in the prediction of the relationship between load and settlement of several plane-plate loading experiments. Through comparison and verification, it is displayed that the predicted results by cusp catastrophe model are accordance with the test results in a degree.
(2)Study on cusp catastrophe mutation of slope destabilization
Identification methods of slope destabilization are summarized and theirs characteristic and application are pointed out. The feasibility of monitoring time-slope displacement is studied and the application of cusp model to actual monitored data is suggested. Combined practical data of slope the proposed model is tested, which demonstrates the feasibility. Moreover, the prediction of time-displacement rate is performed.
(3)Description of soil constitutive relationship and analysis of flowing rule for soft clay with cusp catastrophe model
Soil constitutive mode that can represent both soft soil's gradual failure and hard soil's abrupt failure is established by using cusp catastrophe theory, which makes the hard and soft's soil model unified in one model. The precision on determining initial shear modulus using the model satisfies practical requirement. Qualitative and quantitive analysis of description of stress-strain relationship for soil with cusp-catastrophe model is made. Analysis and comparison represent that the proposed model is more effective. For saturated soft clay only when the shear stress is greater than the long-term strength, the soil obeys the ideal plastic rule. But when the shear stress is smaller than the long-term strength the deformation of the soil decays gradually under a constant shear stress. A "γ-τ-t" relation with the cusp catastrophe model is proposed which agrees with the test data.
3. Get a series test data on the model with the resonant apparatus of own patent and the computation of middle displacement of Euler pole after bucking.
(1)The computation of middle displacement of Euler pole after bucking
Pole's bucking is one of break problem in engineering. When pressure is smaller than bifurcate load, exoteric disturbance will make the pole deviate initial balanceable form. Allowing for non-linearity of Euler's pole, its differential equation by a precise expression of curvature is established. A program is written to compute it. The relationship between the load, when it is larger than critical load and the displacement of mid-pole is obtained. The study shows that Euler's pole does not lose its bearing capacity when the load is added up to the critical one. Its bearing capacity will be strengthened instead. The results agree well with the test.
(2) The paper also get a series test results on the model of building structure with the resonant apparatus which the author had his own patent.The resonant apparatus adjusted its deviatonic or the inverter so as to get approximately continuously motor force while the motor roated velocityωcould change to any value in its restrict area .So did the motor force.In the dynmatic experiment, amplitude of the top had justment phenomenon.To that suddenly changed amplitude,the thesis gave a catastrophe theory idea constitution to explain the sudden changing amplitude.
引文
[1]Rene.Thom.Structural stability and morphogenesis.New York:Benjan-Addison Wealer,1975.
[2]Steawart I.Seven elementary catastrophes.New Scientist,1975,20:79-84.
[3]Zeeman E C.Catastrophetheory.In:Zeeman E C.SelectedPapers 1972-1977.London:Addison-Wesley,1977:78-96.
[4]张业民,崔春义.突变理论在土工中应用的哲学基础.辽宁工学院学报,2003,2:15-18.
[5]Gilmore R著.湛垦华等译.科学与工程中的基本突变理论.西安:西安交通大学出版社,1989:86-99.
[6]阿诺午德(苏)著.周燕华译.突变理论.北京:高等教育出版社,1990:96-120.
[7]Poston T and Steawart I.Catastrophe theory and its application.London:Pitman Publishing Limited,1978:45-68.
[8]桑博德著.凌复华译.突变理论入门.上海:上海交通大学出版社,1983:56-84.
[9]张业民.浅基承载力破坏的突变模型.青年力学协会,第四届全国学术年会论文集,武汉,1990:286-290.
[10]John M.Cubitt,Brian Shaw.The Geological Implication of steady-state mechanism in catastrophe theory.Math.Geo,1976,8(4):657-661.
[11]Henley S.Catastrophe theory model in geology.Math.Geo,1976,8(6):6-11.
[12]Potier-Ferry M.Towards a catastrophe theory for the mechanics of plasticity and fracture.Int J Engng Sci,1985,23(8):821-837.
[13]凌复华.突变理论及其应用.上海:上海交通大学出版社,1987:45-69
[14]张业民.模糊数学和突变理论分析场地砂土液化势:(硕士学位论文).大连:大连工学院,1987.
[15]殷有泉,郑顾团.断层地震的尖角型突变模型.地球物理学报,1988,31(6):657-633.
[16]唐春安,徐小荷.岩石破裂过程失稳的尖点突变模.岩石力学与工程学报,1990,9(2):100-107.
[17]秦四清,何怀锋.狭窄煤柱冲击地压失稳的突变理论分析.水文地质工程地质,1995,5(4):17-20.
[18]张业民,宋长清.软粘土流动性的尖顶突变模型分析.岩土工程学报,1995,17(4):67-70.
[19]许强,黄润秋.地震作用下结构非线性响应的突变分析.岩土工程学报,1997,19(4):25-29.
[20]王志强,厉志娟.构件受扭脆坏的折迭突变模型.青岛建筑工程学院学报,2004,25(2):15-30.
[21]张业民.以突变理论探讨无粘性土本构关系.中国土木工程学会第六届土力学及基础工程学术会议论文集,北京,1991.
[22]汪祖民.用突变理论分析高速公路路堤土体稳定性.苏州科技学院学报,2003,16(3):21-24.
[23]房营光.土质边坡失稳的突变性分析.力学与实践,2004,4(26):24-27.
[24]崔春义.尖点突变模型在土静力学中的应用:(硕士学位论文).锦州:辽宁工学院,2002.
[25]高大钊,孙钧.岩土工程的回顾与前瞻.北京:人民交通出版社,2001.
[26]谢定义,刘颖,谢君斐,等.砂土震动液化.北京:地震出版社,1984:96-120.
[27]蒋彭年.土的本构关系.北京:科学出版社,1982.
[28]张业民.土木工程新理论新技术.北京:高等教育出版社,2003.
[29]周健,白冰,徐建平.土动力学理论与计算.北京:中国运输工业出版社,2000:86-98.
[30]Ishihara K.Undrained deformation and liquefaction of sand under cyclic stress.Soils and Foundation,1980,15(1):56-69.
[31]Seed H B,Idriss I M.Soil moduli and damping factors for dynamic response analyses.Califomia:Earthquake Engineering Research Center,1970:120-132.
[32]汪闻韶.土的动力强度和液化特性.北京:中国电力出版社,1997:56-67.
[33]吴世明.土动力学.北京:中国建筑工业出版社,2000,9:185-196.
[34]Seed HB.Dynamic analysis of the slide in the lower San Femando dam during the earthquake of Februry 9,1971.Engrg.Div.,ASCE,1975,101(GT5):45-56.
[35]Dobry R,Ladd R S,Yokel,et al.Prediction of pore water pressure buildup and liquefaction of sands during earthquakes by the cyclic strain method.Building Science,1982,138:140-151.
[36]岩崎敏男.地盘流动化的判定方法.土木技术资,1978,20(4):120-131.
[37]Seed HB.The genneration and dissipation of pore water pressure during soil liquefaction.Universityof California,1975,8:230-251.
[38]何广讷,曹亚林.饱和无粘性土动力反应的能量分析原理与方法.土木工程学报,1990,23(3):45-67.
[39]Nemat S,Shokooh A.A unified approach to densification and liquefaction of cohesionless sand in cyclic shearing..Ir.Canadian Geotech,1979,16(4):89-94.
[40]David R O,Berrill J B.Energy dissipation and seismic ligvafaction in soils.Earthquake Engineering and Structural Danamics,1982,10(1):73-86.
[41]曹亚林,何广讷,林皋.土中振动孔隙水压力增长程度的能量分析法.大连工学院学报,1987,26(3):86-92.
[42]Finn WDL.Liguefaction potential developments since 1976.Int.Conf.on Recent Advances in Geo technical Earthquake Engineeringand Soil Dynamics,London,1981:55-59.
[43]Seed HB,Booker R.Stabilization of potentially liquefiable sand deposits using gravel drains.Jr.of Geotech.Engrg.Div.,1977,103(GT7):56-67.
[44]Rchifman RL.Consolidation of soil under time dependent loading and vary permeability.Research Board,1985,2:56-68.
[45]Wilson NE,Elgohari MM.Consolidations of soils under cyclic loading.Canadian Geotech,1974,2(3):78-93.
[46]Baligh M M,Lavadoux J N.Consolidation theory for cyclic loading.Jr.of Geotech.Engrg.Div.,ASCE,1978,104(GT4):89-95.
[47]Alonso EE,Krizek RJ.Randomness of Settlement rate unter stochastic load.Jr.of Geotech.Engineering Div.,1974,100(6):29-35.
[48]Hall RT,Richart FE.Dissipation of elastic wave energy in granular soils.Journal of the Soil Mechanics and Foundations Division,ASCE 1978,89(SM6):56-68.
[49]徐志英,沈珠江.土坝地震孔隙水压力的产生、扩散和消散的有限元法动力分析.华东水利学院学报,1981,9(4):56-86.
[50]史宏彦,谢定义.饱和砂土地基动力反应分析的瞬态有效应力分析.第5届全国土力学及基础工程学术会议论文选集.北京:中国建筑工业出版社,1987:23-35.
[51]石桥.孔隙水压力上升机理与土的液化.地基基础译文集(1).北京:中国建筑工业出版社,1979:56-67.
[52]周健.尾矿坝在地震作用下的三维两相有效应力动力分析.工程抗震,1995,1:56-67.
[53]周健,徐志英.土(尾矿)坝的三维有效应力的动力反应分析.地震工程与工程震动,1984,14(3):42-53.
[54]Zienkiewicz.Soils and other saturated media under transient dynamic conditions.In:John Wiley and Son.Soil Mechanics Transient and Cyclic Loading.London:1982:56-74.
[55]Wang J N.Pore pressure development during nonuiform cyclic loding.Soils and Foundation,1989,29(2):26-28.
[56]刘汉龙,井和进.大型沉箱式码头岸壁地震反应分析.岩土工程学报,1998,20(2):45-68.
[57]Hardin B O,Drenvich V P.Shear modulus and damping in solid:design equation and curves.Journalof Soil Mechnanics and Foundations Division,ASCE,1972,98(SM7):46-57.
[58]李顺群,张吉明,张业民,等.考虑持时作用的地震能量表达方式.辽宁工程技术大学学报,2004,3(23):306-308.
[59]李顺群,张业民,张爽,等.砂沸的应力演进过程研究.辽宁工程技术大学学报,2003,22(6):769-771.
[60]Casagrand A.Liquefaction and Cyclic Deformation of Sands:A Critical Review[A].Presented at Fifth Panamerican Conference on Soil Mechanics and Foundation Engineering[C].Harvred Soil Mechanics Series,1975,11(88):32-34.
[61]Seed HB,Lee KL.Liquefaction of saturated sands during cyclic loading.ASCE,Jr.of SMFD,1966,92(6):55-58.
[62]Seed HB,Idriss IM.Simplified procedures for evaluating soil liquefaction protential.Jr.of Soil Mechanics and Foudation Div.,1971,97(9):23-31.
[63]Finn W D L,Lee K W,Martin G R.An effective stress model for liquefaction.Jr.of Geotech.Engrg.Div.,ASCE,1976,102(GT4):45-56.
[64]许成顺.复杂应力条件下饱和砂土剪切特性试验研究及本构模型:(博士学位论文):大连理工大学,2006.
[65]Martin GB,finn WDL,Seed HB.Fundamentals of Liquefaction under cyclic loading.Jr.of Geotach.Engrg.Div.,ASCE,1975,101(GT5):45-68.
[66]Mejia LH,Seed HB.Three dimensional dynamic response analysis of earth dams.Report EERC,1987,81(15):65-72.
[67]谢定义,张建民.往返荷载下饱和砂土强度变形瞬态变化的机理.土木工程学报,1987,20(3):78-86.
[68]Finn WDL,Bhatia SK.Prediction of seismic pore water pressures.Proc.ICSMFE,1981,10(3):89-93.
[69]Yemin Zhang.A design approach to geosynthetie reinforced slopes for the agriculture saving heat room.International Symposium Erath Reinforcement,1996,1:299-302.
[70]中华人民共和国建设部.中华人民共和国国家标准建筑抗震设计规范.北京:中国建筑工业出版社.2001:63-72.
[71]沈聚敏,周锡元,高小旺,等.抗震工程学.北京:中国建筑工业出版社,2000:235-251.
[72]Seed HB,Martin PP,Lysmer J.Pore water pressure changes during soil liquefaction.Engrg.Div.,ASCE,1976,102(GT4):44-49.
[73]何广讷,朱范宇,张业民.场地砂土地震液化的模糊聚类分析.地震工程与工程振动,1989,9(4):83-91.
[74]何广讷,郭莹,张业民,等.场地地震液化势的模糊概率分析.大连理工大学学报,1992,(2):209-217.
[75]水本雅晴.模糊数学及其应用.北京:科学出版社,1984:86-98.
[76]石原言而..Prediction of Liquefaction Occurrence of Sand Deposits During Earthquakes by a Stalistical method.土木学会论文报告集,1976:165-186.
[77]Yemin Zhang,Song Changqing.A New Sand Constitution with CUSP Catastrophe.International Comference on computational Methods in Structural and Geotechnical Engineering,Hong Kong,1994.
[78]李顺群,张业民,焦学英,等.基于尖点突变模型的地震液化和孔压研究.应用力学学报,2004,21(4):151-155.
[79]Peiji Yu,Richart FE.Stress effects on shear modulus of dry sand.Jr.Geotech Eng.Div.ASCE,1984,110(3):45-62.
[80]Christian J T,Swiger W F.Statistics of Liquefaction and SPT Results.J Geot Eng Div.ASCE,1975,101(11):1135-1150.
[81]Bazant ZP,et al.Endochronic models for soils.Soil Mechanics-Transient and Cyclic Loads,1982:29-31.
[82]Briaud J L,Tucker L.Coefficient of Variation of in Situ Test Results in Sand.Proceeding of a Symposium Spousored by the ASCE Geot Eng Div in Conjuntion with the ASCE Convention in Attanta,Georgia,1984.
[83]Bowles J E.Foundation Analysis and Design(Second Edition).Me Graw Hill Book Company,1977,141:168-179.
[84]Dafa lisa YF,Herrmann LR.Boundary surface formulation of soil plasticity.Soil Mechanics Transient and Cyclic loading,1982,5:67-81.
[85]Yegian MK,Whitman RV.Risk Analysis for Ground Falure by Liquefaction.J Geot Eng Div.ASCE,1987,104(7):921-938.
[86]张业民,Luan Mao-tian.Estimmion of Liquefaction Based on Catastrophe Theory.计算力学学报,2008.4:43-45.
[87]张业民,郝冬雪.浅基承载力破坏的突变模型,辽宁工程勘察与岩土工程学术会议论文集,2003,9:194-198.
[88]张业民,郝冬雪,栾茂田.尖点突变模型在平板荷载试验中应用及预测研究.大连理大学学报,2007,47(3):392-397.
[89]张业民,刘义贤,吕培印,等.高层建筑地基基础概论.沈阳:辽宁教育出版社,2002:168-169.
[90]黄润秋.岩石工程高边坡稳定性研究的某些理论与实践问题探讨.岩土工程青年专家学术论坛文集.北京:中国建筑工业出版社,1998:210-230.
[91]高大钊.岩土工程的回顾与前瞻.北京:人民交通出版社,2001:123-132.
[92]周乐.尖点突变模型在边坡稳定性中的应用与研究:(硕士学位论文).锦州:辽宁工学院,2006.
[93]周乐,张业民.边坡稳定性判别的几种方法.辽宁工学院学报,2005,24(增刊):47-49.
[94]王在泉.复杂边坡工程系统稳定性研究.徐州:中国矿业大学出版社,1999.
[95]易顺民,晏同珍.滑坡定量预测的非线性理论方法.地学前缘,1997,5(4):17-20.
[96]郝冬雪,张业民,王芳.突变理论在土工中应用的研究进展与展望.辽宁工学院学报,2004,12(24):40-43.
[97]黄文熙.土的工程性质.南京:水利电力出版社,1983:156-168.
[98]张业民.基本建设学术综论.北京:中国社会科学出版社,2005:126-128.
[99]郑颖人,沈珠江,龚晓南.岩土塑性力学原理.北京:中国建筑出版社,2002.
[100]张业民,栾茂田,李顺群.尖点突变模型描述土应力应变特性的可行.武汉理工大学学报,2004,26(8):38-40.
[101]Gere.Timoshenko.材料力学.北京:世界图书出版公司,1992:727-728.
[102]张业民.细长杆屈曲后中点位移的确定.力学与实践,2002,6:36-38.
[103]颜庆津.数值分析.北京:北京航空航天大学出版社,2000:232-243.
[104]应怀樵.振动测试和分析.北京:中国铁道出版社,1987:147-156.
[105]王芳,庞荣丽,张业民.振动检测在砖砌体结构中的应用研究.辽宁工学院学报,2005,4:37-40.
[106]刘习军,贾启芬,张文德.工程振动与测试技术.天津:天津大学出版社,2002:142-151.
[107]骆振黄.工程振动导引.上海:上海交通大学出版社,1988:142-151.
[108]李方泽,刘馥清,王正.共振振动测试与分析.北京:高等教育出版社,1992:157-162.
[109]唐照千,黄文虎.振动与冲击手册(第一卷).北京:国防工业出版社,1988:147-151.
[110]吴尚君,张业民.超有限元法在结构动力计算中应用.第六届国际结构工程青年专家会,2000,8:354-360.
[111]吴尚君,张业民.Super Finite Element Method in dynamic analysis of Shaft Wall.第三届亚太地区计算力学国际会议,汉城,1996.
[112]李顺群,张业民,王英红,等.土木工程结构中隔震技术的发展.辽宁工学院学报,2001,21(5):64-65.
[113]欧珠光.工程振动.武汉:武汉大学出版社,2003:19-21.
[114]王芳,张业民.共振检测的工作原理.土木工程理论与实践,2004,5:97-99.
[115]Yemin Zhang.Building resoname device.Recent Development of Geoteachnical and GEO-ENVIRONMENTAL ENGINEERING IN ASIA,2006,12:585-588.
[116]张业民,苏会.建筑共振装置.建筑振动理论与实践.第四届全国建筑振动学术会议论文集,2004,10:123-129.
[117]张业民等.建筑共振装置.中国,国家实用新型专利公报,ZL 01251069.6.2002.7.31.
[118]刘习军.工程振动理论与测试技术.北京:高等教育出版社,2005:21-31.
[119]任兴民.工程振动基础.北京:机械工业出版社,2006:21-31.
[2]Steawart I.Seven elementary catastrophes.New Scientist,1975,20:79-84.
[3]Zeeman E C.Catastrophetheory.In:Zeeman E C.SelectedPapers 1972-1977.London:Addison-Wesley,1977:78-96.
[4]张业民,崔春义.突变理论在土工中应用的哲学基础.辽宁工学院学报,2003,2:15-18.
[5]Gilmore R著.湛垦华等译.科学与工程中的基本突变理论.西安:西安交通大学出版社,1989:86-99.
[6]阿诺午德(苏)著.周燕华译.突变理论.北京:高等教育出版社,1990:96-120.
[7]Poston T and Steawart I.Catastrophe theory and its application.London:Pitman Publishing Limited,1978:45-68.
[8]桑博德著.凌复华译.突变理论入门.上海:上海交通大学出版社,1983:56-84.
[9]张业民.浅基承载力破坏的突变模型.青年力学协会,第四届全国学术年会论文集,武汉,1990:286-290.
[10]John M.Cubitt,Brian Shaw.The Geological Implication of steady-state mechanism in catastrophe theory.Math.Geo,1976,8(4):657-661.
[11]Henley S.Catastrophe theory model in geology.Math.Geo,1976,8(6):6-11.
[12]Potier-Ferry M.Towards a catastrophe theory for the mechanics of plasticity and fracture.Int J Engng Sci,1985,23(8):821-837.
[13]凌复华.突变理论及其应用.上海:上海交通大学出版社,1987:45-69
[14]张业民.模糊数学和突变理论分析场地砂土液化势:(硕士学位论文).大连:大连工学院,1987.
[15]殷有泉,郑顾团.断层地震的尖角型突变模型.地球物理学报,1988,31(6):657-633.
[16]唐春安,徐小荷.岩石破裂过程失稳的尖点突变模.岩石力学与工程学报,1990,9(2):100-107.
[17]秦四清,何怀锋.狭窄煤柱冲击地压失稳的突变理论分析.水文地质工程地质,1995,5(4):17-20.
[18]张业民,宋长清.软粘土流动性的尖顶突变模型分析.岩土工程学报,1995,17(4):67-70.
[19]许强,黄润秋.地震作用下结构非线性响应的突变分析.岩土工程学报,1997,19(4):25-29.
[20]王志强,厉志娟.构件受扭脆坏的折迭突变模型.青岛建筑工程学院学报,2004,25(2):15-30.
[21]张业民.以突变理论探讨无粘性土本构关系.中国土木工程学会第六届土力学及基础工程学术会议论文集,北京,1991.
[22]汪祖民.用突变理论分析高速公路路堤土体稳定性.苏州科技学院学报,2003,16(3):21-24.
[23]房营光.土质边坡失稳的突变性分析.力学与实践,2004,4(26):24-27.
[24]崔春义.尖点突变模型在土静力学中的应用:(硕士学位论文).锦州:辽宁工学院,2002.
[25]高大钊,孙钧.岩土工程的回顾与前瞻.北京:人民交通出版社,2001.
[26]谢定义,刘颖,谢君斐,等.砂土震动液化.北京:地震出版社,1984:96-120.
[27]蒋彭年.土的本构关系.北京:科学出版社,1982.
[28]张业民.土木工程新理论新技术.北京:高等教育出版社,2003.
[29]周健,白冰,徐建平.土动力学理论与计算.北京:中国运输工业出版社,2000:86-98.
[30]Ishihara K.Undrained deformation and liquefaction of sand under cyclic stress.Soils and Foundation,1980,15(1):56-69.
[31]Seed H B,Idriss I M.Soil moduli and damping factors for dynamic response analyses.Califomia:Earthquake Engineering Research Center,1970:120-132.
[32]汪闻韶.土的动力强度和液化特性.北京:中国电力出版社,1997:56-67.
[33]吴世明.土动力学.北京:中国建筑工业出版社,2000,9:185-196.
[34]Seed HB.Dynamic analysis of the slide in the lower San Femando dam during the earthquake of Februry 9,1971.Engrg.Div.,ASCE,1975,101(GT5):45-56.
[35]Dobry R,Ladd R S,Yokel,et al.Prediction of pore water pressure buildup and liquefaction of sands during earthquakes by the cyclic strain method.Building Science,1982,138:140-151.
[36]岩崎敏男.地盘流动化的判定方法.土木技术资,1978,20(4):120-131.
[37]Seed HB.The genneration and dissipation of pore water pressure during soil liquefaction.Universityof California,1975,8:230-251.
[38]何广讷,曹亚林.饱和无粘性土动力反应的能量分析原理与方法.土木工程学报,1990,23(3):45-67.
[39]Nemat S,Shokooh A.A unified approach to densification and liquefaction of cohesionless sand in cyclic shearing..Ir.Canadian Geotech,1979,16(4):89-94.
[40]David R O,Berrill J B.Energy dissipation and seismic ligvafaction in soils.Earthquake Engineering and Structural Danamics,1982,10(1):73-86.
[41]曹亚林,何广讷,林皋.土中振动孔隙水压力增长程度的能量分析法.大连工学院学报,1987,26(3):86-92.
[42]Finn WDL.Liguefaction potential developments since 1976.Int.Conf.on Recent Advances in Geo technical Earthquake Engineeringand Soil Dynamics,London,1981:55-59.
[43]Seed HB,Booker R.Stabilization of potentially liquefiable sand deposits using gravel drains.Jr.of Geotech.Engrg.Div.,1977,103(GT7):56-67.
[44]Rchifman RL.Consolidation of soil under time dependent loading and vary permeability.Research Board,1985,2:56-68.
[45]Wilson NE,Elgohari MM.Consolidations of soils under cyclic loading.Canadian Geotech,1974,2(3):78-93.
[46]Baligh M M,Lavadoux J N.Consolidation theory for cyclic loading.Jr.of Geotech.Engrg.Div.,ASCE,1978,104(GT4):89-95.
[47]Alonso EE,Krizek RJ.Randomness of Settlement rate unter stochastic load.Jr.of Geotech.Engineering Div.,1974,100(6):29-35.
[48]Hall RT,Richart FE.Dissipation of elastic wave energy in granular soils.Journal of the Soil Mechanics and Foundations Division,ASCE 1978,89(SM6):56-68.
[49]徐志英,沈珠江.土坝地震孔隙水压力的产生、扩散和消散的有限元法动力分析.华东水利学院学报,1981,9(4):56-86.
[50]史宏彦,谢定义.饱和砂土地基动力反应分析的瞬态有效应力分析.第5届全国土力学及基础工程学术会议论文选集.北京:中国建筑工业出版社,1987:23-35.
[51]石桥.孔隙水压力上升机理与土的液化.地基基础译文集(1).北京:中国建筑工业出版社,1979:56-67.
[52]周健.尾矿坝在地震作用下的三维两相有效应力动力分析.工程抗震,1995,1:56-67.
[53]周健,徐志英.土(尾矿)坝的三维有效应力的动力反应分析.地震工程与工程震动,1984,14(3):42-53.
[54]Zienkiewicz.Soils and other saturated media under transient dynamic conditions.In:John Wiley and Son.Soil Mechanics Transient and Cyclic Loading.London:1982:56-74.
[55]Wang J N.Pore pressure development during nonuiform cyclic loding.Soils and Foundation,1989,29(2):26-28.
[56]刘汉龙,井和进.大型沉箱式码头岸壁地震反应分析.岩土工程学报,1998,20(2):45-68.
[57]Hardin B O,Drenvich V P.Shear modulus and damping in solid:design equation and curves.Journalof Soil Mechnanics and Foundations Division,ASCE,1972,98(SM7):46-57.
[58]李顺群,张吉明,张业民,等.考虑持时作用的地震能量表达方式.辽宁工程技术大学学报,2004,3(23):306-308.
[59]李顺群,张业民,张爽,等.砂沸的应力演进过程研究.辽宁工程技术大学学报,2003,22(6):769-771.
[60]Casagrand A.Liquefaction and Cyclic Deformation of Sands:A Critical Review[A].Presented at Fifth Panamerican Conference on Soil Mechanics and Foundation Engineering[C].Harvred Soil Mechanics Series,1975,11(88):32-34.
[61]Seed HB,Lee KL.Liquefaction of saturated sands during cyclic loading.ASCE,Jr.of SMFD,1966,92(6):55-58.
[62]Seed HB,Idriss IM.Simplified procedures for evaluating soil liquefaction protential.Jr.of Soil Mechanics and Foudation Div.,1971,97(9):23-31.
[63]Finn W D L,Lee K W,Martin G R.An effective stress model for liquefaction.Jr.of Geotech.Engrg.Div.,ASCE,1976,102(GT4):45-56.
[64]许成顺.复杂应力条件下饱和砂土剪切特性试验研究及本构模型:(博士学位论文):大连理工大学,2006.
[65]Martin GB,finn WDL,Seed HB.Fundamentals of Liquefaction under cyclic loading.Jr.of Geotach.Engrg.Div.,ASCE,1975,101(GT5):45-68.
[66]Mejia LH,Seed HB.Three dimensional dynamic response analysis of earth dams.Report EERC,1987,81(15):65-72.
[67]谢定义,张建民.往返荷载下饱和砂土强度变形瞬态变化的机理.土木工程学报,1987,20(3):78-86.
[68]Finn WDL,Bhatia SK.Prediction of seismic pore water pressures.Proc.ICSMFE,1981,10(3):89-93.
[69]Yemin Zhang.A design approach to geosynthetie reinforced slopes for the agriculture saving heat room.International Symposium Erath Reinforcement,1996,1:299-302.
[70]中华人民共和国建设部.中华人民共和国国家标准建筑抗震设计规范.北京:中国建筑工业出版社.2001:63-72.
[71]沈聚敏,周锡元,高小旺,等.抗震工程学.北京:中国建筑工业出版社,2000:235-251.
[72]Seed HB,Martin PP,Lysmer J.Pore water pressure changes during soil liquefaction.Engrg.Div.,ASCE,1976,102(GT4):44-49.
[73]何广讷,朱范宇,张业民.场地砂土地震液化的模糊聚类分析.地震工程与工程振动,1989,9(4):83-91.
[74]何广讷,郭莹,张业民,等.场地地震液化势的模糊概率分析.大连理工大学学报,1992,(2):209-217.
[75]水本雅晴.模糊数学及其应用.北京:科学出版社,1984:86-98.
[76]石原言而..Prediction of Liquefaction Occurrence of Sand Deposits During Earthquakes by a Stalistical method.土木学会论文报告集,1976:165-186.
[77]Yemin Zhang,Song Changqing.A New Sand Constitution with CUSP Catastrophe.International Comference on computational Methods in Structural and Geotechnical Engineering,Hong Kong,1994.
[78]李顺群,张业民,焦学英,等.基于尖点突变模型的地震液化和孔压研究.应用力学学报,2004,21(4):151-155.
[79]Peiji Yu,Richart FE.Stress effects on shear modulus of dry sand.Jr.Geotech Eng.Div.ASCE,1984,110(3):45-62.
[80]Christian J T,Swiger W F.Statistics of Liquefaction and SPT Results.J Geot Eng Div.ASCE,1975,101(11):1135-1150.
[81]Bazant ZP,et al.Endochronic models for soils.Soil Mechanics-Transient and Cyclic Loads,1982:29-31.
[82]Briaud J L,Tucker L.Coefficient of Variation of in Situ Test Results in Sand.Proceeding of a Symposium Spousored by the ASCE Geot Eng Div in Conjuntion with the ASCE Convention in Attanta,Georgia,1984.
[83]Bowles J E.Foundation Analysis and Design(Second Edition).Me Graw Hill Book Company,1977,141:168-179.
[84]Dafa lisa YF,Herrmann LR.Boundary surface formulation of soil plasticity.Soil Mechanics Transient and Cyclic loading,1982,5:67-81.
[85]Yegian MK,Whitman RV.Risk Analysis for Ground Falure by Liquefaction.J Geot Eng Div.ASCE,1987,104(7):921-938.
[86]张业民,Luan Mao-tian.Estimmion of Liquefaction Based on Catastrophe Theory.计算力学学报,2008.4:43-45.
[87]张业民,郝冬雪.浅基承载力破坏的突变模型,辽宁工程勘察与岩土工程学术会议论文集,2003,9:194-198.
[88]张业民,郝冬雪,栾茂田.尖点突变模型在平板荷载试验中应用及预测研究.大连理大学学报,2007,47(3):392-397.
[89]张业民,刘义贤,吕培印,等.高层建筑地基基础概论.沈阳:辽宁教育出版社,2002:168-169.
[90]黄润秋.岩石工程高边坡稳定性研究的某些理论与实践问题探讨.岩土工程青年专家学术论坛文集.北京:中国建筑工业出版社,1998:210-230.
[91]高大钊.岩土工程的回顾与前瞻.北京:人民交通出版社,2001:123-132.
[92]周乐.尖点突变模型在边坡稳定性中的应用与研究:(硕士学位论文).锦州:辽宁工学院,2006.
[93]周乐,张业民.边坡稳定性判别的几种方法.辽宁工学院学报,2005,24(增刊):47-49.
[94]王在泉.复杂边坡工程系统稳定性研究.徐州:中国矿业大学出版社,1999.
[95]易顺民,晏同珍.滑坡定量预测的非线性理论方法.地学前缘,1997,5(4):17-20.
[96]郝冬雪,张业民,王芳.突变理论在土工中应用的研究进展与展望.辽宁工学院学报,2004,12(24):40-43.
[97]黄文熙.土的工程性质.南京:水利电力出版社,1983:156-168.
[98]张业民.基本建设学术综论.北京:中国社会科学出版社,2005:126-128.
[99]郑颖人,沈珠江,龚晓南.岩土塑性力学原理.北京:中国建筑出版社,2002.
[100]张业民,栾茂田,李顺群.尖点突变模型描述土应力应变特性的可行.武汉理工大学学报,2004,26(8):38-40.
[101]Gere.Timoshenko.材料力学.北京:世界图书出版公司,1992:727-728.
[102]张业民.细长杆屈曲后中点位移的确定.力学与实践,2002,6:36-38.
[103]颜庆津.数值分析.北京:北京航空航天大学出版社,2000:232-243.
[104]应怀樵.振动测试和分析.北京:中国铁道出版社,1987:147-156.
[105]王芳,庞荣丽,张业民.振动检测在砖砌体结构中的应用研究.辽宁工学院学报,2005,4:37-40.
[106]刘习军,贾启芬,张文德.工程振动与测试技术.天津:天津大学出版社,2002:142-151.
[107]骆振黄.工程振动导引.上海:上海交通大学出版社,1988:142-151.
[108]李方泽,刘馥清,王正.共振振动测试与分析.北京:高等教育出版社,1992:157-162.
[109]唐照千,黄文虎.振动与冲击手册(第一卷).北京:国防工业出版社,1988:147-151.
[110]吴尚君,张业民.超有限元法在结构动力计算中应用.第六届国际结构工程青年专家会,2000,8:354-360.
[111]吴尚君,张业民.Super Finite Element Method in dynamic analysis of Shaft Wall.第三届亚太地区计算力学国际会议,汉城,1996.
[112]李顺群,张业民,王英红,等.土木工程结构中隔震技术的发展.辽宁工学院学报,2001,21(5):64-65.
[113]欧珠光.工程振动.武汉:武汉大学出版社,2003:19-21.
[114]王芳,张业民.共振检测的工作原理.土木工程理论与实践,2004,5:97-99.
[115]Yemin Zhang.Building resoname device.Recent Development of Geoteachnical and GEO-ENVIRONMENTAL ENGINEERING IN ASIA,2006,12:585-588.
[116]张业民,苏会.建筑共振装置.建筑振动理论与实践.第四届全国建筑振动学术会议论文集,2004,10:123-129.
[117]张业民等.建筑共振装置.中国,国家实用新型专利公报,ZL 01251069.6.2002.7.31.
[118]刘习军.工程振动理论与测试技术.北京:高等教育出版社,2005:21-31.
[119]任兴民.工程振动基础.北京:机械工业出版社,2006:21-31.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |