动力机器基础设计理论研究
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摘要
本文首先讨论了质量—弹簧—阻尼器理论和弹性半空间理论两种理论的优缺点,然后根据弹性半空间理论近几十年的发展成果,采用方程对等法推演出一套适合质量—弹簧—阻尼器理论的复合集总参数模型。该模型的可靠性已经过理论和试验证明,并通过工程实例(采用本文所提出的模型对125000kN压力机基础的动力响应计算)进一步说明该模型的可靠性。在中国工程建设标准化协会课题“动力机器基础设计理论及其应用研究”的资助下,本文作者经过多年研究,完成以下主要研究工作：
1.根据弹性半空间理论及基础振动试验和数值计算的最新成果,采用方程对等法推演出一套适合任意形状、任意埋置状况、任意频率和任意泊松比的块体基础竖向、扭转、滑移和摇摆振动的复合集总参数模型。
2.运用该模型对复杂形状明置和埋置块体基础分别在竖向、扭转、水平和摇摆谐和扰力作用下的动力响应进行计算,并将计算结果与采用弹性半空间理论所得到的刚度和阻尼系数计算公式(由大量试验、数值计算所证实)的计算结果进行比较,结果表明,两者计算结果非常吻合,误差分别为：竖向明置基础1.95%,埋置基础10.7%；扭转明置基础3.13%,埋置基础2.31%；滑移明置基础9.16%,埋置基础22.91%；摇摆明置基础0.17%,埋置基础12.31%。
3.在20m×10mx4m土坑内,分别采用底面形状为0.5m×0.5m,质量283kg和底面1.0mx0.5m,质量566kg混凝土块体模型基础,采用自制脱钩装置使质量5.5kg的圆形钢球发生自由落体运动和圆弧运动,分别对两种不同底面形状在明置和埋置状况下的块体模型基础施加竖向和水平冲击荷载使基础发生竖向和扭转自由振动。
4.将试验结果与采用基础竖向、扭转振动复合集总参数模型的计算结果进行比较,结果表明,试验结果与计算结果吻合较好。竖向振动时底面形状0.5mx0.5m和1.0mx0.5m明置基础误差分别为16.2%和44.4%,埋置基础误差分别为33.2%和26.3%；扭转振动时底面形状0.5mx0.5m和1.0mx0.5m明置基础误差分别为7.8%和15.5%,埋置基础误差分别为14.1%和14.5%。
5.采用本文所提出的复合集总参数模型对125000kN压力机基础动力响应进行计算,并将计算结果与采用《动力机器基础设计规范》、波的散射理论的计算结果及实测结果进行比较,结果表明,本文所提出的复合集总参数模型是正确的,在这3种计算模型的计算结果中,本文所提出的复合集总参数模型所计算的振幅值是最小的,因此采用本文所提出的模型进行动力机器基础设计是最即经济的。
本文推导出的块体基础复合集总参数模型,把弹性半空间理论基础振动所得到的与激振力频率有关的动力特性参数,转化为与激振力频率无关的定参数。该模型具有概念明确、计算简单的优点,对于任意形状、任意埋置状况的动力设备块体基础都能使用。采用该模型可以不做试验或少做试验,只要已知地基土的剪切模量、基础底面形状及埋置状况就可以利用机械多自由度振动理论计算弹性半空间上块体基础的动力响应。本模型不受无量纲频率因数的影响,理论上可以适用于包括连续频率在内的所有频率,对于结构工程的地震响应计算具有参考意义。
The advantages and disadvantages of the theory of quality-spring-damper and the theory of elastic half-space were discussed in this dissertation first, and based on the results of the development of elastic half-space theory in recent decades, developed a set of composite lumped parameter model compatible with the theory of quality-spring-damper using equation equivalence method, its reliability has been proved by the theory and the author,s experiment, And using the engineering examples (the dynamic response of125000kN press foundation was calculated by making use of this model), the results of calculations were compared to further illustrate the reliability of the model. In the underfunded of China Association for Engineering Construction Standardization project'study of dynamic machine foundation design theory and its application', the main achievements of this dissertation what the author studys after years are described as follows:
1.Based on elastic half-space theory and the latest research results of the foundations oscillating experiments and numerical analysis, a set of the composite lumped parameter model (CLPM) was developed by adopting equation equivalence method, which suits to vertical, torsional, swaying and rocking vibration of the lumped foundation. All of oscillation frequencies, a realistic range of Poisson's ratios, all foundation base shapes, and complicated embedment are considered.
2. With the new model, dynamic responses of a complicatedly-shaped surface and embedment foundation vibration harmonic vertically, torsionally, horizontally, rockily is calculated respectively and in good agreement with the results obtained by the formulas(supported by results of comprehensive experimental and numerical analysis), which have been developed by the theory of elastic half-space for computing the dynamic stiffness and damping coefficient of foundations harmonically oscillating on a homogeneous half-space, the amplitude difference of surface and embedment foundation is:verticality1.95%and embedment10.7%, torsion3.13%and embedment2.31%, horizontality9.16%and embedment22.91%, in lateral direction, rock0.17%and embedment12.31%, respectively.
3. In the pits of20m×10m×4m, based on concrete lumped model of foundation designed for0.5m×0.5m,283kg and1.0m×0.5m,566kg, a steel ball of5.5kg happens free-fall motion and circular motion by the initial velocity. Free vibration of foundation perturbed vertically and torsionally was achieved in case of surface and embedment respectively.
4. Compare the result of experiment to the result of calculation performed with vertical and torsional CLPM, which shows a better closed agreement is found. The difference of vertically vibration of0.5m×0.5m and1.0m×0.5m surface foundation is16.2%and44.4%respectively, embedment foundation is33.2%and26.3%respectively; the difference of torsion vibration of0.5m×0.5m and1.0m×0.5m surface foundation is7.8%and14.1%respectively, embedment foundation is15.5%and14.5%respectively.
5.The dynamic response of125000kN press foundation was calculated by making use of this CLPM proposed in this paper and the cod for design of dynamic machine foundation and the theory of wave scattering, the results of calculations were compared with the experimental results to further illustrate the model is correct. The amplitude of calculation of125000kN press foundation by making use of three models, the amplitude of calculations of the CLPM proposed in this paper is the smallest that it is the most economical in the design of dynamic machine foundation by using the model presented in this paper.
The CLPM of block foundation deduced in this paper translates the dynamic parameter of the relevant frequency parameters based on theory of half-space elastic, into constant parameters which has nothing to do with frequency of perturbation load. The advantages of the composite lumped parameter model are clear concept and simple calculation. It is practical for power equipment lumped foundation of arbitrarily shaped and complicatedly embedded lumped foundations. Adopting CLPM can reduce or omit experiments. The multiple degrees of mechanical vibration theory can be used to canculate the dynamic response of block foundation based on elastic half-space as long as the known of foundation soil shear modulus, basic bottom shape and buried for status. This model from the dimensionless frequency factor influence, theoretically, applies to all frequencies including continuous frequency, playing an important reference role for the earthquake response analysis of structural engineering.
1.根据弹性半空间理论及基础振动试验和数值计算的最新成果,采用方程对等法推演出一套适合任意形状、任意埋置状况、任意频率和任意泊松比的块体基础竖向、扭转、滑移和摇摆振动的复合集总参数模型。
2.运用该模型对复杂形状明置和埋置块体基础分别在竖向、扭转、水平和摇摆谐和扰力作用下的动力响应进行计算,并将计算结果与采用弹性半空间理论所得到的刚度和阻尼系数计算公式(由大量试验、数值计算所证实)的计算结果进行比较,结果表明,两者计算结果非常吻合,误差分别为：竖向明置基础1.95%,埋置基础10.7%；扭转明置基础3.13%,埋置基础2.31%；滑移明置基础9.16%,埋置基础22.91%；摇摆明置基础0.17%,埋置基础12.31%。
3.在20m×10mx4m土坑内,分别采用底面形状为0.5m×0.5m,质量283kg和底面1.0mx0.5m,质量566kg混凝土块体模型基础,采用自制脱钩装置使质量5.5kg的圆形钢球发生自由落体运动和圆弧运动,分别对两种不同底面形状在明置和埋置状况下的块体模型基础施加竖向和水平冲击荷载使基础发生竖向和扭转自由振动。
4.将试验结果与采用基础竖向、扭转振动复合集总参数模型的计算结果进行比较,结果表明,试验结果与计算结果吻合较好。竖向振动时底面形状0.5mx0.5m和1.0mx0.5m明置基础误差分别为16.2%和44.4%,埋置基础误差分别为33.2%和26.3%；扭转振动时底面形状0.5mx0.5m和1.0mx0.5m明置基础误差分别为7.8%和15.5%,埋置基础误差分别为14.1%和14.5%。
5.采用本文所提出的复合集总参数模型对125000kN压力机基础动力响应进行计算,并将计算结果与采用《动力机器基础设计规范》、波的散射理论的计算结果及实测结果进行比较,结果表明,本文所提出的复合集总参数模型是正确的,在这3种计算模型的计算结果中,本文所提出的复合集总参数模型所计算的振幅值是最小的,因此采用本文所提出的模型进行动力机器基础设计是最即经济的。
本文推导出的块体基础复合集总参数模型,把弹性半空间理论基础振动所得到的与激振力频率有关的动力特性参数,转化为与激振力频率无关的定参数。该模型具有概念明确、计算简单的优点,对于任意形状、任意埋置状况的动力设备块体基础都能使用。采用该模型可以不做试验或少做试验,只要已知地基土的剪切模量、基础底面形状及埋置状况就可以利用机械多自由度振动理论计算弹性半空间上块体基础的动力响应。本模型不受无量纲频率因数的影响,理论上可以适用于包括连续频率在内的所有频率,对于结构工程的地震响应计算具有参考意义。
The advantages and disadvantages of the theory of quality-spring-damper and the theory of elastic half-space were discussed in this dissertation first, and based on the results of the development of elastic half-space theory in recent decades, developed a set of composite lumped parameter model compatible with the theory of quality-spring-damper using equation equivalence method, its reliability has been proved by the theory and the author,s experiment, And using the engineering examples (the dynamic response of125000kN press foundation was calculated by making use of this model), the results of calculations were compared to further illustrate the reliability of the model. In the underfunded of China Association for Engineering Construction Standardization project'study of dynamic machine foundation design theory and its application', the main achievements of this dissertation what the author studys after years are described as follows:
1.Based on elastic half-space theory and the latest research results of the foundations oscillating experiments and numerical analysis, a set of the composite lumped parameter model (CLPM) was developed by adopting equation equivalence method, which suits to vertical, torsional, swaying and rocking vibration of the lumped foundation. All of oscillation frequencies, a realistic range of Poisson's ratios, all foundation base shapes, and complicated embedment are considered.
2. With the new model, dynamic responses of a complicatedly-shaped surface and embedment foundation vibration harmonic vertically, torsionally, horizontally, rockily is calculated respectively and in good agreement with the results obtained by the formulas(supported by results of comprehensive experimental and numerical analysis), which have been developed by the theory of elastic half-space for computing the dynamic stiffness and damping coefficient of foundations harmonically oscillating on a homogeneous half-space, the amplitude difference of surface and embedment foundation is:verticality1.95%and embedment10.7%, torsion3.13%and embedment2.31%, horizontality9.16%and embedment22.91%, in lateral direction, rock0.17%and embedment12.31%, respectively.
3. In the pits of20m×10m×4m, based on concrete lumped model of foundation designed for0.5m×0.5m,283kg and1.0m×0.5m,566kg, a steel ball of5.5kg happens free-fall motion and circular motion by the initial velocity. Free vibration of foundation perturbed vertically and torsionally was achieved in case of surface and embedment respectively.
4. Compare the result of experiment to the result of calculation performed with vertical and torsional CLPM, which shows a better closed agreement is found. The difference of vertically vibration of0.5m×0.5m and1.0m×0.5m surface foundation is16.2%and44.4%respectively, embedment foundation is33.2%and26.3%respectively; the difference of torsion vibration of0.5m×0.5m and1.0m×0.5m surface foundation is7.8%and14.1%respectively, embedment foundation is15.5%and14.5%respectively.
5.The dynamic response of125000kN press foundation was calculated by making use of this CLPM proposed in this paper and the cod for design of dynamic machine foundation and the theory of wave scattering, the results of calculations were compared with the experimental results to further illustrate the model is correct. The amplitude of calculation of125000kN press foundation by making use of three models, the amplitude of calculations of the CLPM proposed in this paper is the smallest that it is the most economical in the design of dynamic machine foundation by using the model presented in this paper.
The CLPM of block foundation deduced in this paper translates the dynamic parameter of the relevant frequency parameters based on theory of half-space elastic, into constant parameters which has nothing to do with frequency of perturbation load. The advantages of the composite lumped parameter model are clear concept and simple calculation. It is practical for power equipment lumped foundation of arbitrarily shaped and complicatedly embedded lumped foundations. Adopting CLPM can reduce or omit experiments. The multiple degrees of mechanical vibration theory can be used to canculate the dynamic response of block foundation based on elastic half-space as long as the known of foundation soil shear modulus, basic bottom shape and buried for status. This model from the dimensionless frequency factor influence, theoretically, applies to all frequencies including continuous frequency, playing an important reference role for the earthquake response analysis of structural engineering.
引文
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