土—细长结构物相互作用的非线性动力学研究
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摘要
在土木工程领域，土-结构相互作用问题是结构动力响应分析及相关设计的重要组成部分。在地震动激励下，以大跨度桥梁和重大岩土工程为例，其下部结构物的动力响应均对结构体系的抗震性能有重要影响。由工程实际可知，结构物的下部基础通常为细长结构物，且按基本特征可分为横向细长结构物(弹性地基梁)和纵向细长结构物(桩)。从传统的观点看，已有研究普遍认为弹性地基对其支承结构物有较强的约束作用，并将显著抑制土-结构相互作用的动力响应。因此，对于土-细长结构物相互作用的已有研究则多关注其线性特性，并弱化了土-结构相互作用特性对于结构物动力响应的影响效应。显然，将非线性动力学理论运用到土-细长结构物相互作用动力响应建模及分析的研究仍十分少见。
为精确揭示土-细长结构物相互作用的动力响应，需要将土-结构相互作用效应在结构动力响应中的贡献引入到系统的建模分析中。通过系统研究可知，若考虑土-结构相互作用引起的二次弯矩效应，则土-细长结构物相互作用精细化模型的非线性动力学方程中将含有多种非线性项：平方非线性、立方非线性和参数激励项。因此，从非线性动力学角度看，此时土-细长结构物相互作用的动力响应中可能存在非常丰富的非线性动力学现象。为全面揭示土-细长结构物相互作用的非线性动力学特性，本论文考虑土-结构相互作用影响效应及细长结构物的几何非线性，建立了弹性地基梁和桩的精细化动力学模型。进而，结合非线性动力学理论，运用多尺度方法对土-细长结构物的非线性动力响应进行系统研究。同时，基于理论计算结果，分析了弹性地基参数、地基模型、边界约束等对土-细长结构物相互作用非线性动力响应的影响。最终，为促进研究成果的应用，与理论试验设计和统计分析相结合，针对土-细长结构物相互作用的非线性动力响应提出了动力参数筛选及设计方法。本论文的主要内容及创新点为以下几个方面：
1.鉴于土-结构相互作用问题的重要性，本文首次将土-结构相互作用引起的二次弯矩效应引入到非线性动力学研究中。基于本文研究可知，土-结构相互作用引起的非线性特性可归为一类新的非线性现象。新非线性特性的发现拓展了非线性动力学的理论研究，有重要的理论意义。
2.为研究弹性地基模型对其支承结构物动力响应特性的影响，本文在推导出三参数(Kerr模型)地基反力的显式近似表达式的基础上，给出了四种常见模型(Winkler、Vlasov、Pasternak、Kerr)地基反力的统一表达式。进而，提出了弹性地基模型对结构物动力响应影响效应的对比评价方法。
3.将土-结构相互作用产生的二次弯矩效应引入到土-细长结构物的动力学建模中，分别利用Newton法和Hamilton原理建立了弹性地基梁的非线性动力学模型。进而，研究了土-结构相互作用效应对于弹性地基梁非线性动力响应特性的影响。并且，通过弹性地基梁非线性内共振响应研究发现，二次弯矩效应导致了连续系统保守特性的破坏。
4.基于本文所建模型，对弹性地基梁的自由振动进行了分析，发现其面内运动固有频率谱中存在截止频率。进而，对比研究了系统在截止频率前后的模态构型及线性和非线性动力响应特性。显然，本文提出的精细化模型可更全面地揭示不同场地支承时细长结构物的动力学特性。
5.将二次弯矩效应影响引入到纵向细长结构物的动力响应研究中，运用Hamilton原理建立了水平/轴向受荷桩的非线性动力学分析模型。进而，与非线性动力学理论相结合，研究了桩的多阶屈曲现象及屈曲频率问题。为拓展研究并结合工程实践需求，在群桩基础的非线性动力响应研究中考虑群桩效应影响，并对比研究了群桩效应对系统动力响应中土-结构相互作用效应的影响。
6.基于理论试验设计和统计分析方法，提出了土-细长结构物相互作用的动力参数设计。利用该动力参数设计方法，可有效地筛选出对目标响应影响显著的关键参数，并可量化和直观展现参数的影响效应，进而为结构的动力设计和优化提供理论指导。
In the civil engineering, the soil-structure interaction problem is an important partof the dynamic design and analyze of the structure. In general, the dynamics responses ofthe substructure play an important role in the seismic behavior of the large-span bridgesand major geotechnical engineering. Based on the engineering practice, the foundationof the structure usually can be defined as the slender structure, including the transverseslender structure (the beam on the elastic foundation) and the vertical slender structure(the pile foundation). As we know, the researchers usually think that the foundations playan role of strong constraint on the structure supported by them, which may significantlyinhibit the dynamic response of the soil-structure interaction system. Obviously, there areonly few studies have focused on the modelling and nonlinear response of the soil-slenderstructure via the theory of the nonlinear dynamics.
To accurately reveal the vibration nature of the soil-slender structure interaction, therefined model of the soil-slender structure should be proposed considering the efect of thesoil-structure interaction on the dynamic response of the system. Obviously, consideringthe second-order moment, the nonlinear motion equation of the refined model of the soil-slender structure includes a variety of nonlinear terms: the quadratic nonlinear, cubicnonlinear and parametric excitation terms. Predictably, the more complex nonlineardynamics of the soil-slender structure would be observed. Applying the theory of thenonlinear dynamics and considering the efect of the second-order moment and geometricnonlinearity of the slender structure, the nonlinear dynamics models of the beam onelastic foundation and the pile are obtained. Then, applying the theory of nonlineardynamics, the nonlinear response of the soil-slender structure are studied via the methodof multiple scales. Moreover, based on the numerical results, the efects of the foundationmodels, the parameters of the foundation and the boundary condition of the structureon the nonlinear response of the system is investigated. Finally, applying the design ofexperiment and the statistical analysis, the dynamic parameter design of the soil-slenderstructure is proposed. The main contribution of this paper as following:
1. In view of the soil-structure interaction problem is very importance, the efect ofthe second-order moment caused by the soil-structure interaction is considered inthe research of the nonlinear dynamics. Based on the present study, it is need topoint out that the nonlinearity of interaction can be defined as a new class of thenonlinear dynamical nature. In general, the find of the new nonlinear nature expands the theory of nonlinear dynamics, which has the important theoretical significance.
2. To analyze the efect of the foundation models on the dynamic response of the struc-ture, the same mathematical form of the subgrade reaction of diferent foundationmodels (Winkler, Vlasov, Pasternak, Kerr) is proposed based on the the explicitexpression of the subgrade reaction of the Kerr model. Moreover, the assessment ofthe foundation models is investigated.
3. Considering the second-order moment cased by soil-structure interaction, the refinedmodel of the beam on the elastic foundation is derived via the Newton’s secondlaw of motion and the Hamilton primary, respectively. Then, the efect of the soil-structure interaction on the nonlinear response of the beam on the elastic foundationis investigated. Moreover, the results of the internal resonance response of thebeam of the elastic foundation show that, the second-order moment destroys theconservative nature of the soil-structure interaction system.
4. Applying the present model of the beam on the elastic foundation, the analysis of thefree vibration of the beam on the elastic foundation is investigated. The numericalresults show that the cut-of frequency is discovered in the in-plane natural frequencyspectrum of the beam on the elastic foundation. Moreover, the mode shapes andlinear or nonlinear response of the beam on the system is investigated. Obviously,the present model can reflect the nonlinear response of the soil-structure interactionsystem, in any cases.
5. The nonlinear dynamics model of the pile foundation subjected to the lat-eral/vertical excitation is obtained via the Hamilton primary. Moreover, combinedwith the theory of nonlinear dynamics, the multi-order buckling phenomenon andthe variation of the frequencies of the pile are investigated. To meet the engineer-ing practice, the efect of the pile-group-efect on the nonlinear response of the pilefoundation is performed. Compared the nonlinear vibration of diferent piles inthe pile group, the efect of the pile-group-efect on the soil-structure interaction isinvestigated.
6. Based on the design of experiment and the statistical analysis, the dynamic parame-ter design of the soil-slender structure interaction system is proposed. Applying thismethod, the key parameter of the nonlinear response of the system can be screenedout, and can be used for the dynamic design and optimization of structure.
为精确揭示土-细长结构物相互作用的动力响应，需要将土-结构相互作用效应在结构动力响应中的贡献引入到系统的建模分析中。通过系统研究可知，若考虑土-结构相互作用引起的二次弯矩效应，则土-细长结构物相互作用精细化模型的非线性动力学方程中将含有多种非线性项：平方非线性、立方非线性和参数激励项。因此，从非线性动力学角度看，此时土-细长结构物相互作用的动力响应中可能存在非常丰富的非线性动力学现象。为全面揭示土-细长结构物相互作用的非线性动力学特性，本论文考虑土-结构相互作用影响效应及细长结构物的几何非线性，建立了弹性地基梁和桩的精细化动力学模型。进而，结合非线性动力学理论，运用多尺度方法对土-细长结构物的非线性动力响应进行系统研究。同时，基于理论计算结果，分析了弹性地基参数、地基模型、边界约束等对土-细长结构物相互作用非线性动力响应的影响。最终，为促进研究成果的应用，与理论试验设计和统计分析相结合，针对土-细长结构物相互作用的非线性动力响应提出了动力参数筛选及设计方法。本论文的主要内容及创新点为以下几个方面：
1.鉴于土-结构相互作用问题的重要性，本文首次将土-结构相互作用引起的二次弯矩效应引入到非线性动力学研究中。基于本文研究可知，土-结构相互作用引起的非线性特性可归为一类新的非线性现象。新非线性特性的发现拓展了非线性动力学的理论研究，有重要的理论意义。
2.为研究弹性地基模型对其支承结构物动力响应特性的影响，本文在推导出三参数(Kerr模型)地基反力的显式近似表达式的基础上，给出了四种常见模型(Winkler、Vlasov、Pasternak、Kerr)地基反力的统一表达式。进而，提出了弹性地基模型对结构物动力响应影响效应的对比评价方法。
3.将土-结构相互作用产生的二次弯矩效应引入到土-细长结构物的动力学建模中，分别利用Newton法和Hamilton原理建立了弹性地基梁的非线性动力学模型。进而，研究了土-结构相互作用效应对于弹性地基梁非线性动力响应特性的影响。并且，通过弹性地基梁非线性内共振响应研究发现，二次弯矩效应导致了连续系统保守特性的破坏。
4.基于本文所建模型，对弹性地基梁的自由振动进行了分析，发现其面内运动固有频率谱中存在截止频率。进而，对比研究了系统在截止频率前后的模态构型及线性和非线性动力响应特性。显然，本文提出的精细化模型可更全面地揭示不同场地支承时细长结构物的动力学特性。
5.将二次弯矩效应影响引入到纵向细长结构物的动力响应研究中，运用Hamilton原理建立了水平/轴向受荷桩的非线性动力学分析模型。进而，与非线性动力学理论相结合，研究了桩的多阶屈曲现象及屈曲频率问题。为拓展研究并结合工程实践需求，在群桩基础的非线性动力响应研究中考虑群桩效应影响，并对比研究了群桩效应对系统动力响应中土-结构相互作用效应的影响。
6.基于理论试验设计和统计分析方法，提出了土-细长结构物相互作用的动力参数设计。利用该动力参数设计方法，可有效地筛选出对目标响应影响显著的关键参数，并可量化和直观展现参数的影响效应，进而为结构的动力设计和优化提供理论指导。
In the civil engineering, the soil-structure interaction problem is an important partof the dynamic design and analyze of the structure. In general, the dynamics responses ofthe substructure play an important role in the seismic behavior of the large-span bridgesand major geotechnical engineering. Based on the engineering practice, the foundationof the structure usually can be defined as the slender structure, including the transverseslender structure (the beam on the elastic foundation) and the vertical slender structure(the pile foundation). As we know, the researchers usually think that the foundations playan role of strong constraint on the structure supported by them, which may significantlyinhibit the dynamic response of the soil-structure interaction system. Obviously, there areonly few studies have focused on the modelling and nonlinear response of the soil-slenderstructure via the theory of the nonlinear dynamics.
To accurately reveal the vibration nature of the soil-slender structure interaction, therefined model of the soil-slender structure should be proposed considering the efect of thesoil-structure interaction on the dynamic response of the system. Obviously, consideringthe second-order moment, the nonlinear motion equation of the refined model of the soil-slender structure includes a variety of nonlinear terms: the quadratic nonlinear, cubicnonlinear and parametric excitation terms. Predictably, the more complex nonlineardynamics of the soil-slender structure would be observed. Applying the theory of thenonlinear dynamics and considering the efect of the second-order moment and geometricnonlinearity of the slender structure, the nonlinear dynamics models of the beam onelastic foundation and the pile are obtained. Then, applying the theory of nonlineardynamics, the nonlinear response of the soil-slender structure are studied via the methodof multiple scales. Moreover, based on the numerical results, the efects of the foundationmodels, the parameters of the foundation and the boundary condition of the structureon the nonlinear response of the system is investigated. Finally, applying the design ofexperiment and the statistical analysis, the dynamic parameter design of the soil-slenderstructure is proposed. The main contribution of this paper as following:
1. In view of the soil-structure interaction problem is very importance, the efect ofthe second-order moment caused by the soil-structure interaction is considered inthe research of the nonlinear dynamics. Based on the present study, it is need topoint out that the nonlinearity of interaction can be defined as a new class of thenonlinear dynamical nature. In general, the find of the new nonlinear nature expands the theory of nonlinear dynamics, which has the important theoretical significance.
2. To analyze the efect of the foundation models on the dynamic response of the struc-ture, the same mathematical form of the subgrade reaction of diferent foundationmodels (Winkler, Vlasov, Pasternak, Kerr) is proposed based on the the explicitexpression of the subgrade reaction of the Kerr model. Moreover, the assessment ofthe foundation models is investigated.
3. Considering the second-order moment cased by soil-structure interaction, the refinedmodel of the beam on the elastic foundation is derived via the Newton’s secondlaw of motion and the Hamilton primary, respectively. Then, the efect of the soil-structure interaction on the nonlinear response of the beam on the elastic foundationis investigated. Moreover, the results of the internal resonance response of thebeam of the elastic foundation show that, the second-order moment destroys theconservative nature of the soil-structure interaction system.
4. Applying the present model of the beam on the elastic foundation, the analysis of thefree vibration of the beam on the elastic foundation is investigated. The numericalresults show that the cut-of frequency is discovered in the in-plane natural frequencyspectrum of the beam on the elastic foundation. Moreover, the mode shapes andlinear or nonlinear response of the beam on the system is investigated. Obviously,the present model can reflect the nonlinear response of the soil-structure interactionsystem, in any cases.
5. The nonlinear dynamics model of the pile foundation subjected to the lat-eral/vertical excitation is obtained via the Hamilton primary. Moreover, combinedwith the theory of nonlinear dynamics, the multi-order buckling phenomenon andthe variation of the frequencies of the pile are investigated. To meet the engineer-ing practice, the efect of the pile-group-efect on the nonlinear response of the pilefoundation is performed. Compared the nonlinear vibration of diferent piles inthe pile group, the efect of the pile-group-efect on the soil-structure interaction isinvestigated.
6. Based on the design of experiment and the statistical analysis, the dynamic parame-ter design of the soil-slender structure interaction system is proposed. Applying thismethod, the key parameter of the nonlinear response of the system can be screenedout, and can be used for the dynamic design and optimization of structure.
引文
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