Nonlinear Dynamics Response Of The Soil-slender Structure System

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.