Structural Dynamic Analysis & Vibration Isolation Analysis Based On ODE Solver For Large-sized Aqueduct With High Pier

In this paper, by using ODE (Ordinary Differential Equation) solver, the analysis of dynamic characteristic, seismic response and nonlinear vibration isolation for large-sized aqueduct with high pier is converted to solving ODEs' eigenvalue problem analytically and general boundary value problem semi-analytically. With clear physical concept, low computational cost, reliable results and easy parameter modification, these analytical and semi-analytical methods are particularly useful for preliminary design of high-pier aqueduct. The main contents are as follows:(1) Applying Housner Model, the differential equations and boundary conditions (BCs), which describe the in-plane bending vibration of high-pier aqueduct, are derived based on Hamilton principle, and corresponding quasi 2D and 3D CEL (Coupled Eulerian-Lagrangian) finite element models are defined respectively for further comparison.(2) Featuring eigenvalue in BCs, the ODE system is derived for the free vibration of high-pier aqueduct. From this ODE system, the mode orthogonalization and normalization conditions are obtained. Then, by means of trival ODE and equivalent ODE technique, an analytical algorithm including linear inverse interation and nonlinear Newton's method is introduced for natural frequence extraction of high-pier aqueduct. The code programmed in this algorithm proves not only the accuracy and reliability in its results, but also the convinence in parameter modification. Besides, it shows that the change of pier height only affects aqueduct's low-order modes significantly, while the change of water depth just influences water's low-order modes notably.(3) A semi-analytical modal superposition in terms of small number of analytically solved eigenmodes is presented to obtain seismic response of high-pier aqueduct. Firstly, based on Galerkin method, it requires to derive the variation principle and corresponding functional from the forced vibration differential equation system. Secondly, applying Ritz method and mode orthogonalization, we obtain the uncoupled equations of motion in terms of norm coordinates from the variation principle and functional. Finally, the Duhamel integrals of these uncoupled single DOF systems are calculated to obtain the seismic response. The code programmed in this algorithm proves that its results are in good agreement with the FEM results and its computational cost is inexpensive, therefore, it is applicable to predicte structrue's peak seismic response?? addition, it also shows that the earthquake's predominant frequency and the aqueduct's basic frequency are closely related to the seismic response.(4) A semi-analytical Newmark integration sheme is presented for nonlinear vibration isolation analysis of high-pier aqueduct, which involves firstly deriving the differential equations and boundary conditions based on Hamilton principle for the LRB isolation system, and then obtaining the ODE system of direct integration sheme by Newmark discretizaztion in time domain. The code programmed in this algorithm calculates the seismic response of structures with different LRBs defined by bilinear restoring force model. It shows that the semi-analytical method leads to satisfactory results. What's more, it also proves that LRB has a great effect on reducing structural dynamic response.