Matrix Perturbation Method For Natural Model Analysis Of Bridge With Little Modified Parameters

Under the function of vehicle moving load, individual crowdmoving load, wind force and earthquake ground movement, innerforce in the bridge structure will exceed that calculated underthe action of static force because of vibration, and partialfatigue damage of structure maybe occur, then vibrationtransmutation and acceleration which affect comfort and safetyof vehicles moving on the bridge will come into being, even thebridge will be destroyed completely. In short the vibration isone of the important factors that affect safety and usage ofbridge.Now the analysis of bridge vibration has already beenapplied to various domain of bridge engineering extensively, butfor all the analyses the dynamic properties of natural frequencyand modal must be confirmed first. Utilize the certain relationbetween natural frequency and stiffness, mass, we can avoidcoupling between the vibration fountain frequency of forcedvibration -wind, vehicle etc and natural frequency of the bridgeat design stage, for example anti-wind calculation, anti-earthquake calculation and vehicle-bridge vibration analysisin dynamic analysis of bridge. In recent years the diagnosisbridge disease is also according to the change of naturalfrequency, so it is very important to confirm the naturalfrequency and model accurately.The mass matrix and stiffness matrix of bridge willalternate because of its element parameters modification atdesign stage, system transformation and construction error atconstruction stage, abrasion and damage at service stage,meanwhile the dynamic properties of the bridge will alsoalternate. If these parameters vary little frequently, with theclassical method to acquire its dynamic properties we need solvegeneralized eigenvalue problem many times, it is verytroublesome and time consuming for large and complex structures. In this thesis in order to save computing time and predigestthe fussy process of inputting initial data for structure usingcommon program, matrix perturbation method with the finiteelement method qua basis is brought forward in allusion tomodification process of bridge design to set up promptquantitative change relation between parameters of members andfrequencies. There are five chapters in this paper, Chapter Oneexpounds the status of current research nowadays,Chapter Twonarrates the principle of the finite element method and matrixperturbation method for Matrix Perturbation Method for NaturalModel Analysis of Bridge with Little Modified Parameters,Chapter Three introduces the implemental method of matrixperturbation combined with ANSYS and one example is adopted tovalidate it. Chapter Four introduces the application of themethod brought forward in this thesis with suspension bridge quaexamples and narrate how to solve question with this method, inChapter five the main conclusions of this thesis are given andthe work needed to do further are prospected. First this paper narrates the process and method ofcantilever beam and suspension bridge'FEM model with ANSYS-thelarge universal software, how to deal with the special problemsand the concrete method of the finite element calculation. Afterthe calculation the unit stiffness matrix , unit mass matrix,frequencies and vibration shapes will be distilled, then theyare used as the input data of matrix perturbation method tocalculate the frequencies of the structure whose membersparameters are modified. At last the former results will becompared with that calculated by the finite element method. The matrix perturbation method for natural model analysisof bridge with little modified parameters brought forward inthis paper tries combine the finite element method and matrixperturbation method to discuss quantitative change of naturalfrequencies after member parameters are modified. Somequestions of how to gain the data and translate the date intothe forms needed by the matrix perturbation method, how toimprove the precision of perturbation solution are the kernelof this method and emphases, difficulty of this work. For theformer questions some beneficial searches are done in thispaper. The matrix perturbation method for natural model analysisof bridge with little modified parameters is expounded in thispaper, some main conclusions are described as follow: 1.Through the way that the data needed by the matrixperturbation method are obtained by the finite analysis of FEMwith the finite element software, the process of materialparameters and geometry parameters etc prepared with the commonnon-visual finite element software can be cut short largely, itis very necessary for large structure. 2.The forms of data distilled after the finite elementanalysis can't accord with that needed by the matrixperturbation method completely, so some little programs shouldbe design to read these data and deposited them as the forms thatcan be transferred by matrix perturbation method, then thisquestion can be solved 3.For vibration analyses, many generalized eigenvalueproblem can be avoided with matrix perturbation method. This newidea that breaks tradition can bring good method for questionwe face. Now there are following methods to solve the naturalfrequencies and vibration shapes in bridge vibration analyses,a. the structure is predigested and solved by analytic method,b. the structure is analyzed by two-dimension finite elementwith the finite element program, both of the former methods arequick and concision, but they can't reflect the coupling ofevery direction vibration; c. the structure is analyzed bythree-dimension finite element with the finite element program,the precision of results is high, but much calculation time isneeded; d . test methods have many factors and the expense ismuch reversely. All the former methods are not too suited tolarge and complex structures. The matrix perturbation method fornatural model analysis of bridge with little modified parameters...