Study On Dynamic Stiffness Matrix Method For Dynamic Analysis Of Ship And Offshore Structure

The concept of the dynamic stiffness matrix (DSM) method was first developed byKolousek. It is a powerful means of solving vibration problems in structural engineering,particularly when higher frequencies and better accuracies are required. Thismethod is basedon exact shape functions obtained from the solution of the element differential equations. Sothe method provides the researcher with much better model accuracy compared to finiteelement or other approximate methods. The resulting element matrix features exactly themass and stiffness properties of the element and leads to a transcendental eigenvalue problem.Since the element properties are derived exactly, no matter what the frequency is, the resultsobtained by this method are exact, without mesh refinement as the frequency increases. In thispaper the DSM method is introduced to the dynamic analysis for ship and offshore structures.It is used to analyze the vibration characteristic of ship hull, calculate the dynamiccharacteristics of stiffened plate in high-frequency range and control the vibrational responsesof offshore platforms. The present work is divided into the following parts.The DSM technique is applied to compute overall vibrational characteristics of hullgirder in this paper. The analytical expressions of dynamic stiffness matrix of a Timoshenkobeam for transverse vibration are presented in which all the effects of rotatory inertia andshear deformation are taken into account in the formulation. The resulting dynamic stiffnessmatrix combined with the Wittrick-Williams algorithm is used to compute natural frequenciesand mode shapes of the 299,500 DWT VLCC, and then the vibrational responses are solvedby the mode superposition method. The computational results are compared with thoseobtained from other approximate methods and experiment. It is shown that with the DSMmethod, the mesh division can be determined by the cabin arrangement to avoid recalculatingweight distribution, simplify computational model and make the data preparation moreconvenient. In addition, this method can make each element meet the requirements of beamtheory, get more accurate calculation results in the ranges needed by engineering and furnish afast and simple method to carry out overall dynamic analysis for ship.A dynamic stiffness matrix is presented for the analysis of stiffened moderate thick platein this paper. The plate differential equations are based on Mindlin thick plate theory andinclude the in,plane vibrations. The stiffeners are taken to be smeared over the surface of theelement by energy equivalent, and Hamilton's principle is used to derive the appropriate modifications which must be made to the plate differential equations. The resulting dynamicstiffness matrix provides the DSM method a new element type, and can be used to analyzeenergy transmission between stiffened plates in middle and high frequency ranges. In thispaper, the coupling loss factors of the junction are calculated by the DSM method, and thecalculated results are compared with those obtained by other numerical methods andexperiment to verify the effectiveness and feasibleness of the presented method. On the otherhand, the calculated coupling loss factors can be directly used by the statistical energyanalysis method to predict more accurate noise levels of ship cabin. In addtion, the DSMtechnique is applied to calculate the energy flow of the coupled stiffened plates. The effects ofshear deformation and rotary inertia and the in-plane vibrations are also discussed, and someuseful conclusions are drawn in this paper.In this paper, a new active control scheme for jacket offshore platforms, based on theDSM method, is presented. According to the characteristic of DSM method in quick accuratemodeling, the actual model of controlled platform can be considered by the artificialintelligence control algorithm. In the DSM based fuzzy neural network (FNN) adaptivepredictive inverse control (APIC) scheme, a real time measurement of the random waveforces is made by the pressure transducers which are placed on the leg of the offshoreplatform. And then the responses on the top of the platform under these random wave forcesare quickly and accurately calculated by the DSM method. The calculated responses are takenas the input signals of FNN adaptive predictive inverse controller, through which the controlforce for the imminent time of the platform is forecasted. Moreover, a feedback adaptivepredictive inverse, controller is designed for the purpose of disturbance canceling and errorreduction. The numerical results obtained in this paper show that the DSM based FNN APICscheme which has excellent anti-disturbance capability is feasible and effective, and canfinally overcome the time delay.The study shows that the DSM method has a comprehensive application in the dynamicanalysis of ship and offshore structures. With the advantages of few elements, higheraccuracy and speed, not only can the natural frequency and structural response be calculatedeffectively, but also the dynamic characteristics of structures can be solved in a wide range offrequencies by using DSM method. It is a powerful tool to analyze overall vibrationcharacteristics of ship with higher accuracy and simplified computational model. It is nodoubt that the dynamic stiffness matrix for stiffened Mindlin plate deduced in this paperextends element type of DSM method and provides a useful way to investigate energytransmission between stiffened plates with middle and high frequencies, which expandsapplied range of traditional methods. The presented DSM based FNN APIC scheme undoubtedly provides an efficient way to reduce the vibration responses for jacket offshoreplatforms.