【作者】 周平；

【导师】 赵德有；

【作者基本信息】 大连理工大学 ， 船舶与海洋结构物设计制造， 2007， 博士

【摘要】 动态刚度阵法最早由Kolousek于20世纪40年代初提出，是解决工程中结构动力学问题的一个强有力工具，它尤其适合于需要获得更高阶固有频率和更高精度的结构动力特性分析问题。动态刚度阵法通常也被称为精确方法，这是因为它的单元刚度阵是从单元运动微分方程的解析解推导而来的，其中的各元素都是频率的超越函数，并同时具有质量和刚度属性。因而，动态刚度阵法可以通过极少的自由度数准确的计算出结构固有频率和振动响应，而且随着计算频率的升高，动态刚度阵法也无需进一步细划单元。采用动态刚度阵法计算结构动力特性时，可以按结构自然节点划分单元，单元组装方法与常规有限元方法完全相同。本文着重将动态刚度阵法引入并推广到船舶与海洋结构动力分析中，利用它对船舶总体振动特性、局部加筋板结构中高频动力特性以及海洋平台的智能控制进行研究。论文主要包括以下几个方面内容：本文首次将动态刚度阵法应用于船舶总体振动特性和响应研究中，利用它来简化计算模型，提高计算速度和精度。考虑到垂向和水平振动时船体所带的附加水质量不同，所以可利用平面Timoshenko梁单元的动态刚度阵来分别计算两个方向的总振动固有频率和响应。本文采用动态刚度阵法结合Wittrick-Williams算法对299，500DWT超大型油船的总体振动固有特性进行预报，所得固有频率和固有振型通过模态叠加法来求解该船在螺旋桨激励下的总体振动响应，计算结果分别与一维梁有限元模型和三维全船有限元模型计算结果以及实测值进行比较，以验证本方法的精确性和有效性。研究表明，船舶总体振动的刚度主要取决于平行中体的惯性矩和剪切面积，而其沿船长方向的分布对它的固有频率影响较小，反而船舶质量沿船长分布情况对固有频率的影响较大。因此，如果按理论站的位置来划分船体梁的单元时，可能会因为一个舱室的质量分布在若干个站内，需要按力和力矩等效的原则来重新调整质量分布，而采用动态刚度阵法计算时，当船舶舱室较多时可直接按照舱室分布来划分单元，避免了对船舶质量分布的重新调整，简化了计算模型，方便了数据准备工作，而且还能同时保证各单元满足梁理论的要求，提高了工程需要阶数内固有频率计算结果的准确性，为船舶总体振动特性分析研究提供了一个快速而便捷的计算方法。本文推导了考虑平面内振动影响的双向加筋Mindlin板动态刚度阵，为动态刚度阵法提供了一种新的单元类型，进而为研究加筋板间的能量传递开辟了一个新途径。本文以加筋中厚矩形板为研究对象，通过Hamilton原理建立考虑平面内振动影响的双向加筋Mindlin板运动微分方程，再利用方程的解析解来推导其动态刚度阵，所得动态刚度阵被用于加筋板的中高频动力特性问题研究之中。首先采用动态刚度阵法对L型加筋板间的耦合损耗因子进行计算，计算结果与实测值和有限元方法分别进行了比较，以验证本文方法的可行性、准确性和高效性；所得加筋板间的耦合损耗因子可与统计能量分析方法相结合，来更为准确地对船舶舱室噪声进行预报。此外，本文还利用动态刚度阵法研究了加筋板间的能量传输关系，讨论了平面内振动、剪切变形和转动惯量对加筋板间弯曲能量传输的影响，并给出了一些相关结论。本文提出了一种新的基于动态刚度阵法的导管架式海洋平台模糊神经网络自适应预测逆控制模型。该模型是将实时采集的海洋平台所受波浪力提供给动态刚度阵建立的计算模型，通过它来快速而准确地计算出平台项部的响应，再将此响应作为模糊神经网络预测逆控制器的输入信号，由它预测出下一时刻平台顶部的控制力来对海洋平台振动响应进行控制；同时对控制后的平台响应进行实时测量，所得响应误差和扰动一起作为反馈自适应预测逆控制器的输入信号，它的输出力信号直接反馈到被控平台的项部，以此来消除被控对象的内部噪声和外部扰动。最后的数值算例结果表明，本文所提出的导管架式海洋平台主动控制模型既能很好地解决控制系统中存在的时滞问题，又具有较强的抗干扰能力，可以有效地控制海洋平台的振动响应。本文研究表明，动态刚度阵法凭借着所需单元少、计算速度快、计算精度高以及适用频率范围广等特点，可以用来便捷高效地计算结构的动力特性，在船舶与海洋结构动力分析中有着广阔的应用前景。利用该方法对船舶总体振动特性分析过程中可以提高计算精度，简化计算模型，是一个不可多得的简便实用工具。毫无疑问，本文所推导的双向加筋Mindlin板单元的动态刚度阵为动态刚度阵法提供了一个新的单元类型，为研究加筋板间中高频区域内的动力特性提供了一个强有力的工具。所提出的基于动态刚度阵法的导管架式海洋平台主动控制模型，为海洋平台的主动振动控制提供了一个新思路。更多还原

【Abstract】 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.更多还原