A NEW METHOD FOR DYNAMIC ANALYSIS OF PLATES AND PLATE ASSEMBILES

在飞机和其他主要工业中，建立结构的振动特性是一项重要的设计活动。许多这样的结构被建模为板块和板块组合。提出的研究重点是提高精确求解板振动问题的能力，从而更有效地设计和制造具有更好振动性能的结构。一种新的方法，称为动态有限条法将被开发。这将通过将现有的三种著名的方法，即动刚度法、有限带法和有限元法结合起来并发挥其优点来实现。新公式的一个重要特点是将一维精细化梁理论用于金属梁和复合梁，并将其扩展到二维结构（如板）的重要情况，以研究其自由振动特性。在这项工作中，金属或复合板将被分割成许多条，这些条由受到动态运动的梁表示。板的动态特性将通过结合单个条带的特性来获得，其中每个条带被理想化为经历动态运动的梁。众所周知，符号计算是处理结构力学中经常需要的复杂代数表达式的有力工具。在发展新理论时将充分利用这一工具。Wittrick和Williams在70年代早期开发的一种既定算法（称为W-W算法）将被扩展为新方法，并随后用作求解技术来获得结果。最后，以某运输机重要结构部件翼盒为例，对其动力特性进行了分析，验证了该方法的有效性。

Establishing the vibration behaviour of structures is an important activity in design within the aircraft and other major industries. Many of these structures are modelled as plates and plate assemblies. The proposed research is focused on improving the capabilities of solving plate vibration problems accurately that will lead to more efficient design and manufacture of structures with improved vibration performance. A new method, called the dynamic finite strip method will be developed. This will be achieved by bringing together and getting the best out of three well-known existing methods, the dynamic stiffness, the finite strip and the finite element methods. An important feature of the new formulation will be the use of one-dimensional refined beam theories for both metallic and composite beams and extend them to the important cases of two dimensional structures such as plates to investigate the free vibration characteristics. In this work, a metallic or composite plate will be split into a number of strips represented by beams subjected to dynamic motion. The dynamic behaviour of the plate will be obtained by combining the behaviour of the individual strips where each strip is idealised as a beam undergoing dynamic motion. It is well known that symbolic computation is a powerful tool in manipulating complicated algebraic expressions often required in structural mechanics. Full advantage of this tool will be taken of when developing the new theory. An established algorithm developed by Wittrick and Williams in the early seventies (known as the W-W algorithm) will be extended for the new method and subsequently used as solution technique to obtain the result. Finally in order to verify the method, a wing box which is an important structural part of a transport airliner will be analysed for its dynamic properties.