Research On Dynamic Stiffness Method For Free Vibration Of Planar Curved Beams

It is of great significance to make efficient and accurate analysis to the free vibration of curved beam structure, which have wide applications in many field of engineering, like civil engineering, mechanism, aircraft etc. Dynamic stiffness method based on the Wittrick-Williams algorithm is an accurate, useful method for the free vibration analysis of structures, which has successfully applied in the structures combined with straight and constant cross-section members. This thesis extends this accurate method to the curved beam structures and sets up an exact algorithm for them.Firstly, according to the Hamilton principle, governing differential equations for the free vibration of curved beams are derived and changed to the Hamilton form. Secondly, the governing differential equations are solved by using ordinary differential equations solver-COLSYS, then by using dynamic stiffness method, the element and total dynamic stiffness matrixes are got, also, approximately intervals for the natural frequencies are determined. Finally, the Guided and Guard Newton Method is used to calculate the exact natural frequencies and modes of curved beams.The main work of this paper is as follows:1. The differential equations governing the free in-plane vibration of curved beam are derived, then the dynamic stiffness method is set up, the Wittrick-Williams algorithm and the Guided and Guard Newton Method are used to calculate the the exact natural frequencies and modes of curved beams. The effect of shear deformation, rotary inertia, variable cross section and curvature, boundary conditions on natural frequencies is also researched.2. The differential equations governing the free out-of-plane vibration of curved beam are derived, then the dynamic stiffness method is set up, the Wittrick-Williams algorithm and the Guided and Guard Newton Method are used to calculate the the exact natural frequencies and modes of curved beams. The effect of shear deformation, rotary inertia, variable cross section and curvature, boundary conditions on natural frequencies is also researched, without considering warping effect.3. The differential equations governing the spatial free vibration of thin-walled curved beam are derived, then the dynamic stiffness method for in-plane and out-of-plane free vibration of monosymmetric thin-walled curved beams is set up, the Wittrick-Williams algorithm and the Guided and Guard Newton Method are used to calculate the the exact natural frequencies and modes of thin-walled curved beams.The"thickness-curvature"and warping effects are considered. Computer programs have been developed for these problems, and representative numerical examples were analyzed. The theoretical research and numerical tests show that the method is accurate, efficient and reliable, the program can produce the natural frequency and vibration mode which are satisfied the error tolerance. With this method, most shortcomings in other existing methods are overcome. This method provides a new way ti solve the free vibration of planar curved beams.