Wave Motion Method For Dynamic Analysis Of Cable And Beam Structures

This paper studies the precise vibration response of the cable and beam structures, uses the wave motion and wave and finite element method to analyze the vibration characteristics of the cable and beam structures, respectively, the validity of the results is proved with using the finite element method, the main innovative results are as follows:Firstly, the advantages and disadvantages of the conventional finite element and wave motion method are compared, and the characteristics of the two methods and their application are discussed. Based on the wave motion method, then the element state transition and state transfer equations of beam, cable and rod are derived, the universal wave equation these structures are established. It provides a theoretical groundwork for solving the analytical solution of the frame structure, the cable net structure and the truss structure in the future work.Secondly, the normal vibrations of the taut strings are introduced to simulate the pre-tension cable tension, and the wave equation of taut string is derived, and dynamic model of its units is established. The concept of the node equilibrium conditions with more than one wave number is proposed and the wave modes of the section are defined. Then the wave motion dynamic models of arbitrary planar topological fluctuations cable net structure are founded, general method for solving the analytical solution of these models is given, natural frequencies and frequency response of cable net structures can be gotten with more than one wave number, compared with the result of the finite element method. The formulas of the section and node power flow of cable net structures are also derived, numerical examples are given. With much more nodes and boundaries, the power flow response is much more complicated. This work provides a theoretical reference of the vibration control cable net structures, and promotes the application of the wave motion method on the flexible structures.Finally, the general equation that based on wave and finite element method for solving the frequency response is derived. Then the wave motion method, finite element method and wave and finite element method are used to solve the frequency response of cantilever beam and free-free beam structures, respectively. The three response results are organized together, the conclusion can be drew that the wave and finite element method is much more accurate to the analytical solution than the method of the finite element method. Then, the wave and finite element method and wave motion method are used to solve for the frequency response of the fixed-hinged beam structures which are consisted of two beams. The two beams of the first structure are made of the same material, while the others of the second structure are made of different material. It can be concluded that the second structure with two beams which are made of different material will reflect and transmit more times occur at the boundary nodes.