Precise Calculational Method And Application Studies For Structural Dynamic Equations

The problems for structural responses are very important, and have aroused a lot of scientific interests in last decades. In this dissertation, solutions for dynamic equations are explored based on high-precise methods, thus a new method is presented, and then the response of viso-elastic composite structures is studied. The main research works can be described as follows:In the first chapter, the progresses of structures dynamics and methodologies have been reviewed, in which some development of high-precise method is presented in detail. In addition, the research significances of visco-elastic composite structure are briefly introduced.In the second chapter, five kinds of high-precise methods presented before are compared and their advantages and disadvantages are characterized, as well as their own application range. The conclusions are proved by a numerical example.In the third chapter, a new precise time step integration method is obtained. To approach the exact solutions at each interpolation point at every time step, the piecewise cubic spline is applied in computing the numerical results. Meanwhile, the high-precise method has been used to avoid the loss of precision as well as the calculation matrix inversion. A numerical example is given to demonstrate the accuracy and stability of the method.In the fourth chapter, by using the dimension expanding high-precise method, the dynamic responses of viso-elastic composite structure are investigated based on the standard model. The state equations of composite structure and the solution is established. Finally, the dynamic responses of the composite structure with 2n-DOF subjected to the step/sinusoidal excitation are studied. An example proves the effectiveness and accuracy of this method by comparing with the existed methods.