Abstract
The analysis of dynamic response plays an important role in dynamic system analysis. Generally, there are two ways to solve the differential equations of dynamic systems; direct integration method and mode superposition method. Here, an improved direct integration method based on cubic spline interpolation is given to solve the inhomoge-neous dynamic equations. With this method, when the applied loading is variable in sinusoidal form or linear form, a new integrand is obtained by simulating the exponential matrix in integral items with cubic spline. After several times of integration by parts, a new precise time step integration method is proposed. The calculation technique of matrix exponential function is used in the construction of cubic spline interpolation function to avoid the loss of effective digits. In addition, this new method avoids the computation of the inverse matrixes from which the HPD-F algorithm suffers, so the stability of this algorithm is improved greatly. Numerical example is given to demonstrate the validity and efficiency of the algorithm proposed.
| Original language | English |
|---|---|
| Pages (from-to) | 75-77+82 |
| Journal | Zhendong yu Chongji/Journal of Vibration and Shock |
| Volume | 26 |
| Issue number | 9 |
| State | Published - Sep 2007 |
Keywords
- Cubic spline
- Exponential matrix
- High precise direct integration method
- Structural dynamic equations
- Time integration