Higher-order explicit and implicit dynamic time integration methods

General procedures are presented for the use of higher-order approximations of a system\u27s dynamic response using new time integration schemes. Traditional methods assume a constant or linearly varying acceleration in between discrete time points. Both explicit and implicit methods are developed and presented that make use of higher-order polynomial acceleration variations for single-degree-of-freedom and multi-degree-of-freedom dynamic structural analyses. An implicit method that makes use of a variable &thgr; to increase the stability and accuracy of the method is also presented. Both direct time integration and modal analysis algorithms are developed and implemented in computer programs to investigate their accuracy and usefulness. The relative merits and stability aspects of the methods are described. The higher-order methods are compared to traditional explicit methods, such as the Central Difference and Runge-Kutta Methods, and traditional implicit methods, such as the Linear Acceleration, Wilson-&thgr;, Newmark, and Houbolt Methods. Amplitude decay and period elongation comparisons are used to measure the accuracy of the methods when applied to a single-degree-of-freedom free vibration problem. The equivalent peak displacement percent difference and percent time difference to peak displacement are used to measure the accuracy of the methods when applied to multi-degree-of-freedom problems