Abstract
The mode superposition method only applies to vibration analysis of linear systems due to its basis on the principle of superposition. To remove this restriction, this chapter introduces the commonly used step-by-step integration method, which is applicable to the dynamic response analysis of linear and nonlinear systems. The basic idea of the step-by-step integration method is first introduced. Then, three algorithms, the linear acceleration method, Wilson-θ method, and Newmark method, are discussed in detail. Finally, the Wilson-θ method is used as the example to illustrate the procedure for analyzing the stability and accuracy, and how to select relevant parameters is discussed for the commonly used integration methods.
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