Error Analysis for Pseudodynamic Test Method. II: Application

Abstract

Error propagation characteristics for the pseudodynamic test method based on implicit time‐integration schemes are evaluated and compared to those for an explicit time‐integration scheme. For random errors and a linear structure with one degree of freedom, the error amplification factor for the implicit scheme is generally lower than that for the explicit scheme. The difference is small when the time step is small compared to the period of oscillation of the structure, and increases for larger time steps. The advantages of the implicit scheme become more apparent for an N‐degree‐of‐freedom structure consisting of N equal masses connected by shear springs of equal stiffness, and errors that occur independently from one story to the next. In this case, the error amplification factor at first increases as the number of degrees of freedom is increased, but then decreases and appears to approach an asymptotic value of unity when the number of degrees of freedom becomes very large. As an example of an inelastic system, the effect of random measurement errors on the response of an elastic‐perfectly plastic oscillator is evaluated. This example serves to verify the range over which linearity of the error structure is applicable.