The higher modes have a negligible effect since the earthquake acceleration input is discretized every 0.01 second. (This solution is calculated using the FORTRAN program contained in the file cantilever_exact.f.) The number of modes included in this solution has been found by trial, which has shown that using the six lowest modes (up to 61.9 Hz) gives displacements that are accurate to 0.01%. An exact benchmark solution is readily obtained by integrating the eigenvalues and eigenvectors of the structure exactly in time over the first 10 seconds of the acceleration input (see, for example, Hurty and Rubinstein, 1964). The seismic analysis is performed using the El Centro N-S acceleration history, which is discretized every 0.01 second. Two different baseline corrections are then applied, and the results with and without baseline correction are compared. In this example the analyses are first performed without baseline correction. The correction to the acceleration record is piecewise quadratic in time.

Baseline correction is used to modify the acceleration record by adding a correction to the acceleration record to minimize the mean square velocity over the time of the event. Response spectrum analyses, based on spectra calculated from the same earthquake record, are also performed and compared with the exact solution.Įxamples are also included to illustrate the use of baseline correction. Direct time integration is also used in this problem to illustrate the accuracy of the time integration operator. In problems such as this one, the modal dynamic procedure is the analysis method of choice because it is computationally inexpensive and it is very accurate (provided that enough modes are extracted), since the integration of the modal amplitudes (the “generalized coordinates”) is exact. Three types of analyses are illustrated: modal dynamics in the time domain, direct time integration, and response spectrum analysis. This example demonstrates the use of Abaqus in a seismic analysis where the forcing function is given by the time history of acceleration at an anchor point of the structure.

Quake 4 1.4.3