NEWMARK IMPLICIT TIME INTEGRAL FOR APPLICATION IN PSEUDO-DYNAMIC TESTING - MATHEMATICAL VERIFICATION

In recent years, Pseudo-dynamic (PsD) technique is being adopted as an alternate to conventional shake-table technique to evaluate the seismic performance of structures. The shake-table technique has the merit of simulating all the three force parameters namely inertial, damping and elastic forces in the tested structure realistically; however the technique needs sophisticated shake-table driven by servo controlled actuators with appropriate control electronics. On contrary, PsD technique simulates the three force parameters by using a static actuator through application of an equivalent pseudo-dynamic force system with computation of inertial forces in the back-ground. Such a hybrid technique needs specialized algorithm based on an appropriate mathematical model for the off-line time integration and computation of inertial forces. Several time integrals have been proposed for application in PsD testing and majority of them are derived from Newmark-β family of algorithms. The traditional PsD testing uses constant acceleration version of Newmark time integral in explicit form for mathematical simplicity. This simplified explicit formulation results in numerical damping leading to considerable amplitude error in PsD testing, limiting its application to simple structures. However, for complicated structures improvement is needed in the time integral form leading to unconditional stability and zero numerical damping. This paper presents an improved form of Newmark implicit time integral for PsD testing. The improvement is based on the inclusion of an additional term in displacement predictor, which not only renders the algorithm more consistent, but also eliminates numerical damping and makes the algorithm unconditionally stable. The paper presents the analytical study carried out on the stability and energy dissipation properties of the improved time integral by evaluating its spectral characteristics for verifying its suitability in PsD testing.