Improved formulations of the CR and KR methods for structural dynamics

Although the Chen-Ricles (CR) method and the Kolay-Ricles (KR) method have been applied to conduct pseudodynamic tests, they have both been found to have some adverse numerical properties, such as conditional stability for stiffness hardening systems and an unusual overshoot in the steady-state response of a high-frequency mode. An improved formulation for each method can be achieved by using a stability amplification factor to boost the unconditional stability range for stiffness hardening systems and a loading correction term to eliminate the unusual overshoot in the steady-state response of a high-frequency mode. The details for developing improved formulations for each method are shown in this work.