Energy Transfer to High-Frequency Modes of a Building due to Sudden Change in Stiffness at Its Base

Previous studies have demonstrated that a sudden change in stiffness at the base of a building (e.g., due to nonlinear deformation in the base isolator including sudden sliding) during seismic excitations may result in an increase in the floor-level acceleration responses when compared with the results of the same building but modeled as a linear structure (i.e., without allowing any stiffness change). It has also been demonstrated that this phenomenon occurs due to high-frequency modes getting excited during the nonlinear phase of the motion as a result of energy transfer from the adequately excited fundamental mode. In this part, a systematic analytical study is carried out to understand this energy-transfer phenomenon by formulating the equations of motions for different stages of hysteresis. For simplicity, an initial velocity profile proportional to the fundamental mode of a multi-degree-of-freedom (MDOF) system is considered and the free-vibration response of the system is studied. A numerical investigation is then carried out in which the influence of different parameters on the energy transfer to higher modes of a system is studied. Further, using the results of the perturbation approach, simplified approximate expressions are also obtained to understand the contribution of different terms. It has been shown that the second mode receives the maximum amount of energy from the fundamental mode and the transfer of energy reduces with the increase in mode number. Further, it has been observed that the transfer of energy to the second mode increases for (1) higher initial energy content of the fundamental mode, (2) less spacing between the second and fundamental modes, and (3) lower postyield stiffness of the bilinear spring. To validate the energy-transfer phenomenon experimentally, shake table experiments with a scaled model were conducted alternatively with two different base conditions: (1) fixed base, and (2) structure isolated by sliding isolators. To better understand the energy-transfer phenomenon, a secondary component was also attached to the second floor of the structure with its frequency tuned to the second mode of the structure. A low-amplitude sinusoidal base excitation followed by a sudden jerk was considered. From the recorded floor accelerations and component acceleration responses, it is concluded that energy transfer from the adequately excited fundamental mode to higher modes occurs due to a sudden change in stiffness of the structure as a result of sudden sliding.