Nonlinear Dynamics of Flexible Posttensioned Rocking Walls

Abstract

Posttensioned rocking systems have gained attention, as they limit damage to the primary structure and simplify repairs after extreme events. The literature on posttensioned rocking walls is extensive; however, much of it is focused on numerical modeling and exploration of complex system level behavior. The present paper focuses on an analytical study of the amplitude-dependent frequencies of posttensioned flexible rocking walls. A simplified analytical model is introduced to investigate the interplay between rocking wall deformation and rocking. The study borrows analysis tools from the study of nonlinear normal modes (NNMs) and includes unforced and forced dynamics. A finite element model is also used for comparison with the static and dynamic response from the analytical model. The work shows that the unforced dynamics are able to predict peak response of forced vibration and furthermore illustrate the transition in behavior from fixed-base to flexible rocking walls. In addition, coexisting steady-state solutions were observed from the forced response. The NNMs of flexible rocking walls may aid earthquake/wind engineers in tailoring rocking systems to improve performance in the same way linear modal analysis is used in practice.