A Rate-Independent Phenomenological Model for the Characterization of Pressurized Sand Dampers

Abstract

This study presents the mathematical characterization of the recently developed pressurized sand damper (PSD) in which a steel sphere or bolt is moving within a cylindrical tube filled with sand under pressure. The experimental results, presented in previous studies, revealed that the force output exhibited by the PSDs is stable, symmetric, and nearly velocity-independent. Thus, the PSDs are response-modification devices that offer rate-independent dissipation. In addition, when tested at various levels of pressure, displacement amplitude, and frequency, the PSD displays hysteresis loops with pronounced pinching. To accurately reproduce their response, a recently formulated phenomenological model [the Vaiana Rosati model (VRM)] is employed. The VRM allows for the evaluation of the output variable by means of analytical closed form expressions or equivalent rate equations; in addition, it captures, with good accuracy, the experimental responses of the PSDs obtained for both periodic and nonperiodic displacement time-histories. When natural hazards such as strong earthquakes, high winds, and wave actions occur, they impose extreme dynamic loads on our civil structures and to structural systems that exhibit inelastic behavior. In an effort to explain the behavior of such systems when subjected to these cyclic loads, load-displacement curves are plotted. The enclosed area of each loop reveals the dissipated energy over a full cycle of loading–unloading, which is referred to as hysteresis. In lay terms, the hysteresis can be considered as the memory of an inelastic system, since the restoring force depends not only on the current value of each moment, i.e., on the current deformation but also on the past history of the input motion; thus, a number of state variables need to be known. The dynamic characteristics of nonlinear hysteretic systems that can dissipate large amounts of energy can accurately be predicted with the study of their hysteresis loop. The characterization of inelastic systems that can dissipate energy and generate large hysteresis loops is achieved with phenomenological models. In this study, a newly developed phenomenological model that allows for the evaluation of the output variable by means of analytical closed form expressions or equivalent rate equations is used to simulate the typical pinched hysteresis loops characterizing the rate-independent behavior of pressurized sand dampers.