Dynamic shakedown of structures with variable appended masses and subjected to repeated excitations

Elastic shakedown for discrete, or finite-element discretized, structures subjected to combinations of static and time-variable loads is addressed in the hypothesis of elastic-perfectly plastic material behavior. The static load is conceived as the weight of an additional mass appended to the structure, whereas the time-variable load is conceived as an unknown sequence of excitations belonging to a specified domain, with intervals between subsequent excitations during which the structure is considered as being motionless. It is shown that, in the plane of the static and time-variable load parameters, the structure's dynamic shakedown domain is nonconvex and that its boundary curve generally exhibits local minima and maxima at those static load values at which a resonant and anti-resonant structural behavior, respectively occurs. It is also shown that, for static loads close to the resonant behavior values, the shakedown limit load can be sensibly smaller than the value computed without taking the appended mass into account. The problem of evaluating the shakedown limit load is discussed and a numerical example presented.