Hysteretic damping in an elastic body with frictional microcracks

Tuned mass systems with the Bouc-Wen and a hybrid hysteresis

“…With the above motivation, in this paper we first study the TMD system with the Bouc-Wen model, and subsequently, the TMD system with the Bouc-Wen model and a rate independent scalar hysteresis model developed in Ref. [27]. The hysteresis model of [27] is motivated by a study of an elastic plate with several frictional microcracks.…”

“…The Bouc-Wen hyteresis model and the hysteresis model of 27 are briefly discussed below. The Bouc-Wen hysteresis model is given bywhere A > 0, β > 0, γ ∈ [ − β , β ] and n > 0 are the model parameters.…”

“…(b) A typical response of the hysteresis model of. 27 Parameters used: κ = 4, θ a = 2, β 0 = 1.8 and ϵ = 10 −6 . Here, f ( t ) = θ ( t ) z ( t ).…”

“…(c) A typical response of the hysteresis model combined with both the Bouc-Wen model and the hysteresis model of. 27 Here, the same hysteresis model parameters are used as in cases (a) and (b), for the Bouc-Wen model and the hysteresis model of, 27 respectively. The output force f ( t ) is the sum of hysteretic output of two models.…”

“…The rate-independent scalar hysteresis model of 27 is given bywhere z ( t ) is the input displacement to the system and θ ( t ) is an internal variable. Here, θ a , κ , β 0 are model parameters and ϵ is a very small regularizing parameter.…”