Modelling of single degree of freedom SMA oscillators by using rheological schemes

Abstract

Introduction. The interest to the SMA elements in civil engineering is constantly increasing. Regarding the field of civil engineering, the devices incorporating SMA elements mostly find applications in mitigation of natural disaster hazards, such as earthquakes. The promising results of applications are possible due to unique properties of SMA, such as shape memory effect (recovering of relatively high strains while material is heated) and superelasticity (recovering of strains upon load removal). The most common approach to the formulation of SMAs constitutive relations is a thermomechanical modelling, in which constitutive equations are dependent on internal state variables. Materials and methods. The article describes the phenomenological approach to modelling of single degree of freedom SMA oscillators by using rheological schemes. Results. Certain sets of rheological components are presented and their influence on the oscillator response is examined. As an example of numerical application of presented approach, the simple one-dimensional oscillator is used in order to solve the case of forced vibrations of a cantilever with embedded SMA reinforcement. Conclusions. One of the advantages of the phenomenological modelling approach presented in the article is a possibility of formulation of constitutive relationships as a set of explicit differential equations. Such system of equations can be easily implemented in mathematical software or in the commercial FEM codes as a user’s subroutines.