The Biot Model and Its Application in Viscoelastic Composite Structures

Application of viscoelastic materials in vibration and noise attenuation of complicated machines and structures is becoming more and more popular. As a result, analytical and numerical techniques for viscoelastic composite structures have received a great deal of attention among researchers in recent years. Development of a mathematical model that can accurately describe the dynamic behavior of viscoelastic materials is an important topic of the research. This paper investigates the procedure of applying the Biot model to describe the dynamic behavior of viscoelastic materials. As a minioscillator model, the Biot model not only possesses the capability of its counterpart, the GHM (Golla-Hughes-McTavish) model, but also has a simpler form. Furthermore, by removing zero eigenvalues, the Biot model can provide a smaller-scale mathematical model than the GHM model. This procedure of dimension reduction is studied in detail here. An optimization method for determining the parameters of the Biot model is also investigated. With numerical examples, these merits, the computational efficiency, and the accuracy of the Biot model are illustrated and proved.