Elastic and viscoelastic foundations: a review on linear and nonlinear vibration modeling and applications

This paper presents a comprehensive review on different theoretical elastic and viscoelastic foundation models in oscillatory systems. The review covers the simplest foundation models to the most complicated one and fully tracks the recent theories on the topic of mechanical foundations. It is fully discussed why each theory has been developed, what limitations each one contains, and which approaches have been applied to remove these limitations. Moreover, corresponding theories about structures supported by such foundations are briefly reviewed. Subsequently, an introduction to popular solution methods is presented. Finally, several important practical applications related to the linear and nonlinear foundations are reviewed. This paper provides a detailed theoretical background and also physical understanding from different types of foundations with applications in structural mechanics, nanosystems, bio-devices, composite structures, and aerospace-based mechanical systems. The presented information of this review article can be used by researchers to select an appropriate kind of foundation/structure for their dynamical systems. The paper ends with a new idea of intelligent foundations based on nanogenerators, which can be exploited in future smart cities for both energy harvesting and self-powered sensing applications.