Dynamics and control of viscoelastic solids with contact and friction effects (original) (raw)

Dynamics and control of distributed systems subjected to frictional forces have been a longstanding challenge in the fields of partial differential equations and elastodynamics. Previous research highlighted the limitations of Coulomb's friction law in characterizing actual interactions, leading to the development of a more appropriate constitutive equation that aligns better with experimental data. This paper establishes the existence of optimal controls for linear viscoelastic bodies under friction, demonstrating that specific control forms can minimize distance between system responses and target motions over a stipulated time interval. The study culminates in offering new insights into optimal control strategies in viscoelastodynamics amidst complexities introduced by contact and friction.