.... , and Smyshlyaev , A. , 2008 , Boundary Control of PDEs: A Course on Backstepping Designs , Vol. 16 , SIAM , Philadelphia, PA . [31] Jansen , J. D. , and van den Steen , L. , 1995 , “ Active Damping of Self-Excited Torsional Vibrations in Oil Well Drillstrings ,” J. Sound. Vib. , 179 ( 4...

... continuum mechanics. In this study, exponential decay rate of a vibrating nonclassical microscale Euler–Bernoulli beam is investigated using a linear boundary control law and by implementing a proper Lyapunov functional. To illustrate the performance of the designed controllers, the closed-loop PDE model...

... equations. The fluid is assumed to be Newtonian, barotropic, and compressible. For the stability analysis of the coupled system, the boundary control method is used; a boundary feedback is constructed to stabilize the vibrations of the dam and the fluid simultaneously. The control force consists...

... displacement in the normal direction to the plate, the plate displacements in in-plane directions are not dispensable, and strains and governing equations for transverse vibration and in-plane motions are nonlinear; therefore, the nonlinear boundary control method is proposed to be utilized to stabilize...

... designed for the rigid subsystem based on inverse dynamic law, and the other one is an exponential stabilizing controller for the flexible subsystem based on boundary control (BC) laws. Exponential stabilization is proved by using a metric containing kinetic and potential energies of the fast subsystem...

..., the proposed boundary control (BC) method does not require any information about vibration along the beam except at the end points, nor requires discretizing the partial differential equation of beam vibration to a set of ordinary differential equations. So, the method avoids the need for instruments...

... that by numerical simulation and by an experiment for the nontraveling string. 25 12 2005 13 02 2007 12 11 2007 belts shapes (structures) vibration control acoustic waves finite difference methods string wave control vibration control boundary control finite difference method...