ON THE NUMERICAL DAMPING OF STRING VIBRATIONS USING SEVERAL STATIONARY ACTUATORS

The task is to transfer the string from the initial disturbed state to a state of rest in the shortest possible time. The damping of the string vibrations is carried out using several stationary actuators. The minimized functional is a certain integral. Vibration damping is controlled using a function included in the right part of the hyperbolic equation describing the transverse vibrations of the string and simulating the actions of the actuators. Computational algorithms for solving the problem based on the grid method and the gradient method of finding the minimum of functions of many variables have been developed, and the gradient is calculated using the method of rapid automatic differentiation proposed by Yu. G. Yevtushenko. Examples of calculations of string vibration damping using a different number of actuators are given.

damping of string vibrations, rapid automatic differentiation