Related papers: Damping optimization of discrete mechanical system…
In this work, the problem of optimizing damper positions in vibrational systems is investigated. The objective is to determine the positions of external dampers in such a way that the influence of the input on the output is minimized. The…
Vibrating systems can respond to an infinite number of initial conditions and the overall dynamics of the system can be strongly affected by them. Therefore, it is of practical importance to have methods by which we can determine the…
Vibrational structures are susceptible to catastrophic failures or structural damages when external forces induce resonances or repeated unwanted oscillations. One common mitigation strategy is to use dampers to suppress these disturbances.…
We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…
In this article, we consider vibrational systems with semi-active damping that are described by a second-order model. In order to minimize the influence of external inputs to the system response, we are optimizing some damping values. As…
Common criteria used for measuring performance of vibrating systems have one thing in common: they do not depend on initial conditions of the system. In some cases it is assumed that the system has zero initial conditions, or some kind of…
Optimal damping aims at determining a vector of damping coefficients $\nu$ that maximizes the decay rate of a mechanical system's response. This problem can be formulated as the minimization of the trace of the solution of a Lyapunov…
A novel optimization concept for an oscillator with two degrees of freedom is proposed. By using specially defined motion ratios, we control the action of springs and dampers to each degree of freedom of the oscillator. If the potential…
Problem of damping of an arbitrary number of linear oscillators under common bounded control is considered. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the…
If a contact of two purely elastic bodies with no sliding (infinite coefficient of friction) is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears, that is not dependent on…
We study the dynamical behavior of a single degree of freedom mechanical system with a particle damper. The particle (granular) damping was optimized for the primary system operating condition by using an appropriate gap size for a…
The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…
This paper revisits the concept of damping torque in a multimachine power system and its relation to the dissipation of oscillation energy in synchronous machine windings. As a multimachine extension of an existing result on a…
We introduce an autonomous system with closed-loop damping for first-order convex optimization. While, to this day, optimal rates of convergence are almost exclusively achieved by non-autonomous methods via open-loop damping (e.g.,…
This paper is devoted to the study of the robustness properties of the 1-D wave equation for an elastic vibrating string under four different damping mechanisms that are usually neglected in the study of the wave equation: (i) friction with…
We consider new performance measures for vibrational systems based on the $H_2$ norm of linear time invariant systems. New measures will be used as an optimization criterion for the optimal damping of vibrational systems. We consider both…
We formulate the quadratic eigenvalue problem underlying the mathematical model of a linear vibrational system as an eigenvalue problem of a diagonal-plus-low-rank matrix $A$. The eigenvector matrix of $A$ has a Cauchy-like structure.…
This paper investigates the exponential stabilization of a coupled two-string system joined by a dynamic interior mass. The combined effect of three feedback mechanisms, boundary damping from tip velocity, higher-order nodal damping from…
We develop an asymptotical control theory for one of the simplest distributed oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of string states that admit…
We consider frequency-weighted damping optimization for vibrating systems described by a second-order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the…