Damping optimization in mechanical systems with external force

Fast optimization of viscosities for frequency-weighted damping of second-order systems

“…Remark 3.2 As a final step of our algorithm, note that we also follow a suggestion of Taslaman [29, section 4.3] to refine the accuracy of computed eigenvectors by doing a single step of inverse iteration for each eigenvector; due to the particular structure of C(v), the SMW formula can be used to do a single-step of inverse iteration in only O(n) work per eigenvector. Similar application of the SMW formula in damped systems for efficient computations can be found in [34,33,24,31,3].…”

Optimization of damping positions in a mechanical system

“…For more details, see, e.g., [23,34,36]. This problem was considered in [34], where the authors provided an explicit formula for the objective function for the structured system, in particular, all dampers have the same damping viscosities and internal damping is neglected. Moreover, a more general case, which includes the arbitrary time τ in criterion (2.4), was considered in [23].…”

“…The above approach is usually called the "average displacement amplitude" minimization and has been widely used in different areas, like for example in aeronautics and astronautics [28] or [27] or in physics [11] and engineering [16] and applied mathematics in [36], [34] and [23]. Except this criterion, one can also consider the "average energy amplitude" minimization that in general gives different optimal values.…”

“…Obviously, this approach is computationally infeasible for dimensions larger than n ∼ O (10), thus in this paper we will consider several different approaches that can efficiently optimize damping. For that purpose, we propose a novel approach which combines approaches from [34], [32] and [5] with the one from [19].…”

Stochastic Stability and Bifurcation of A High Speed Rotor-Bearing System with Random Excitation

“…Hu and Xian [1] established a mathematical model of an asymmetric double-disc rotor-bearing system and use nonlinear dynamics theory to consider nonlinear oil-film force and rub-impact force. And then, Ninoslav Truhar et al [2] considered a mechanical system excited by external force with the development of nonlinear dynamics theory, nonlinear dynamics connects with rotor dynamics tightly, which makes the research on rotor dynamics present a new outlook. In the past decade, many researches about the nonlinear stochastic dynamics and controls which have been shifted from Lagrange system to Hamilton system, and the nonlinear stochastic dynamical system is expressed as dissipative Hamilton system with stochastic excitation.…”