Modal approximations to damped linear systems
نویسنده
چکیده
We consider a finite dimensional damped second order system and obtain spectral inclusion theorems for the related quadratic eigenvalue problem. The inclusion sets are the ’quasi Cassini ovals’ which may greatly outperform standard Gershgorin circles. As the unperturbed system we take a modally damped part of the system; this includes the known proportionally damped models, but may give much sharper estimates. These inclusions are then applied to derive some easily calculable sufficient conditions for the overdampedness of a given damped system.
منابع مشابه
Modal identification of linear non-proportionally damped systems by wavelet transform
A time-frequency identification technique based on wavelet transform is formulated and applied to free-decay responses of linear systems with non-proportional viscous damping. The Cauchy mother wavelet is used. Frequencies, modal damping ratios and complex mode shapes are identified from output-only free vibration signals. This identification technique has also shown to be effective when the (n...
متن کاملAb initio self-consistent laser theory and random lasers
We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by fully time-dependent numerical simulations or by using major approximations which neglect non-linear modal interactions and/or the openness of the laser sys...
متن کاملDamping Models for Structural Vibration
This dissertation reports a systematic study on analysis and identification of multiple parameter damped mechanical systems. The attention is focused on viscously and non-viscously damped multiple degree-offreedom linear vibrating systems. The non-viscous damping model is such that the damping forces depend on the past history of motion via convolution integrals over some kernel functions. The ...
متن کاملModeling and modal analysis to oscillations of IPMC cantilever beam and simulating as an actuator
The purpose of this article is modal analysis of ionic polymer metal composite beams, then briefing the system to the unique parameters to help in up modeling of the actuator. In this paper at first using of Mathematical analysis and Closed form transfer function of cantilever beam dynamic response to the forces of different inputs (intensive and continuous) is calculated and for different type...
متن کاملModal Analysis of Linear Dynamic Systems: Physical Interpretation
The modal analysis procedure for calculating the dynamic response of classically damped linear structural systems is reformulated with the objective of developing the physical significance of the elements of the solution and defining modal contribution factors. The resulting concepts are used to develop an approach for predicting how the relative contributions of various modes to the response a...
متن کامل