1,721,190 research outputs found
Zero and root loci of disturbed spring-mass systems
No full textModels consisting of chains of particles that are coupled to their neighbours appear in many applications in physics or engineering, such as in the study of dynamics of mono-atomic and multi-atomic lattices, the resonances of crystals with impurities and the response of damaged bladed discs. Analytical properties of the dynamic responses of such disturbed chains of identical springs and masses are presented, including when damping is present. Several remarkable properties in the location of the resonances (poles) and anti-resonances (zeros) of the displacements in the frequency domain are presented and proved. In particular, it is shown that there exists an elliptical region in the frequency–disturbance magnitude plane from which zeros are excluded and the discrete values of the frequency and disturbance at which double poles occur are identified. A particular focus is on a local disturbance, such as when a spring or damper is modified at or between the first and last masses. It is demonstrated how, notably through normalization, the techniques and results of the paper apply to a broad category of more complex systems in physics, chemistry and engineering
An introduction to Bayesian methods and illustration of their application
No full textSeminar presentation - An introduction to Bayesian methodsand illustration of their applicatio
Interpolatory model reduction of uncertain dynamic and vibro-acoustic systems in the mid- and high-frequency ranges
No full textAnalysis of the exact statistics of uncertain structural dynamic systems: "what does a random component really change?"
No full textA frequency averaging framework for the solution of complex dynamic systems
No full textA frequency averaging framework is proposed for the solution of complex linear dynamic systems. It is remarkable that, while the mid-frequency region is usually very challenging, a smooth transition from low- through mid- and high-frequency ranges is possible and all ranges can now be considered in a single framework. An interpretation of the frequency averaging in the time domain is presented and it is explained that the average may be evaluated very efficiently in terms of system solutions
Simplicity and intricacy of the propagation of uncertainty in linear structural dynamic systems
No full textAn efficient Krylov model reduction approach for the direct evaluation of the analytical frequency average of transfer functions in the low-, mid-, and high-frequency ranges
No full textAnalytical expressions for the Gaussian frequency average and frequency variance of transfer functions, of linear dynamic systems are available from the author’s previous work [1].Since these expressions are valid and can be evaluated at any frequency, independently of thesystem complexity and modal density, and since they also give the frequency average of the energy, they provide a natural framework in which to study the transition from low- to highfrequency ranges. In principle, the analytical expressions would require the knowledge of the modal characteristics of the dynamic system of interest. The fact that modal information is not needed to evaluate the frequency average of transfer functions is highlighted. Rather, the average can be evaluated up to desired precision by using an analytical Krylov model reduction approach. The efficiency of this approach is demonstrated on systems of different dimensions and modal densities. It is further demonstrated that system characteristics that are important at different frequency ranges can be integrated into a single reduced model and that low- to high-frequency ranges analysis can be run with a single model
- …
