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A frequency averaging framework for the solution of complex dynamic systems.

Lecomte C - Proc. Math. Phys. Eng. Sci. (2014)

Bottom Line: A 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.

View Article: PubMed Central - PubMed

Affiliation: Associate Member, Southampton Statistical Sciences Research Institute , University of Southampton , Southampton, UK.

ABSTRACT
A 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.

No MeSH data available.


Illustration of the complex spring–mass system benchmark.
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RSPA20130743F1: Illustration of the complex spring–mass system benchmark.

Mentions: The benchmark system considered here is made of a large oscillator connected to a set of substructures, as illustrated in figure 1. Similar prototypes of complicated systems made of a large mass with many attached spring–mass systems have recurrently appeared in the literature of the last 20 years. One of the first occurrences was, for example, the undamped system that Weaver [41] used to illustrate the (ensemble) averaging approach he proposed as an alternative and extension to previous work on fuzzy and complex structures as by Soize [20] and Pierce et al. [21]. Although apparently simple, such complex systems are representative of engineering systems that are conceptually difficult to model because they exhibit a combination of low-, mid- and high-frequency characteristics. Their behaviour having actually proved to be far from simple and rather particularly interesting, they have been used in a form or another either to illustrate various theories or to study them in their own right. A salient example of the latter is the analysis in [19,42–44] and other publications of how the undamped additional spring–masses provide apparent equivalent damping to the larger mass.Figure 1.


A frequency averaging framework for the solution of complex dynamic systems.

Lecomte C - Proc. Math. Phys. Eng. Sci. (2014)

Illustration of the complex spring–mass system benchmark.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4042715&req=5

RSPA20130743F1: Illustration of the complex spring–mass system benchmark.
Mentions: The benchmark system considered here is made of a large oscillator connected to a set of substructures, as illustrated in figure 1. Similar prototypes of complicated systems made of a large mass with many attached spring–mass systems have recurrently appeared in the literature of the last 20 years. One of the first occurrences was, for example, the undamped system that Weaver [41] used to illustrate the (ensemble) averaging approach he proposed as an alternative and extension to previous work on fuzzy and complex structures as by Soize [20] and Pierce et al. [21]. Although apparently simple, such complex systems are representative of engineering systems that are conceptually difficult to model because they exhibit a combination of low-, mid- and high-frequency characteristics. Their behaviour having actually proved to be far from simple and rather particularly interesting, they have been used in a form or another either to illustrate various theories or to study them in their own right. A salient example of the latter is the analysis in [19,42–44] and other publications of how the undamped additional spring–masses provide apparent equivalent damping to the larger mass.Figure 1.

Bottom Line: A 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.

View Article: PubMed Central - PubMed

Affiliation: Associate Member, Southampton Statistical Sciences Research Institute , University of Southampton , Southampton, UK.

ABSTRACT
A 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.

No MeSH data available.