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IUTAM Symposium on the Vibration Analysis of Structures with Uncertainties Proceedings of the IUTAM Symposium on the Vibration Analysis of Structures with Uncertainties held in St. Petersburg, Russia, July 5-9, 2009

:	Robin S. Langley, Alexander K. Belyaev
:	Alexander K. Belyaev, Robin S. Langley
:	IUTAM Symposium on the Vibration Analysis of Structures with Uncertainties Proceedings of the IUTAM Symposium on the Vibration Analysis of Structures with Uncertainties held in St. Petersburg, Russia, July 5-9, 2009
:	Springer-Verlag
:	9789400702899
:	1
:	CHF 135.30
:

:	Maschinenbau, Fertigungstechnik
:	English

:	470
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

The Symposium was aimed at the theoretical and numerical problems involved in modelling the dynamic response of structures which have uncertain properties due to variability in the manufacturing and assembly process, with automotive and aerospace structures forming prime examples. It is well

known that the difficulty in predicting the response statistics of such structures is immense, due to the complexity of the structure, the large number of variables which might be uncertain, and the inevitable lack of data regarding

the statistical distribution of these variables.

The Symposium participants presented the latest thinking in this very active research area, and novel techniques were presented covering the full frequency spectrum of low, mid, and high frequency vibration problems. It was demonstrated that for high frequency vibrations the response statistics

can saturate and become independent of the detailed distribution of the uncertain system parameters. A number of presentations exploited this physical behaviour by using and extending methods originally developed in both

phenomenological thermodynamics and in the fields of quantum mechanics and random matrix theory.

For low frequency vibrations a number of presentations focussed on parametric uncertainty modelling (for example, probabilistic models, interval analysis, and fuzzy descriptions) and on methods of propagating this uncertainty through a large dynamic model in an effi cient way. At mid frequencies

the problem is mixed, and various hybrid schemes were proposed.

It is clear that a comprehensive solution to the problem of predicting the vibration response of uncertain structures across the whole frequency range requires expertise across a wide range of areas (including probabilistic and non-probabilistic methods, interval and info-gap analysis, statistical energy analysis, statistical thermodynamics, random wave approaches, and large

scale computations) and this IUTAM symposium presented a unique opportunity to bring together outstanding international experts in these fields.

	Preface	6
	Contents	8
	Non-probabilistic and related approaches	20
	Linear Bounds on an Uncertain Non-Linear Oscillator: An Info-Gap Approach	21
	Introduction	21
	Dynamics, Uncertainty and Robustness	22
	Example: Uncertain Cubic Non-Linearity	25
	Example: Multiple Uncertainties	28
	Robustness as a Proxy for Probability	30
	Conclusion	31
	References	32
	Quantification of uncertain and variable model parameters in non-deterministic analysis	33
	Introduction	33
	Numerical representation of parameter uncertainty and variability	34
	Definitions	35
	Discussion and extension of the definitions	36
	Literature review on uncertain model and material data	37
	Non-probabilistic models	37
	Probabilistic models	38
	Material data	40
	Other model properties	43
	Alternative approaches: non-parametric model concept and info-gap theory	43
	Summary of observations	44
	Conclusions	44
	References	45
	Vibrations of layered structures with fuzzy core stiffness/fuzzy interlayer slip	47
	Introduction	47
	Fuzzy sandwich beams	48
	Three-layer beams	48
	Modal analysis of the three-layer beam, hard-hinged support	51
	Numerical results	53
	Isosceles uncertainty	53
	Constraints affected to the uncertain natural frequencies	56
	Some effects of non-symmetric uncertainty	59
	Conclusions	59
	References	60
	Vibration Analysis of Fluid-Filled Piping Systems with Epistemic Uncertainties	61
	Introduction	62
	Classification, Representation and Propagation of Uncertainty	62
	Uncertainty Classification and Representation	62
	Uncertainty Propagation Based on the Transformation Method	64
	Fluid-Filled Piping System	66
	Modeling Approach	66
	Experimental Setup	69
	Comprehensive Modeling and Simulation	69
	Modeling of Epistemic Uncertainties	69
	Simulation Results	71
	Measures of Influence	72
	Conclusions	73
	References	73
	Fuzzy vibration analysis and optimization of engineering structures: Application to Demeter satellite	75
	Introduction	75
	Aims of the study	76
	Description of the study	76
	Building of fuzzy optimization problem	77
	Fuzzy vibration analysis	80
	PAEM method	80
	Numerical application	81
	Fuzzy optimization	81
	Design methodology	82
	Improvement of the initial design	84
	Conclusion	85
	References	87
	Numerical dynamic analysis of uncertain mechanical structures based on interval fields	88
	Introduction	88
	Interval finite element analysis	90
	Interval fields	91
	General concept	91
	Interval fields as uncertain input parameters	92
	Interval fields as uncertain analysis results	94
	Application of interval fields for vibro-acoustic analysis	96
	Vibro-acoustic analysis based on the ATV concept	96
	Interval analysis based on structural FRF interval fields	97
	Numerical example	98
	Conclusions	99
	References	100
	From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs under Interval and p-Box Uncertainty	101
	Formulation of the Problem	101
	Interval Computations: Brief Reminder	104
	Constraint-Based Set Computations	105
	References	114
	Dynamic Steady-State Analysis of Structures under Uncertain Harmonic Loads via Semidefinite Program	115
	Introduction	115
	Uncertain equations for steady state vibration	117
	Governing equations	117
	Uncertainty model	117
	ULE in real variables	118
	Bounds for complex amplitude	119