Response Analysis of Acoustic Field With Convex Parameters

Baizhan Xia · Dejie Yu

17 citations0/0 files storedJournal of vibration and acoustics

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Probabilistic and Robust Engineering Design Acoustic Wave Phenomena Research Advanced Numerical Analysis Techniques

Abstract

The acoustic field with convex parameters widely exists in the engineering practice. The vertex method and the anti-optimization method are not considered as appropriated approaches for the response analysis of acoustic field with convex parameters. The shortcoming of the vertex method is that the local optima out of vertexes cannot be identified. The disadvantage of the anti-optimization method is that the analytical formulation of response may be not obtained. To analyze the acoustic field with convex parameters efficiently and effectively, a first-order convex perturbation method (FCPM) and a second-order convex perturbation method (SCPM) are presented. In FCPM, the response of the acoustic field with convex parameters is expanded with the first-order Taylor series. In SCPM, the response of the acoustic field with convex parameters is expanded with the second-order Taylor series neglecting the nondiagonal elements of Hessian matrix. The variational bounds of the expanded responses in FCPM and SCPM are yielded by the Lagrange multiplier method. The accuracy and efficiency of FCPM and SCPM are investigated by numerical examples.

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References

1998Antioptimization of structures with large uncertain-but-non-random parameters via interval analysis 2012Structural reliability analysis using non-probabilistic convex model 2001Anti-optimisation of uncertain structures using interval analysis 2007The static displacement and the stress analysis of structures with bounded uncertainties using the vertex solution theorem 2001Interval static displacement analysis for structures with interval parameters 2003Comparison of static response of structures using convex models and interval analysis method 2012Modified sub-interval perturbation finite element method for 2D acoustic field prediction with large uncertain-but-bounded parameters 2013Interval and subinterval perturbation methods for a structural-acoustic system with interval parameters

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