Reduced models for the medium-frequency dynamics of stochastic systems

Area of Science:

• Mechanical Engineering
• Vibration Analysis
• Computational Mechanics

Background:

• Traditional modal analysis and statistical energy analysis (SEA) face challenges in the medium-frequency range.
• Uncertainty in structural systems arises from complex couplings with secondary systems, hindering conventional modeling.
• Existing methods struggle with computational and conceptual difficulties for randomly parameterized structures.

Purpose of the Study:

• To present a novel frequency domain vibration analysis procedure for randomly parameterized structural systems.
• To address the limitations of existing methods in the medium-frequency vibration analysis.
• To develop a robust methodology for analyzing complex structural systems with uncertainties.

Main Methods:

• Coupling probabilistic reduction methods with dynamical reduction methods.
• Utilizing Karhunen-Loeve and Polynomial Chaos decompositions of stochastic processes.
• Employing an operator decomposition scheme based on the spectrum of an energy operator.

Main Results:

• A new procedure for vibration analysis in the medium-frequency range is established.
• The methodology effectively handles uncertainties in structural systems.
• Computational and conceptual difficulties of traditional methods are overcome.

Conclusions:

• The proposed method offers a robust solution for medium-frequency vibration analysis of complex structures.
• This approach enhances the analysis of systems with inherent parameter uncertainties.
• The coupling of probabilistic and dynamical reduction techniques provides a powerful framework for structural dynamics.