Vibro-acoustic dynamics in the presence of uncertainty and nonlinearity

The statistics of the vibro-acoustic response for an ensemble of systems with uncertain properties, such as those arising from manufacturing and material imperfections, is critical in the design of built-up structures. This is particularly important in the mid-frequency range, where sensitivity to uncertainty can lead to significant variation in the robustness of the response within components of a built-up assembly. Consequently, it is appropriate to model the mix of dynamic behaviour using a combination of deterministic and statistical approaches that are well suited to each regime. The Hybrid FE-SEA method combines the most prevalent of these respective techniques, namely the Finite Element (FE) method and Statistical Energy Analysis (SEA). This partitions the system into an assembly of statistically behaving subsystems and a deterministic master system, which are modelled using the FE method and SEA respectively, and yields significant computational benefit in predicting the response statistics. This has been developed as a linear approach and therefore is only applicable to linear systems. However, it is typical for nonlinearity to arise in real engineering systems. This may be localised, for instance, in a joint of a structure due to mechanisms like friction, or more distributed in a component, such as in cases of geometric nonlinearity or material hysteresis. The objective of this work is to extend the Hybrid FE-SEA method to nonlinear systems, particularly those with localised nonlinearities, which can be described deterministically as part of the master system. A linearisation scheme for an ensemble of nonlinear systems under random loading has therefore been developed to establish a linearised Hybrid FE-SEA method. Although this motivated its development, the linearisation itself is completely general in its derivation. Additionally, this highlighted two further shortcomings in the Hybrid FE-SEA method. These are also addressed and are consequently useful for both linear and nonlinear systems. The first establishes a framework for introducing general stochastic loading, that allows the correlation between random loads to be specified. This requires the underlying statistics describing the subsystem to be reconsidered employing results from random point process theory. The second extends the Hybrid FE-SEA method to determine the ensemble statistics of the broadband-averaged response. Following validation of the developed theory, each of these contributions is employed within the linearised Hybrid FE-SEA method, which is numerically validated against benchmark nonlinear Monte Carlo simulations.

Name dc:type.qualificationname

Doctor of Philosophy (PhD)

Level dc:type.qualificationlevel

Doctoral

Grantor dc:publisher.institution

University of Cambridge

Year dc:date.issued

2025

Author dc:creator

• Allen, Henry

Advisor dc:contributor.advisor

• Langley, Robin

• structural dynamics
• vibration
• stochastic processes
• nonlinearity
• linearisation
• statistical energy analysis
• Hybrid FE-SEA

Licence

• https://www.repository.cam.ac.uk/bitstreams/2c1c914a-0675-45b9-8279-fd3618a8f65e/download
• http://purl.org/NET/rdflicense/allrightsreserved

Language dc:language

eng

DOI dc:identifier.doi

https://doi.org/10.17863/CAM.124938

OAI identifier oai:identifier

oai:www.repository.cam.ac.uk:1810/395421