Dynamic Sub-structuring Analysis for Complex System Vibration
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Solution Overview
Problem
Current sub-structuring methods for dynamic analysis of complex systems, such as those used in acoustic and vibration studies, face inefficiencies in computational time and accuracy when optimizing designs, particularly in reducing the size of models while maintaining performance quality.
Innovation Solution
The method involves sub-structuring systems into multiple components, modeling interfaces, and performing dynamic analysis using orthogonalized eigenvectors and singular value decomposition to select a reduced set of interface basis functions, which are then used to constrain and reduce the sub-structure models, allowing for efficient coupling and assembly.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If sub-structuring methods are used to reduce model size and computational cost, then computational efficiency is improved, but accuracy is lost due to model condensation
Solution Approach 1:
The system is divided into multiple sub-structures that can be processed independently. Each sub-structure is discretized and analyzed separately, with interface degrees of freedom identified at the boundaries. This segmentation allows parallel processing and reduces the computational burden of analyzing the entire system as a single unit.
Solution Approach 2:
The patent employs dynamic condensation techniques that adaptively reduce the system model based on frequency ranges and modal characteristics. The reduction process is not static but dynamically adjusted to preserve accuracy in critical frequency ranges while maximizing computational efficiency in less critical ranges.
2Measurement precision
If more sub-structures are created to improve model detail, then model accuracy is improved, but computational time increases
Solution Approach 1:
Different levels of discretization and modeling detail are applied to different sub-structures based on their importance to the overall system behavior. Critical sub-structures receive finer discretization and more detailed modeling, while less critical sub-structures use coarser models, optimizing the balance between accuracy and computational cost.
Solution Approach 2:
The patent changes key parameters such as the number of interface degrees of freedom, the frequency range of interest, and the level of discretization based on the specific analysis requirements. These parameter adjustments allow the model to adapt to different accuracy and computational time requirements.
3Measurement precision
If interface degrees of freedom are increased to improve coupling accuracy, then interface modeling accuracy is improved, but the size of the reduced system model increases
Solution Approach 1:
The patent applies partial action by selectively including only the necessary interface degrees of freedom that significantly contribute to the overall system accuracy. Not all possible interface DOFs are included; rather, only those that provide the most benefit relative to the increase in model size are retained.
Data Source
AI summary
Methods for performing a dynamic analysis of complex systems are described. The dynamic analysis of complex systems is performed by sub-structuring of the system into a plurality of sub-structures. The sub-structures and the interfaces between the sub-structures are modelled using a generalized eigenvector analysis of a discretized model of a full system or a subassembly thereof comprising at least two sub-structures. The sub-structures then are combined at the interfaces into a combined system. The combined system then is solved. Optionally, selected sub-structures may be reduced. Performing such a dynamic analysis allows studying characteristics such as e.g. vibration and/or acoustical effects in a computational efficient way. Such methods can be applied for optimizing designs of such complex systems.