Goal Oriented Estimation of Errors due to Modal Reduction in Dynamics

The aim of this thesis is the estimation of errors due to reduction in modal superposition method. Mode superposition methods are used to calculate the dynamic response of linear systems. In modal superposition method, it becomes unnecessary to consider all the modes of a particular system. In generally only a few number of modes contribute significantly to the solution. The main aim of the study is to identify the significant modes required for good approximation….


1 Notation
2 Introduction
3 Theory
3.1 Mode superposition method
3.2 The discrete system
3.3 Forced harmonic response
3.4 Undamped modal analysis
4 Modal Synthesis for Forced Harmonic Response
4.1 Complete basis-Diagonalization
4.2 Reduced basis-Diagonalization
5 Error Analysis
5.1 The residual and the error
5.2 Output functions
5.3 The error representation using a dual solution
5.4 Error contributions
6 Simulation and results
6.1 Numerical Example: Cantilever beam under harmonic load
6.2 Finite element model
6.3 Mode shapes
6.4 Displacement in X direction
6.4.1 Dual problem solution
6.4.2 Exact Error
6.4.3 Error estimation
6.4.4 Comparison-Estimated error v/s Exact error
6.4.5 Error Contribution
6.5 Displacement in Y direction
6.5.1 Dual problem solution
6.5.2 Exact Error
6.5.3 Error estimation
6.5.4 Error contribution
6.6 In plane stress σxx
6.6.1 Dual problem solution
6.6.2 Exact Error
6.6.3 Error estimation
6.6.4 Error contribution
7 Discussions and conclusions
8 Future work
9 References

Author: Sandeep Shetty, Chukwudi Anthony Okeke

Source: Blekinge Institute of Technology

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