### Abstract

Enhanced modal-based order reduction of forced structural dynamic systems with isolated nonlinearity has been performed using the iterated LELSM (Local equivalent linear stiffness method) modes and new type of Ritz vectors. The iterated LELSM modes have been found via iteration of the modes of the mass normalized local equivalent linear stiffness matrix of the nonlinear systems. The optimal basis vector of principal orthogonal modes (POMs) is found for such system via simulation and used for POD-based order reduction for comparison. Two new Ritz vectors are defined as a static load vectors where one of them gives a static displacement to the mass connected to the periodic forcing load and the other gives a static displacement to the mass connected to the nonlinear element. It is found that the use of these vectors, which are augmented to the iterated LELSM modes in the order reduction modal matrix, reduces the number of modes used in order reduction and considerably enhances the accuracy of order reduction. The combination of the new Ritz vectors with the iterated LELSM modes in the order reduction matrix yields more accurate reduced models than POD-based order reduction of forced and nonlinear systems. Hence, the LELSM modal-based order reduction is essentially enhanced over POD-based and linear-based order reductions by using these new Ritz vectors. In addition, the main advantage of using the iterated LELSM modes for order reduction is that, unlike POMs, they do not require a priori simulation and thus they can be combined with new Ritz vectors and applied directly to the system.

Original language | English (US) |
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Title of host publication | Conference Proceedings of the Society for Experimental Mechanics Series |

Pages | 41-52 |

Number of pages | 12 |

Volume | 2 |

State | Published - 2011 |

Externally published | Yes |

Event | 28th IMAC, A Conference on Structural Dynamics, 2010 - Jacksonville, FL, United States Duration: Feb 1 2010 → Feb 4 2010 |

### Other

Other | 28th IMAC, A Conference on Structural Dynamics, 2010 |
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Country | United States |

City | Jacksonville, FL |

Period | 2/1/10 → 2/4/10 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)
- Computational Mechanics
- Mechanical Engineering

### Cite this

*Conference Proceedings of the Society for Experimental Mechanics Series*(Vol. 2, pp. 41-52)

**Enhanced order reduction of forced nonlinear systems using new ritz vectors.** / Al-Shudeifat, Mohammad A.; Butcher, Eric; Burton, Thomas D.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Conference Proceedings of the Society for Experimental Mechanics Series.*vol. 2, pp. 41-52, 28th IMAC, A Conference on Structural Dynamics, 2010, Jacksonville, FL, United States, 2/1/10.

}

TY - GEN

T1 - Enhanced order reduction of forced nonlinear systems using new ritz vectors

AU - Al-Shudeifat, Mohammad A.

AU - Butcher, Eric

AU - Burton, Thomas D.

PY - 2011

Y1 - 2011

N2 - Enhanced modal-based order reduction of forced structural dynamic systems with isolated nonlinearity has been performed using the iterated LELSM (Local equivalent linear stiffness method) modes and new type of Ritz vectors. The iterated LELSM modes have been found via iteration of the modes of the mass normalized local equivalent linear stiffness matrix of the nonlinear systems. The optimal basis vector of principal orthogonal modes (POMs) is found for such system via simulation and used for POD-based order reduction for comparison. Two new Ritz vectors are defined as a static load vectors where one of them gives a static displacement to the mass connected to the periodic forcing load and the other gives a static displacement to the mass connected to the nonlinear element. It is found that the use of these vectors, which are augmented to the iterated LELSM modes in the order reduction modal matrix, reduces the number of modes used in order reduction and considerably enhances the accuracy of order reduction. The combination of the new Ritz vectors with the iterated LELSM modes in the order reduction matrix yields more accurate reduced models than POD-based order reduction of forced and nonlinear systems. Hence, the LELSM modal-based order reduction is essentially enhanced over POD-based and linear-based order reductions by using these new Ritz vectors. In addition, the main advantage of using the iterated LELSM modes for order reduction is that, unlike POMs, they do not require a priori simulation and thus they can be combined with new Ritz vectors and applied directly to the system.

AB - Enhanced modal-based order reduction of forced structural dynamic systems with isolated nonlinearity has been performed using the iterated LELSM (Local equivalent linear stiffness method) modes and new type of Ritz vectors. The iterated LELSM modes have been found via iteration of the modes of the mass normalized local equivalent linear stiffness matrix of the nonlinear systems. The optimal basis vector of principal orthogonal modes (POMs) is found for such system via simulation and used for POD-based order reduction for comparison. Two new Ritz vectors are defined as a static load vectors where one of them gives a static displacement to the mass connected to the periodic forcing load and the other gives a static displacement to the mass connected to the nonlinear element. It is found that the use of these vectors, which are augmented to the iterated LELSM modes in the order reduction modal matrix, reduces the number of modes used in order reduction and considerably enhances the accuracy of order reduction. The combination of the new Ritz vectors with the iterated LELSM modes in the order reduction matrix yields more accurate reduced models than POD-based order reduction of forced and nonlinear systems. Hence, the LELSM modal-based order reduction is essentially enhanced over POD-based and linear-based order reductions by using these new Ritz vectors. In addition, the main advantage of using the iterated LELSM modes for order reduction is that, unlike POMs, they do not require a priori simulation and thus they can be combined with new Ritz vectors and applied directly to the system.

UR - http://www.scopus.com/inward/record.url?scp=80051565484&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051565484&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:80051565484

SN - 9781441997180

VL - 2

SP - 41

EP - 52

BT - Conference Proceedings of the Society for Experimental Mechanics Series

ER -