### Abstract

In this paper the mathematical framework of an advanced algorithm is presented to efficiently form and solve the equations of motion of a multibody system involving uncertainty in the system parameters and/or the excitations. The uncertainty is introduced to the system through the application of the polynomial chaos expansion. In this scheme, states of the system, nondeterministic parameters, and the constraint loads are expanded using modal values as well as orthogonal basis functions. Computational complexity of the application of traditional methods to solve the stochastic equations of motion of a multibody system drastically grows as a cubic function of the number of the states of the system, uncertain parameters and the maximum degree of the polynomial chosen for the basis function. The presented method forms the equation of motion of the system without forming the entire mass and Jacobian matrices. In this strategy, the stochastic governing equations of motion of each individual body as well as the one associated with the kinematic constraint at the connecting joint are developed in terms of the basis functions and modal coordinates. Then sweeping the system in two passes assembly and disassembly, one can form and solve the stochastic equations of motion. In the assembly pass the non-deterministic equations of motion of the assemblies are obtained. In the disassembly process, these equations are then recursively solved for the modal values of the spatial accelerations and the constraints loads. In the serial and parallel implementations, computational complexity of the method increases as a linear and logarithmic functions of the number of the states of the system, uncertain variables, and the maximum degree of the basis functions used in the expansion.

Original language | English (US) |
---|---|

Title of host publication | 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control |

Publisher | American Society of Mechanical Engineers (ASME) |

Volume | 6 |

ISBN (Print) | 9780791846391 |

DOIs | |

State | Published - 2014 |

Event | ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014 - Buffalo, United States Duration: Aug 17 2014 → Aug 20 2014 |

### Other

Other | ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014 |
---|---|

Country | United States |

City | Buffalo |

Period | 8/17/14 → 8/20/14 |

### Fingerprint

### ASJC Scopus subject areas

- Mechanical Engineering
- Computer Graphics and Computer-Aided Design
- Computer Science Applications
- Modeling and Simulation

### Cite this

*10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control*(Vol. 6). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC201435226

**An efficient application of polynomial chaos expansion for the dynamic analysis of multibody systems with uncertainty.** / Poursina, Mohammad.

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

*10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control.*vol. 6, American Society of Mechanical Engineers (ASME), ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014, Buffalo, United States, 8/17/14. https://doi.org/10.1115/DETC201435226

}

TY - GEN

T1 - An efficient application of polynomial chaos expansion for the dynamic analysis of multibody systems with uncertainty

AU - Poursina, Mohammad

PY - 2014

Y1 - 2014

N2 - In this paper the mathematical framework of an advanced algorithm is presented to efficiently form and solve the equations of motion of a multibody system involving uncertainty in the system parameters and/or the excitations. The uncertainty is introduced to the system through the application of the polynomial chaos expansion. In this scheme, states of the system, nondeterministic parameters, and the constraint loads are expanded using modal values as well as orthogonal basis functions. Computational complexity of the application of traditional methods to solve the stochastic equations of motion of a multibody system drastically grows as a cubic function of the number of the states of the system, uncertain parameters and the maximum degree of the polynomial chosen for the basis function. The presented method forms the equation of motion of the system without forming the entire mass and Jacobian matrices. In this strategy, the stochastic governing equations of motion of each individual body as well as the one associated with the kinematic constraint at the connecting joint are developed in terms of the basis functions and modal coordinates. Then sweeping the system in two passes assembly and disassembly, one can form and solve the stochastic equations of motion. In the assembly pass the non-deterministic equations of motion of the assemblies are obtained. In the disassembly process, these equations are then recursively solved for the modal values of the spatial accelerations and the constraints loads. In the serial and parallel implementations, computational complexity of the method increases as a linear and logarithmic functions of the number of the states of the system, uncertain variables, and the maximum degree of the basis functions used in the expansion.

AB - In this paper the mathematical framework of an advanced algorithm is presented to efficiently form and solve the equations of motion of a multibody system involving uncertainty in the system parameters and/or the excitations. The uncertainty is introduced to the system through the application of the polynomial chaos expansion. In this scheme, states of the system, nondeterministic parameters, and the constraint loads are expanded using modal values as well as orthogonal basis functions. Computational complexity of the application of traditional methods to solve the stochastic equations of motion of a multibody system drastically grows as a cubic function of the number of the states of the system, uncertain parameters and the maximum degree of the polynomial chosen for the basis function. The presented method forms the equation of motion of the system without forming the entire mass and Jacobian matrices. In this strategy, the stochastic governing equations of motion of each individual body as well as the one associated with the kinematic constraint at the connecting joint are developed in terms of the basis functions and modal coordinates. Then sweeping the system in two passes assembly and disassembly, one can form and solve the stochastic equations of motion. In the assembly pass the non-deterministic equations of motion of the assemblies are obtained. In the disassembly process, these equations are then recursively solved for the modal values of the spatial accelerations and the constraints loads. In the serial and parallel implementations, computational complexity of the method increases as a linear and logarithmic functions of the number of the states of the system, uncertain variables, and the maximum degree of the basis functions used in the expansion.

UR - http://www.scopus.com/inward/record.url?scp=84961382128&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961382128&partnerID=8YFLogxK

U2 - 10.1115/DETC201435226

DO - 10.1115/DETC201435226

M3 - Conference contribution

SN - 9780791846391

VL - 6

BT - 10th International Conference on Multibody Systems, Nonlinear Dynamics, and Control

PB - American Society of Mechanical Engineers (ASME)

ER -