Model reduction of systems with localized nonlinearities.

Segalman, Daniel Joseph

Sandia National Laboratories

关键词: Structural Dynamics-Mathematical Models.;    Dynamics Nonlinear Mechanics.;    99 General And Miscellaneous//Mathematics, Computing, And Information Science;    Calculation Methods;    Mathematical Models;   

DOI  :  10.2172/886648
RP-ID  :  SAND2006-1789
RP-ID  :  AC04-94AL85000
RP-ID  :  886648

美国|英语

来源: UNT Digital Library

【 摘 要 】

An LDRD funded approach to development of reduced order models for systems with local nonlinearities is presented. This method is particularly useful for problems of structural dynamics, but has potential application in other fields. The key elements of this approach are (1) employment of eigen modes of a reference linear system, (2) incorporation of basis functions with an appropriate discontinuity at the location of the nonlinearity. Galerkin solution using the above combination of basis functions appears to capture the dynamics of the system with a small basis set. For problems involving small amplitude dynamics, the addition of discontinuous (joint) modes appears to capture the nonlinear mechanics correctly while preserving the modal form of the predictions. For problems involving large amplitude dynamics of realistic joint models (macro-slip), the use of appropriate joint modes along with sufficient basis eigen modes to capture the frequencies of the system greatly enhances convergence, though the modal nature the result is lost. Also observed is that when joint modes are used in conjunction with a small number of elastic eigen modes in problems of macro-slip of realistic joint models, the resulting predictions are very similar to those of the full solution when seen through a low pass filter. This has significance both in terms of greatly reducing the number of degrees of freedom of the problem and in terms of facilitating the use of much larger time steps.