A COMBINED MODAL/FINITE ELEMENT ANALYSIS TECHNIQUE FOR THE DYNAMIC RESPONSE OF A NON-LINEAR BEAM TO HARMONIC EXCITATION

✍ Scribed by M.I. MCEWAN; J.R. WRIGHT; J.E. COOPER; A.Y.T. LEUNG

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 409 KB
• Volume: 243
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.2000.3434

✦ Synopsis

In this paper, a method is proposed for modelling large de#ection beam response involving multiple vibration modes. Signi"cant savings in computational time can be obtained compared with the direct integration non-linear "nite element method. The de#ections from a number of static non-linear "nite element test cases are transformed into modal co-ordinates using the modes of the underlying linear system. Regression analysis is then used to "nd the unknown coupled non-linear modal sti!ness coe$cients. The inclusion of "nite element derived modal masses, and an arbitrary damping model completes the governing non-linear equations of motion. The response of the beam to excitation of an arbitrary nature may then be found using time domain numerical integration of the reduced set of equations. The work presented here extends upon the work of previous researchers to include non-linearly coupled multi-modal response. The particular bene"ts of this approach are that no linearization is imposed, and that almost any commercial "nite element package may be employed without modi"cation.

The proposed method is applied to the case of a homogeneous isotropic beam. Fully simply supported and fully clamped boundary conditions are considered. For the free vibration case, results are compared to those of previous researchers. For the case of steady-state harmonic excitation, results are compared with the direct integration non-linear "nite element method using ABAQUS. In all cases, excellent agreement is obtained.