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Journal of Computational and Nonlinear Dynamics | Volume 7 | Issue 2 | Research Paper
Research Papers

Transformation of Arbitrary Elastic Mode Shapes Into Pseudo-Free-Surface and Rigid Body Modes for Multibody Dynamic Systems

[+] Author and Article Information
Karim Sherif

Dynamics and Structural Control, Linz Center of Mechatronics, Linz, 4040, Austriakarim.sherif@lcm.at

Hans Irschik

 Institute of Technical Mechanics, Johannes Kepler University of Linz, Linz, 4040, Austriairschik@mechatronik.uni-linz.ac.at

Wolfgang Witteveen

 Upper Austria University of Applied Sciences, Wels, 4600, Austriawolfgang.witteveen@fh-wels.at

J. Comput. Nonlinear Dynam 7(2), 021008 (Jan 06, 2012) (10 pages) doi:10.1115/1.4005237 History: Received February 28, 2011; Accepted September 26, 2011; Revised September 26, 2011; Published January 06, 2012; Online January 06, 2012
Article
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Citing Articles

In multibody dynamics, the flexibility effects of each body are captured by using a linear combination of elastic mode shapes. If a co-rotational and co-translating frame of reference is used together with eigenvectors of the unconstraint body, which are free-surface modes, some spatial integrals in the floating frame of reference configuration do vanish. The corresponding coordinate system is the so-called Tisserand (or Buckens) reference frame. In the present contribution, a technique is developed for separating an arbitrary elastic mode shape into a pseudo-free-surface mode and rigid body modes. The generated pseudo-free-surface mode has most of the advantageous characteristics of a free-surface mode, and spans together with the rigid body modes the same solution space as it is spanned by the original mode shape. Due to the fact that, in the floating frame of reference configuration, the rigid body motions are already described by special generalized coordinates, only the resulting pseudo-free-surface modes are finally used to capture the flexibility effects of each body. A result of the generated pseudo-free-surface modes is that some of the spatial integrals do vanish and, thus, the equations of motion are significantly simplified. Two examples are presented in order to illustrate and to demonstrate the potential of the proposed method.
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References

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Figures

Grahic Jump Location
+Deflection magnitude of node # 1133131
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Deflection magnitude of node # 1133131
Figure 6

Deflection magnitude of node # 1133131

Grahic Jump Location
+Jointed beam
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Jointed beam
Figure 5

Jointed beam

Grahic Jump Location
+Elastic mode shape u¯1,f* and u¯2,f*
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Elastic mode shape u¯1,f* and u¯2,f*
Figure 4

Elastic mode shape u¯1,f* and u¯2,f*

Grahic Jump Location
+Elastic mode shape u¯1 and u¯5
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Elastic mode shape u¯1 and u¯5
Figure 3

Elastic mode shape u¯1 and u¯5

Grahic Jump Location
+Screen shot of the deformation at three time steps
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Screen shot of the deformation at three time steps
Figure 7

Screen shot of the deformation at three time steps

Grahic Jump Location
+Two-dimensional beam
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Two-dimensional beam
Figure 2

Two-dimensional beam

Grahic Jump Location
+Floating frame of reference
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Floating frame of reference
Figure 1

Floating frame of reference

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