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Research Papers

Three-Dimensional Natural Vibration Analysis With Meshfree Solution Structure Method

[+] Author and Article Information
Tomislav Kosta

Department of Mechanical
and Materials Engineering,
Florida International University,
Miami, FL 33174
e-mail: tkost001@gmail.com

Igor Tsukanov

Department of Mechanical
and Materials Engineering,
Florida International University,
Miami, FL 33174
e-mail: igor.tsukanov@gmail.com

Such function is also called an implicit function since the equation ωi(x) = 0 implicitly describes the shape of the geometric boundary.

The geometric model was obtained from the CAD models repository at http://www.grabcad.com.

The geometric model was obtained from the CAD models repository at http://www.grabcad.com.

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 14, 2013; final manuscript received June 1, 2014; published online July 25, 2014. Assoc. Editor: Michael Leamy.

J. Vib. Acoust 136(5), 051007 (Jul 25, 2014) (7 pages) Paper No: VIB-13-1365; doi: 10.1115/1.4027844 History: Received October 14, 2013; Revised June 01, 2014

This paper describes the pioneering application of the meshfree solution structure method (SSM) to computer simulation of natural vibrations of 3D mechanical parts and structures. Using several carefully chosen examples, we investigate the accuracy and convergence of the computed natural frequencies. The salient feature of our approach is exact treatment of the prescribed boundary conditions that are enforced using approximate distance functions that vanish on the boundaries of a geometric model. Ability to use spatial meshes that do not necessarily conform to the shape of the geometric model makes it possible to eliminate or substantially simplify the finite element meshing. This defines unprecedented geometric flexibility of the SSM as well as the complete automation of the solution procedure.

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Figures

Grahic Jump Location
Fig. 1

Spur gear: (a) The boundary of the shaft hole is fixed in all coordinate directions. (b) Approximate distance field to the boundary of the shaft hole. (c) First ten natural frequencies computed by the SSM and FEM in SolidWorks Simulation. (d) Convergence of the 9th natural frequency.

Grahic Jump Location
Fig. 2

Robot arm: (a) The boundaries of the holes are fixed in all coordinate directions. (b) Approximate distance field to the fixed boundaries. (c) First ten natural frequencies computed using the SSM and FEM in SolidWorks Simulation. (d) Convergence of the 10th natural frequency.

Grahic Jump Location
Fig. 3

Natural vibration modes of the robot arm. Results of FEA in SolidWorks Simulation: (a) mode 1, (b) mode 2, (c) mode 5, and (d) mode 10. Vibration modes predicted by the SSM: (e) mode 1, (f) mode 2, (g) mode 5, and (h) mode 10. Models that appear in a blue color in Figs. 3(e)3(h) illustrate the shape of the natural vibration modes, while nondeformed model is shown in red (see color figure online).

Grahic Jump Location
Fig. 4

(a) Naja pawn. (b) Approximate distance field to the fixed boundary. (c) First, five natural frequencies of the naja pawn (Fig. 4(a)) computed using the SSM. (d)–(h) First five natural vibration modes of the naja pawn computed using SSM. Models that appear in a blue color illustrate the shape of the natural vibration modes, while nondeformed model is shown in red. (i) Convergence of the 5th natural frequency of the naja pawn (see color figure online).

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