Interaction and multiscale mechanics

  • 제2권4호
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  • Pages.333-352
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  • 2009
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  • 1976-0426(pISSN)
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  • 2092-6200(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Radial basis collocation method for dynamic analysis of axially moving beams

  • Wang, Lihua (School of Aerospace Engineering and Applied Mechanics, Tongji University) ;
  • Chen, Jiun-Shyan (Civil & Environmental Engineering Department, University of California Los Angeles (UCLA)) ;
  • Hu, Hsin-Yun (Mathematics Department, Tunghai University)
  • 투고 : 2009.09.01
  • 심사 : 2009.09.17
  • 발행 : 2009.12.25
⟨ 이전 논문 다음 논문 ⟩

초록

We introduce a radial basis collocation method to solve axially moving beam problems which involve $2^{nd}$ order differentiation in time and $4^{th}$ order differentiation in space. The discrete equation is constructed based on the strong form of the governing equation. The employment of multiquadrics radial basis function allows approximation of higher order derivatives in the strong form. Unlike the other approximation functions used in the meshfree methods, such as the moving least-squares approximation, $4^{th}$ order derivative of multiquadrics radial basis function is straightforward. We also show that the standard weighted boundary collocation approach for imposition of boundary conditions in static problems yields significant errors in the transient problems. This inaccuracy in dynamic problems can be corrected by a statically condensed semi-discrete equation resulting from an exact imposition of boundary conditions. The effectiveness of this approach is examined in the numerical examples.

키워드

참고문헌

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  2. Dynamic response of clamped axially moving beams: Integral transform solution vol.218, pp.2, 2011, https://doi.org/10.1016/j.amc.2011.05.035
  3. Radial Basis Collocation Method for the Dynamics of Rotating Flexible Tube Conveying Fluid vol.07, pp.03, 2015, https://doi.org/10.1142/S1758825115500453
  4. Radial basis functions methods for boundary value problems: Performance comparison vol.84, 2017, https://doi.org/10.1016/j.enganabound.2017.08.019
  5. Variational Iteration Method for Transverse Vibrations of the Elastic, Tensioned Beam vol.5, pp.3, 2017, https://doi.org/10.18178/ijmmm.2017.5.3.315
  6. Radial basis function collocation method for a rotating Bose-Einstein condensation with vortex lattices vol.5, pp.2, 2009, https://doi.org/10.12989/imm.2012.5.2.131
  7. Dynamic stiffness matrix method for axially moving micro-beam vol.5, pp.4, 2009, https://doi.org/10.12989/imm.2012.5.4.385