Mode shapes for free vibration of clamped plates with various geometries based on an quadrilateral element

Lan Hoang That Ton

Authors

Lan Hoang That Ton University of Architecture HCMC https://orcid.org/0000-0002-5195-1856

Keywords:

Mode shape, Free vibration, Clamped plate, CP-DSG4 element

Abstract

This work aims at presenting mode shapes for free vibration of clamped plates with various geometries based on a four-node quadrilateral element, CP-DSG4, related to discrete shear gap (DSG) strategy and adding a center point (CP). The efficiency of the CP-DSG4 element is demonstrated through some numerical tests.

Downloads

Download data is not yet available.

References

T. J. R. Hughes, et al., "Reduced and selective integration techniques in finite element analysis of plates," Nuclear Engineering and Design, vol. 46(1), pp. 203–222, 1978.

K. J. Bathe and E. Dvorkin, "A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation," International Journal for Numerical Methods in Engineering, vol. 21(2), pp. 367–383, 1985.

K. J. Bathe, et al., "The MITC7 and MITC9 plate bending elements," Computers & Structures, vol. 32(3-4), pp. 797–814, 1989.

P. S. Lee and K. J. Bathe, "Development of MITC isotropic triangular shell finite elements," Computers & Structures, vol. 82(11-12), pp. 945–962, 2004.

R. P. R. Cardoso, et al., "Enhanced assumed strain (EAS) and assumed natural strain (ANS) methods for one-point quadrature solid-shell elements," International Journal for Numerical Methods in Engineering, vol. 75(2), pp. 156–187, 2007.

H. Nguyen-Van, et al., "Free vibration analysis of laminated plate/shell structures based on FSDT with a stabilized nodal-integrated quadrilateral element," Journal of Sound and Vibration, vol. 313(1-2), pp. 205–223, 2008.

H. L. Ton-That and H. Nguyen-Van, "A combined strain element in static, frequency and buckling analyses of laminated composite plates and shells," Periodica Polytechnica Civil Engineering, vol. 65(1), pp. 56–71, 2021.

H. Nguyen-Van, et al., "Nonlinear static bending analysis of functionally graded plates using MISQ24 elements with drilling rotations," International Conference on Advances in Computational Mechanics, ACOME 2017, pp. 461–475, 2017.

K. U. Bletzinger, et al., "A unified approach for shear-locking-free triangular and rectangular shell finite elements," Computers & Structures, vol. 75, pp. 321–334, 2000.

M. N. Nguyen, et al., "A 4-node quadrilateral element with center-point based discrete shear gap (CP-DSG4)," Vietnam Journal of Mechanics, VAST, Vol. 43(4), pp. 319–331, 2021.

T. Liu, et al., "Modeling and experimental study on free vibration of plates with curved edges," Journal of Sound and Vibration, vol. 513, p. 116417, 2021.

I. Ramu and S.C. Mohanty, "Study on Free Vibration Analysis of Rectangular Plate Structures Using Finite Element Method," Procedia Engineering, vol. 38, pp. 2758-2766, 2012.

B. R. Isanaka, et al., "Free vibration analysis of thin plates: Bare versus Stiffened," Engineering Research Express, vol. 2, p. 015014, 2020.

P. K. Nkounhawa, et al., "Analysis of the Behavior of a Square Plate in Free Vibration by FEM in Ansys," World Journal of Mechanics, vol. 10(2), 2020.

K. J. Jadee, et al., "Free vibration of isotropic plates with various cutout configurations using finite elements and design of experiments," IOP Conference Series: Materials Science and Engineering, vol. 745, p. 012080, 2020.

S. M. N. Serdouna and S. M. Hamza-Cherif, "Free Vibration Analysis of Isotropic Plates by Alternative Hierarchical Finite Element Method Based on Reddy’s C1 HSDT," American Scientific Research Journal for Engineering, Technology, and Sciences, vol. 9(1), pp. 1-19, 2014.

J. Rouzegar and R. A. Sharifpoor, "Finite Element Formulations for Free Vibration Analysis of Isotropic and Orthotropic Plates using Two-Variable Refined Plate Theory," Scientia Iranica, vol. 23(4), pp. 1787-1799, 2016.

V. Rastogi, "Free Vibration Of Isotropic And Laminated Composite Plate Using Three-Dimensional Finite Element Analysis," Materials Today: Proceedings, vol. 18, pp. 2823-2831, 2019.

M. C. Manna, et al., "Free vibration of tapered isotropic rectangular plates," Journal of Vibration and Control, vol. 18(1), pp. 76-91, 2012.

S. Papkov and J. R. Banerjee, "A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution," Mathematics, vol. 11(3), p. 649, 2023.

A. H. Modaress-Aval, et al., "Free vibration and aeroelastic analyses of rectangular cantilever plates including correlation with experiment," Journal of Theoretical and Applied Vibration and Acoustics, vol. 6(1), pp. 103-118, 2020.