Szczegóły

Tytuł artykułu

Meshless local Petrov-Galerkin method for rotating Rayleigh beam using Chebyshev and Legendre polynomials

Tytuł czasopisma

Archive of Mechanical Engineering

Rocznik

2022

Wolumin

vol. 69

Numer

No 2

Afiliacje

Panchore, Vijay : Department of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal, India

Autorzy

Słowa kluczowe

meshless local Petrov-Galerkin method ; mechanical vibrations ; orthogonal polynomials ; Finite Element Method (FEM) ; rotating beams

Wydział PAN

Nauki Techniczne

Zakres

301-318

Wydawca

Polish Academy of Sciences, Committee on Machine Building

Bibliografia

[1] R. Ganguli. Finite Element Analysis of Rotating Beams. Springer, Singapore, 2017.
[2] R. Ganguli and V. Panchore. The Rotating Beam Problem in Helicopter Dynamics. Springer, Singapore, 2018.
[3] S.N. Atluri. The Meshless Method (MLPG) for Domain and BIE Discretizations. Tech Science Press, Forsyth, 2004.
[4] G.R. Liu. Meshfree Methods. CRC Press, New York, 2003.
[5] I.S. Raju, D.R. Phillips, and T. Krishnamurthy. A radial basis function approach in the meshless local Petrov-Galerkin method for Euler-Bernoulli beam problems. Computational Mechanics, 34:464–474, 2004. doi: 10.1007/s00466-004-0591-z.
[6] D. Hu, Y. Wang, Y. Li, Y. Gu and X. Han. A meshfree-based local Galerkin method with condensation of degree of freedom. Finite Elements in Analysis and Design, 78:16–24, 2014. doi: 10.1016/j.finel.2013.09.004.
[7] S. De Marchi and M.M. Cecchi. The polynomial approximation in finite element method. Journal of Computational and Applied Mathematics, 57(1-2):99–114, 1995. doi: 10.1016/0377-0427(93)E0237-G.
[8] V. Panchore, R. Ganguli, and S.N. Omkar. Meshless local Petrov-Galerkin method for rotating Euler-Bernoulli beam. Computer Modeling in Engineering and Sciences, 104(5):353–373, 2015. doi: 10.3970/cmes.2015.104.353.
[9] V. Panchore, R. Ganguli, and S.N. Omkar. Meshless local Petrov-Galerkin method for rotating Timoshenko beam: a locking-free shape function formulation. Computer Modeling in Engineering and Sciences, 108(4):215–237, 2015. doi: 10.3970/cmes.2015.108.215.
[10] W. Johnson. Helicopter Theory. Dover Publications, New York, 1980.
[11] A. Bokaian. Natural frequencies of beams under tensile axial loads. Journal of Sound and Vibration, 142(3):481–498, 1990. doi: 10.1016/0022-460X(90)90663-K.
[12] S.V. Hoa. Vibration of a rotating beam with tip mass. Journal of Sound and Vibration, 67(3):369–381, 1979. doi: 10.1016/0022-460X(79)90542-X.
[13] H.D. Hodges and M.J. Rutkowski. Free-vibration analysis of rotating beams by a variable-order finite element method. AIAA Journal, 19(11):1459–1466, 1981. doi: 10.2514/3.60082.
[14] J. Chung and H.H. Yoo. Dynamic analysis of a rotating cantilever beam by using the finite element method. Journal of Sound and Vibration, 249:147–164, 2002. doi: 10.1006/jsvi.2001.3856.
[15] R.L. Bisplinghoff, H. Ashley, and R.L. Halfman. Aeroelasticity. Dover Publications, New York, 1996.
[16] V. Giurgiutiu and R.O. Stafford. Semi-analytical methods for frequencies and mode shapes of rotor blades. Vertica, 1:291–306, 1977.
[17] J.B. Gunda and R. Ganguli. Stiff-string basis functions for vibration analysis of high speed rotating beams. Journal of Applied Mechanics, 75(2):0245021, 2008. doi: 10.1115/1.2775497.
[18] V. Panchore and R. Ganguli. Quadratic B-spline finite element method for a rotating non-uniform Rayleigh beam. Structural Engineering and Mechanics, 61(6):765–773, 2017. doi: 10.12989/sem.2017.61.6.765.
[19] V. Panchore and R. Ganguli. Quadratic B-spline finite element method for a rotating non-uniform Euler-Bernoulli beam. International Journal for Computational Methods in Engineering Science and Mechanics, 19(5):340–350, 2018. doi: 10.1080/15502287.2018.1520757.
[20] T. Rabczuk, J-H Song, X. Zhuang, and C. Anitescu. Extended Finite Element and Meshfree Methods. Elsevier, London, 2020.
[21] J.R. Xiao and M.A. McCarthy. Meshless analysis of the obstacle problem for beams by the MLPG method and subdomain variational formulations. European Journal of Mechanics – A/Solids, 22(3):385–399, 2003. doi: 10.1016/S0997-7538(03)00050-0.
[22] J.Y. Cho and S. N. Atluri. Analysis of shear flexible beams, using the meshless local Petrov-Galerkin method, based on a locking-free formulation. Engineering Computations, 18(1-2):215–240, 2001. doi: 10.1108/02644400110365888.
[23] J. Sladek, V. Sladek, S. Krahulec, and E. Pan. The MLPG analyses of large deflections of magnetoelectroelastic plates. Engineering Analysis with Boundary Elements, 37(4):673–682, 2013. doi: 10.1016/j.enganabound.2013.02.001.
[24] S.N. Atluri, J.Y. Cho, and H.-G. Kim. Analysis of thin beams, using the meshless local Petrov-Galerkin method, with generalized moving least squares interpolations. Computational Mechanics, 24:334–347, 1999. doi: 10.1007/s004660050456.
[25] J.R. Banerjee and D.R. Jackson. Free vibration of a rotating tapered Rayleigh beam: A dynamic stiffness method of solution. Computers and Structures, 124:11–20, 2013. doi: 10.1016/j.compstruc.2012.11.010.

Data

6.04.2022

Typ

Article

Identyfikator

DOI: 10.24425/ame.2022.140416 ; ISSN 0004-0738, e-ISSN 2300-1895
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