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Abstract

This paper presents the research studies carried out on the application of lattice Boltzmann method (LBM) to computational aeroacoustics (CAA). The Navier-Stokes equation-based solver faces the difficulty of computational efficiency when it has to satisfy the high-order of accuracy and spectral resolution. LBM shows its capabilities in direct and indirect noise computations with superior space-time resolution. The combination of LBM with turbulence models also work very well for practical engineering machinery noise. The hybrid LBM decouples the discretization of physical space from the discretization of moment space, resulting in flexible mesh and adjustable time-marching. Moreover, new solving strategies and acoustic models are developed to further promote the application of LBM to CAA.

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Authors and Affiliations

Weidong Shao
Jun Li
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Abstract

The numerical solutions are obtained for rotating beams; the inclusion of centrifugal force term makes it difficult to get the analytical solutions. In this paper, we solve the free vibration problem of rotating Rayleigh beam using Chebyshev and Legendre polynomials where weak form of meshless local Petrov-Galerkin method is used. The equations which are derived for rotating beams result in stiffness matrices and the mass matrix. The orthogonal polynomials are used and results obtained with Chebyshev polynomials and Legendre polynomials are exactly the same. The results are compared with the literature and the conventional finite element method where only first seven terms of both the polynomials are considered. The first five natural frequencies and respective mode shapes are calculated. The results are accurate when compared to literature.
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Bibliography

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[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.
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[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.
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[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.
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Authors and Affiliations

Vijay Panchore
1

  1. Department of Mechanical Engineering, Maulana Azad National Institute of Technology, Bhopal, India
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Abstract

In this paper, nonlinear free vibration analysis of micro-beams resting on the viscoelastic foundation is investigated by the use of the modified couple stress theory, which is able to capture the size effects for structures in micron and sub-micron scales. To this aim, the gov-erning equation of motion and the boundary conditions are derived using the Euler–Bernoulli beam and the Hamilton’s principle. The Galerkin method is employed to solve the governing nonlinear differential equation and obtain the frequency-amplitude algebraic equation. Final-ly, the effects of different parameters, such as the mode number, aspect ratio of length to height, the normalized length scale parameter and foundation parameters on the natural fre-quency-amplitude curves of doubly simply supported beams are studied.

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Authors and Affiliations

Jafar Eskandari Jam
1
Milad Noorabadi
1
Nader Namdaran
1

  1. Composite Materials and Technology Cente, Malek Ashtar University of Technology, Tehran, Iran

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