Research Article | OPEN ACCESS
Axisymmetric Free Vibration Analysis of Annular and Circular Mindlin Plates Using the Nonlocal Continuum Theory
Maen S. Sari
Department of Mechanical Engineering, King Faisal University, Al-Hasa, Saudi Arabia
Research Journal of Applied Sciences, Engineering and Technology 2015 8:561-571
Received: March ‎29, ‎2014 | Accepted: June ‎08, ‎2014 | Published: March 15, 2015
Abstract
This study aims to investigate and analyze the axisymmetric free vibration of non-local annular and circular Mindlin plates at the micro/nano scale which are modeled using Eringen’s nonlocal elasticity theory, taking into consideration the small scale effect. The governing equations are derived using the nonlocal differential constitutive relations of Eringen. For this purpose, the resulted eigenvalue problem is solved numerically by applying the Chebyshev collocation method. The effects of the inner to outer radius ratio, the thickness to outer radius ratio, the nonlocal scale effect and the boundary conditions on the natural frequencies are studied.
Keywords:
Annular and circular mindlin plates, axisymmetric vibration, chebyshev collocation method, eigenvalue problem, eringen's non-local elasticity theory, natural frequencies,
References
-
Ansari, R., S. Sahmani and B. Arash, 2010. Nonlocal plate model for free vibrations of single-layered graphene sheets. Phys. Lett. A, 375: 53-62.
CrossRef
-
Duan, W.H. and C.M. Wang, 2007. Exact solutions for axisymmetric bending of micro/nanoscale circular plates based on nonlocal plate theory. Nanotechnolgy, 18: 385704.
CrossRef
-
Eringen, A.C., 1983. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys., 54: 4703-4710.
CrossRef
-
Gürses, M., B. Akgöz and Ö. Civalek, 2012. Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation. Appl. Math. Comput., 219: 3226-3240.
CrossRef
-
Han, J.B. and K.M. Liew, 1999. Axisymmetric free vibration of thick annular plates. Int. J. Mech. Sci., 41: 1189-1109.
CrossRef
-
Hashemi, S.H., M. Zare and R. Nazemnezhad, 2013a. An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity. Compos. Struct., 100: 290-299.
CrossRef
-
Hashemi, S.H., M. Bedroud and R. Nazemnezhad, 2013b. An exact analytical solution for free vibration of functionally graded circular/ annular Mindlin nanoplates via nonlocal elasticity. Compos. Struct., 103: 108-118.
CrossRef
-
Lu, P., H.P. Lee, C. Lu and P.Q. Zhang, 2006. Dynamic properties of flexural b beams using a nonlocal elasticity model. J. Appl. Phys., 99: 073510.
CrossRef
-
Murmu, T. and S.C. Pradhan, 2009a. Vibration analysis of nano-single-layered graphene sheets embedded in elastic medium based on nonlocal elasticity theory. J. Appl. Phys., 105: 064319.
CrossRef
-
Murmu, T. and S.C. Pradhan, 2009b. Vibration analysis of nanoplates under uniaxial prestressed conditions via nonlocal elasticity. J. Appl. Phys., 106: 104301.
CrossRef
-
Murmu, T. and S. Adhikari, 2010a. Nonlocal transverse vibration of double-nanobeam systems. J. Appl. Phys., 108: 083514.
CrossRef
-
Murmu, T. and S. Adhikari, 2010b. Scale-dependent vibration analysis of prestresse-d carbon nanotubes undergoing rotation. J. Appl. Phys., 108: 123507.
CrossRef
-
Reddy, J.N., 2007. Nonlocal theories for bending, buckling and vibration of beams. Int. J. Eng. Sci., 45: 288-307.
CrossRef
-
Sari, M.S. and E.A. Butcher, 2011a. Free vibration analysis of rectangular and annular Mindlin plates with undamaged and damaged boundaries by the spectral collocation method. J. Vib. Control, 18: 1722-1736.
CrossRef
-
Sari, M. and E.A. Butcher, 2011b. Three dimensional analysis of rectangular plates with undamaged and damaged boundaries by the spectral collocation method. Proceedings of the 8th International Conference on Multibody Systems, Nonlinear Dynamics and Control (ASME IDETC’11), Washington, D.C., USA.
CrossRef
-
Sari, M.S. and E.A. Butcher, 2012. Free vibration analysis of non-rotating and rotating Timoshenko beams with damaged boundaries using the Chebyshev collocation method. Int. J. Mech. Sci., 60: 1-11.
CrossRef
-
Sari, M., M. Nazari and E.A. Butcher, 2011. Effects of damaged boundaries on the free vibration of Kirchhoff plates: Comparison of perturbation and spectral collocation solutions. J. Comput. Nonlin. Dyn., 7: 011011.
CrossRef
-
Shakouri, A., T.Y. Ng and R.M. Lin, 2011. Nonlocal plate model for the free vibration analysis of nanoplates with different boundary conditions. J. Comput. Theor. Nanos., 8: 2118-2128.
CrossRef
-
Trefethen, L.N., 2000. Spectral Methods in MATLAB, Software, Enviroments and Tools. SIAM, Philadelphia.
CrossRef
-
Wang, C.M., Y.Y. Zhang and X.Q. He, 2007. Vibration of nonlocal Timoshenko beams. Nanotechnology, 18: 105401.
CrossRef
Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
|
|
|
ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
|
Information |
|
|
|
Sales & Services |
|
|
|