Nonlocal DQM for Large Amplitude Vibration of Annular Boron Nitride Sheets on Nonlinear Elastic Medium

Document Type : Research Paper


1 Faculty of Mechanical Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan,

2 Faculty of Mechanical Engineering, University of Kashan

3 Faculty of Mechanical Engineering, University of Kashan, Kashan


One of the most promising materials in nanotechnology such as sensors, actuators and resonators is annular Boron Nitride sheets (ABNSs) due to excelled electro-thermo-mechanical properties. In this study, however, differential quadrature method (DQM) and nonlocal piezoelasticity theory are used to investigate the nonlinear vibration response of embedded single-layered annular Boron Nitride sheets (SLABNSs). The interactions between the SLABNSs and its surrounding elastic medium are simulated by nonlinear Pasternak foundation. A detailed parametric study is conducted to elucidate the influences of the nonlocal parameter, elastic medium, temperature change and maximum amplitude on the nonlinear frequency of the SLABNSs. Results indicate that with increasing nonlocal parameter, the frequency of the coupled system becomes lower. The results are in good agreement with the previous researches.


[1] Salvetat J.P., Bonard J.M., Thomson N.H., Kulik A.J., Forro L., Benoit W., Zuppiroli L., 1999, Mechanical properties of carbon nanotubes, Applied Physics A 69: 255-260.‏
[2] Baughman R.H., Zakhidov A.A., De Heer W.A., 2002, Carbon nanotubes--the route toward applications, Science 297:787-792.‏
[3] Ma R., Golberg D., Bando Y., Sasaki T., 2004, Syntheses and properties of B–C–N and BN nanostructures, The Royal Society 362: 2161-2186.
[4] Li Y., Dorozhkin P.S., Bando Y., Golberg D., 2005, Controllable modification of SiC nanowires encapsulated in BN nanotubes, Advanced Materials 17:545-549.
[5] Behfar K., Naghdabadi R., 2005, Nanoscale vibrational analysis of a multi-layered graphene sheet embedded in an elastic medium, Composite Science and Technology 65:1159-1164.
[6] Liew K.M., He X.Q., Kitipornchai S., 2006, Predicting nanovibration of multi-layered graphene sheets embedded in an elastic matrix, Acta Materiala 54:4229-4236.
[7] Pradhan S.C., Phadikar J.K., 2009, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration 325:206-223.
[8] Shen L., Shen H.S., Zhang C.L., 2008, Nonlocal plate model for nonlinear vibration of single layer graphene sheets in thermal environments, Computational Material Science 48:680-685.
[9] Ansari R., Rajabiehfard R., Arash B., 2010, Nonlocal finite element model for vibrations of embedded multi-layered graphene sheets, Computational Material Science 49:831-838.
[10] Pradhan S.C., Kumar A., 2010, Vibration analysis of orthotropic graphene sheets embedded in Pasternak elastic medium using nonlocal elasticity theory and differential quadrature method, Computational Material Science 50:239-245.
[11] Ghorbanpour Arani A., Kolahchi R., Mosallaie Barzoki A.A., Mozdianfard M.R., Noudeh Farahani S.M., 2012, Elastic foundation effect on nonlinear thermo-vibration of embedded double-layered orthotropic graphene sheets using differential quadrature method, Proceeding of IMech Part C: Journal of Mechanical Engineering Science 227:1-8.
[12] Mohammadi M., Ghayour M., Farajpour A., 2012, Free transverse vibration analysis of circular and annular graphene sheets with various boundary conditions using the nonlocal continuum plate model, Composite Part B: Engineering 45:32-42.
[13] Salehi-Khojin A., Jalili N., 2008, Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings, Composite Science and Technology 68:1489-1501.
[14] Khodami Maraghi Z., Ghorbanpour Arani A., Kolahchi R., Amir S., Bagheri M.R., 2013, Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid, Composites Part B: Engineering 45:423-432.
[15] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory, Physica B 407: 4281-4286.
[16] Ghorbanpour Arani A., Kolahchi R., Khoddami Maraghi Z., 2013, Nonlinear vibration and instability of embedded double-walled boron nitride nanotubes based on nonlocal cylindrical shell theory, Applied Mathematical Modeling 37: 7685-7707.
[17] Ke L.L., Wang Y.S., Wang Z.D., 2012, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory, Composite Structures 94:2038-2047.
[18] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory, Physica B 407:4458-4465.
[19] Salajeghe S., Khadem S.E., Rasekh M., 2012, Nonlinear analysis of thermoelastic damping in axisymmetric vibration of micro circular thin-plate resonators, Applied Mathematical Modeling 36:5991-6000.
[20] Malekzadeh P., Afsari A., Zahedinejad P., Bahadori R., 2010, Three-dimensional layerwise-finite element free vibration analysis of thick laminated annular plates on elastic foundation, Applied Mathematical Modeling 34:776-790.
[21] Sepahi O., Forouzan M.R., Malekzadeh P., 2010, Large deflection analysis of thermo-mechanical loaded annular FGM plates on nonlinear elastic foundation via DQM, Composite Structures 92: 2369-2378.