ARTICLE
Effect of the thickness to length ratio on the frequency ratio of nanobeams and nanoplates
 
More details
Hide details
1
Eastern Mediterranean University, Department of Mechanical Engineering,Magosa, TRNC Mersin, Turkey
Online publication date: 2020-01-15
Publication date: 2019-04-05
Acceptance date: 2019-07-11
 
Journal of Theoretical and Applied Mechanics 2020;58(1):87–96
KEYWORDS
ABSTRACT
This communication presents the effect of thickness on the frequency ratio of nanobeams and nanoplates using Eringen’s nonlocal theory. Although there exist numerous works regarding the effects of thickness and small scale on the frequency ratio of nanobeams and nanoplates, none has captured and reported the true effects. The main intention of this communication is to correct the misunderstanding regarding this issue. It was found that the frequency ratio is indeed dependent on the thickness to length ratio and its variation with respect to thickness to length ratio is highly dependent on the mode number, combination of boundary conditions, plate aspect ratio, and the nonlocal parameter.
 
REFERENCES (36)
1.
Aghababaei R., Reddy J., 2009, Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates, Journal of Sound and Vibration, 326, 277-289.
 
2.
Arefi M., Zamani M.H., Kiani M., 2018, Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation, Journal of Intelligent Material Systems and Structures, 29, 5, 774-786.
 
3.
Arefi M., Zenkour A.M., 2016, Employing sinusoidal shear deformation plate theory for transient analysis of three layers sandwich nanoplate integrated with piezo-magnetic face-sheets, Smart Materials and Structures, 25, 11, 115040.
 
4.
Arefi M., Zenkour A.M., 2017a, Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin-Voigt viscoelastic nanoplate and two piezoelectric layers, Acta Mechanica, 228, 475-493.
 
5.
Arefi M., Zenkour A.M., 2017b, Size-dependent free vibration and dynamic analyses of piezo-electro-magnetic sandwich nanoplates resting on viscoelastic foundation, Physica B: Condensed Matter, 521, 188-197.
 
6.
Arefi M., Zenkour A.M., 2017c, Size-dependent vibration and bending analyses of the piezomagnetic three-layer nanobeams, Applied Physics A, 123, 3, 202.
 
7.
Aydogdu M., 2009, A general nonlocal beam theory: its application to nanobeam bending, buckling and vibration, Physica E: Low-dimensional Systems and Nanostructures, 41, 1651-1655.
 
8.
Bahrami A., 2017a, A wave-based computational method for free vibration, wave power transmission and reflection in multi-cracked nanobeams, Composites Part B: Engineering, 120, 168-181.
 
9.
Bahrami A., 2017b, Free vibration, wave power transmission and reflection in multi-cracked nanorods, Composites Part B: Engineering, 127, 53-62.
 
10.
Bahrami A., Ilkhani M.R., Bahrami M.N., 2015, Wave propagation technique for free vibration analysis of annular circular and sectorial membranes, Journal of Vibration and Control, 21, 1866-1872.
 
11.
Bahrami A., Teimourian A., 2015a, Free vibration analysis of composite, circular annular membranes using wave propagation approach, Applied Mathematical Modelling, 39, 4781-4796.
 
12.
Bahrami A., Teimourian A., 2015b, Nonlocal scale effects on buckling, vibration and wave reflection in nanobeams via wave propagation approach, Composite Structures, 134, 1061-1075.
 
13.
Bahrami A., Teimourian A., 2016, Study on the effect of small scale on the wave reflection in carbon nanotubes using nonlocal Timoshenko beam theory and wave propagation approach, Composites Part B: Engineering, 91, 492-504.
 
14.
Bahrami A., Teimourian A., 2017a, Small scale effect on vibration and wave power reflection in circular annular nanoplates, Composites Part B: Engineering, 109, 214-226.
 
15.
Bahrami A., Teimourian A., 2017b, Study on vibration, wave reflection and transmission in composite rectangular membranes using wave propagation approach, Meccanica, 52, 231-249.
 
16.
Daneshmehr A., Rajabpoor A., Hadi A., 2015, Size dependent free vibration analysis of nanoplates made of functionally graded materials based on nonlocal elasticity theory with high order theories, International Journal of Engineering Science, 95, 23-35.
 
17.
Dehrouyeh-Semnani A.M., Bahrami A., 2016, On size-dependent Timoshenko beam element based on modified couple stress theory, International Journal of Engineering Science, 107, 134-148.
 
18.
Eltaher M., Emam S.A., Mahmoud F., 2012, Free vibration analysis of functionally graded size-dependent nanobeams, Applied Mathematics and Computation, 218, 7406-7420.
 
19.
Eringen A.C., 1972, Theory of micromorphic materials with memory, International Journal of Engineering Science, 10, 623-641.
 
20.
Eringen A.C., 2002, Nonlocal Continuum Field Theories, Springer Science & Business Media.
 
21.
Hosseini-Hashemi S., Kermajani M., Nazemnezhad R., 2015, An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory, European Journal of Mechanics-A/Solids, 51, 29-43.
 
22.
Hosseini-Hashemi S., Zare M., Nazemnezhad R., 2013, An exact analytical approach for free vibration of Mindlin rectangular nano-plates via nonlocal elasticity, Composite Structures, 100, 290-299.
 
23.
Ilkhani M.R., Bahrami A., Hosseini-Hashemi S.H., 2016, Free vibrations of thin rectangular nano-plates using wave propagation approach, Applied Mathematical Modelling, 40, 1287-1299.
 
24.
Kahrobaiyan M.H., Asghari M., Rahaeifard M., Ahmadian M.T., 2010, Investigation of the size-dependent dynamic characteristics of atomic force microscope microcantilevers based on the modified couple stress theory, International Journal of Engineering Science, 48, 1985-1994.
 
25.
Lim C.W., Zhang G., Reddy J.N., 2015, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, Journal of the Mechanics and Physics of Solids, 78, 298-313.
 
26.
Mindlin R.D., 1964, Micro-structure in linear elasticity, Archive for Rational Mechanics and Analysis, 16, 51-78.
 
27.
Mindlin R.D., Tiersten H.F., 1962, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis, 11, 415-448.
 
28.
Natarajan S., Chakraborty S., Thangavel M., Bordas S., Rabczuk T., 2012, Size-dependent free flexural vibration behavior of functionally graded nanoplates, Computational Materials Science, 65, 74-80.
 
29.
Rahmani O., Pedram O., 2014, Analysis and modeling the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory, International Journal of Engineering Science, 77, 55-70.
 
30.
Reddy J., 2007, Nonlocal theories for bending, buckling and vibration of beams, International Journal of Engineering Science, 45, 288-307.
 
31.
Sarayi S.M.M.J., Bahrami A., Bahrami M.N., 2018. Free vibration and wave power reflection in Mindlin rectangular plates via exact wave propagation approach, Composites Part B: Engineering, 144, 195-205.
 
32.
Thai H.T., 2012, A nonlocal beam theory for bending, buckling, and vibration of nanobeams, International Journal of Engineering Science, 52, 56-64.
 
33.
Yang F., Chong A.C.M., Lam D.C.C., Tong P., 2002. Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures, 39, 2731-2743.
 
34.
Zargaripoor A., Bahrami A., 2018. Free vibration and buckling analysis of third-order shear deformation plate theory using exact wave propagation approach, Journal of Computational Applied Mechanics, 49, 102-124.
 
35.
Zenkour A.M., Arefi M., 2017. Nonlocal transient electrothermomechanical vibration and bending analysis of a functionally graded piezoelectric single-layered nanosheet rest on visco-Pasternak foundation, Journal of Thermal Stresses, 40, 2, 167-184.
 
36.
Zhang J., Fu Y., 2012, Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory, Meccanica, 47, 1649-1658.
 
eISSN:2543-6309
ISSN:1429-2955