Abstract
This study investigates the scale effect on nonlinear behavior of a clamped–clamped circular graphene sheet nanoplate actuator, which is electrostatically actuated by various vdW forces, tensile loads, and hydrostatic pressures. The circular nanoplate model is developed by using Eringen’s nonlocal elasticity theory. The nonlinear behavior of the circular nanoplate actuator subject to nonlocal effect, electrostatic vdW forces, tensile loads, and hydrostatic pressures, is then carefully derived, analyzed and presented. A proposed hybrid differential transformation/finite difference method is first introduced to characterize the influence of scale effect on nonlinear behavior of the circular nanoplate subject to DC loads. The modeling result shows that the pull-in voltage deviates less than 2.71% as compared to that appeared in the literature obtained by using a different approach. The validity of the proposed hybrid method is thus verified and can thus be employed to further characterize the effect of small scale for different electrostatic actuation of tensile loads and hydrostatic pressures in greater details. The structural modeling results indicate that the pull-in voltage increases obviously with increasing scale effects. Overall, the results also reveal that the hybrid method presented in this paper is effective and can be used to accurately quantify the pull-in voltage in circular nanoplate systems under different associated actuation.
Similar content being viewed by others
References
Chen CK, Ho SH (1996) Application of differential transformation to eigenvalue problems. Appl Math Comput 79(2):173–188
Decca RS, López D, Fischbach E, Klimchitskaya GL, Krause DE, Mostepanenko VM (2005) Precise comparison of theory and new experiment for the Casimir force leads to stronger constraints on thermal quantum effects and long-range interactions. Ann Phys 318(1):37–80
Eltaher MA, Mahmoud FF, Assie AE, Meletis EI (2013) Coupling effects of nonlocal and surface energy on vibration analysis of nanobeams. Appl Math Comput 224:760–774
Eringen AC (1983) On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 54(9):4703–4710
Eringen AC (2002) Nonlocal continuum field theories. Springer Science and Business Media, Berlin
Farajpour A, Mohammadi M, Shahidi AR, Mahzoon M (2011) Axisymmetric buckling of the circular graphene sheets with the nonlocal continuum plate model. Phys E 43(10):1820–1825
Farajpour A, Dehghany M, Shahidi AR (2013) Surface and nonlocal effects on the axisymmetric buckling of circular graphene sheets in thermal environment. Compos B Eng 50:333–343
Liu CC (2015) Numerical investigation into dynamic behavior of electrostatically-actuated circular clamped micro-plate subject to squeeze-film damping effect. Microsystem Technologies, pp 1–7
Nabian A, Rezazadeh G, Haddad-derafshi M, Tahmasebi A (2008) Mechanical behavior of a circular micro plate subjected to uniform hydrostatic and non-uniform electrostatic pressure. Microsyst Technol 14(2):235–240
Najar F, El-Borgi S, Reddy JN, Mrabet K (2015) Nonlinear nonlocal analysis of electrostatic nanoactuators. Compos Struct 120:117–128
Osterberg PM (1995) Electrostatically actuated microelectromechanical test structures for material property measurement. Ph.D. dissertation, Mass. Instit. Tech., Cambridge
Osterberg PM, Senturia SD (1997) M-TEST: a test chip for MEMS material property measurement using electrostatically actuated test structures. J Microelectromech Syst 6(2):107–118
Perçin G, Khuri-Yakub BT (2002) Piezoelectrically actuated flextensional micromachined ultrasound transducers. Ultrasonics 40(1):441–448
Ramezani A, Alasty A, Akbari J (2007) Closed-form solutions of the pull-in instability in nano-cantilevers under electrostatic and intermolecular surface forces. Int J Solids Struct 44(14):4925–4941
Reddy JN (2007) Nonlocal theories for bending, buckling and vibration of beams. Int J Eng Sci 45(2):288–307
Suzuki K, Funaki H, Naruse Y (2006) MEMS optical microphone with electrostatically controlled grating diaphragm. Meas Sci Technol 17(4):819
Wang KF, Wang BL, Zeng S (2016) Small scale effect on the pull-in instability and vibration of graphene sheets. Microsystem Technologies, pp 1–9
Yang J, Jia XL, Kitipornchai S (2008) Pull-in instability of nano-switches using nonlocal elasticity theory. J Phys D Appl Phys 41(3):035103
Yu LT, Chen CK (1998) The solution of the Blasius equation by the differential transformation method. Math Comput Model 28(1):101–111
Zhou JK (1986) Differential transformation and its applications for electrical circuits. Huazhong University Press, Wuhan China
Zhou SM, Sheng LP, Shen ZB (2014) Transverse vibration of circular graphene sheet-based mass sensor via nonlocal Kirchhoff plate theory. Comput Mater Sci 86:73–78
Acknowledgements
This study acknowledges the support provided to this research by the Ministry of Science and Technology of Republic of China under Grant No. MOST 104-2221-E-006-174-MY3.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Lin, MX., Lai, HY. & Chen, CK. Analysis of nonlocal nonlinear behavior of graphene sheet circular nanoplate actuators subject to uniform hydrostatic pressure. Microsyst Technol 24, 919–928 (2018). https://doi.org/10.1007/s00542-017-3406-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00542-017-3406-9