Buckling Analysis of Cantilever Nanoactuators Immersed in an Electrolyte: A Close Form Solution Using Duan-Rach Modified Adomian Decomposition Method

Document Type: Research Paper


1 Department of Mechanical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.

2 Department of Electrical Engineering, Dezful Branch, Islamic Azad University, Dezful, Iran.


A new modified Adomian Decomposition Method (ADM) was utilized to obtain an analytical solution for the buckling of the nanocantilever actuators immersed in liquid electrolytes. The nanoactuators in electrolytes are subject to different nonlinear forces including ionic concentration, van der Waals, external voltage and electrochemical forces. The Duan–Rach modified Adomian decomposition method was used to obtain a full explicate solution for the buckling of nanoactuators free of any undetermined coefficients. The results were compared with those of Wazwas ADM and of a finite element method available in the literature and excellent agreement was found between them.


Main Subjects

[1] Martin, O. Gouttenoire, V. Villard, P. Arcamone, J. Petitjean, M. Billiot, G., G., Philippe, J., Puget, P., Andreucci, P., Ricoul, F. and Dupré, C., “Modeling and design of a fully integrated gas analyzer using a μGC and NEMS sensors”, Sensors and Actuators B: Chemical, Vol. 194, pp.220-8, 2014.

[2] Jóźwiak, G. Kopiec, D. Zawierucha, P. Gotszalk, T. Janus, P. Grabiec, P., and , and Rangelow, I. W., “The spring constant calibration of the piezoresistive cantilever based biosensor”, Sensors and Actuators B: Chemical, Vol. 170, pp. 201-206, 2012.

[3] Ekinci, K. L. and Roukes, M. L.,” Nanoelectromechanical  systems”., Review  of  Scientific Instruments, Vol. 76, No.6, 061101, 2005.

[4] Guthy, C., Belov, M. Janzen, A. Quitoriano, N. J. Singh, A. Guthy, C., Belov, M., Janzen, A., Quitoriano, N.J., Singh, A., Wright, V.A., Finley, E., Kamins, T.I. and Evoy, S., “Large-scale arrays of nanomechanical sensors for biomolecular fingerprinting. Sensors and Actuators B” Chemical, Vol. 187, pp. 111-117, 2013.

[5] Choi, W.Y., Osabe, T., and Liu, T. J. K., “Nano-electro-mechanical nonvolatile memory (NEMory) cell design and scaling, Electron Devices” IEEE Transactions on, Vol. 55, No.2, pp. 3482-3488, 2008.

[6] Dumas, N., Trigona, C. Pons, P. Latorre, L., and Nouet, P, “Design of smart drivers for electrostatic MEMS switches”, Sensors and Actuators A: Physical, Vol. 167, pp. 422-432, 201.

[7] Boyd, J. G., and Kim, D.,”Nanoscale electrostatic actuators in liquid electrolytes”, Journal of colloid and interface science, Vol. 301, No. 2, pp. 542-548, 2006.

[8] Noghrehabadi, A., Eslami, M., and Ghalambaz, M., “Influence of size effect and elastic boundary condition on the pull-in instability of nano-scale cantilever beams immersed in liquid electrolytes”, International Journal of Non-Linear Mechanics, Vol. 52, pp. 73-84, 2013.

[9] Boyd, J. G. and Lee, J., “Deflection and pull-in instability of nanoscale beams in liquid electrolytes”, Journal of colloid and interface science, Vol. 356, pp. 387-94, 2011.

[10] Wazwaz, A. M., “The numerical solution of sixth-order boundary value problems by the modified decomposition method”, Applied Mathematics and Computation, Vol.118, pp. 311-325, 2001.

[11] Alam, M. K., Rahim, M. T., Avital, E. J., Islam, S., Siddiqui, A. M., & Williams, J. J. R., “Solution of the steady thin film flow of non-Newtonian fluid on vertical cylinder using Adomian Decomposition Method”, Journal of the Franklin Institute, Vol. 350, No. 4, pp. 818-839, 2013.

[12] Koochi, A., Kazemi, A. S., Tadi Beni, Y., Yekrangi, A., and Abadyan, M., “Theoretical study of the effect of Casimir attraction on the pull-in behavior of beam-type NEMS using modified Adomian method. Physica”, E: Low-dimensional Systems and Nanostructures, Vol. 43, No. 2, pp. 625-632, 2010.

[13] Koochi, A. L. I., Hosseini-Toudeshky, H. Ovesy, H. R., and Abadyan, M.,” Modeling the Influence of Surface Effect on Instability of Nano-Cantilever in Presence of Van Der Waals Force”, International Journal of Structural Stability and Dynamics, Vol. 13, pp. 1250072, 2013.

[14] Soroush, R. Koochi, A. L. I. Kazemi, A. S., and Abadyan, M., “Modeling the Effect of Van Der Waals Attraction on the Instability of Electrostatic Cantilever and Doubly-Supported Nano-Beams Using Modified Adomian Method”, International Journal of Structural Stability and Dynamics, Vol. 12, 1250036, 2012.

[15] Kuang, J. H., and Chen, C. J., “Adomian decomposition method used for solving nonlinear pull-in behavior in electrostatic micro-actuators”, Mathematical and Computer Modelling, Vol. 41, pp. 1479-1491, 2005.

[16] Koochi, A. Kazemi, A. S. Noghrehabadi, A. Yekrangi, A., and Abadyan, M., “New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets”, Materials & Design, Vol. 32, 2949-2955, 2011.

[17] Noghrehabadi, A., Ghalambaz, M., and Ghanbarzadeh, A.,” A new approach to the electrostatic pull-in instability of nanocantilever actuators using the ADM–Padé technique”, Computers & Mathematics with Applications, Vol. 64, pp. 2806-2815, 2012.

[18] Duan, J. S. and Rach, R., “A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations”, Applied Mathematics and Computation, Vol. 218, pp. 4090-41118, 2011.

[19] Duan, J. S., Rach, R., Wazwaz, A. M., Chaolu, T., and Wang, Z.,” A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions”, Applied Mathematical Modelling, Vol. 37, pp. 8687-8708, 2013.

[20] Adomian, G. and Rach, R., “Inversion of nonlinear stochastic operators”, J Math Anal Appl, Vol. 91, pp. 39–46, 1983.

[21] Duan, J. S., Rach, R., and Wang, Z.,” On the effective region of convergence of the decomposition series solution”, Journal of Algorithms & Computational Technology, Vol. 7, pp. 227-248, 2013.

[22] Yazdanpanahi, E., Noghrehabadi, A., and Ghalambaz, M.,” Pull-in instability of electrostatic doubly clamped nano actuators: Introduction of a balanced liquid layer (BLL)”, International Journal of Non-Linear Mechanics, Vol. 58, pp. 128-138, 2014.