On large deformation and stability of microcantilevers under follower load

Dehrouyeh-Semnani, Amir Mehdi

doi:10.1016/j.ijengsci.2021.103549

Cited by 14 publications

(2 citation statements)

References 78 publications

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“…Hence, nonlinear oscillators have attracted numerous attention due to their significant applications [15][16][17]. The governing differential equation of a nonlinear system can be investigated numerically [18][19][20][21][22][23][24][25] or analytically [26][27][28][29][30]. However, analytical methods are of great interest because they provide closed-form solutions, making it easier to investigate the impact of various parameters on nonlinear frequency.…”

Section: Introductionmentioning

confidence: 99%

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Mohammadian,

Ismail

2024

Phys. Scr.

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The non-linear differential equation governing some mechanical systems, such as the non-linear vibrations of FG beams resting on a nonlinear foundation, behaves similarly to the oscillations of a non-linear oscillator with an asymmetric restoring force function that includes both odd and non-odd non-linear terms. The objective of this research is to obtain higher-order approximate analytical solutions for such problems by introducing an enhanced harmonic balance method. By building upon the original problem, two new symmetric systems with odd non-linear terms are introduced, and their higher-order approximate analytical solutions are derived using a novel approach. In proposed method, the restoring force function is represented by its Fourier series expansion. Unlike previous papers, linearizing the equation or taking the first derivative of the Fourier series in the subsequent iteration is unnecessary. However, to enhance the solution’s accuracy, the remaining error from each iteration is utilized in the next one. Finally, by combining the results from the two introduced systems, the analytical period and corresponding periodic solution of the original problem can be obtained. This method is applied to the governing differential equation of FG beams resting on non-linear foundations, a physical non-natural oscillator, and conservative Toda oscillator. The key advantages of this approach are its simplicity and its ability to provide highly precise solutions for both small and large amplitudes in a single iteration.

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Section: Introductionmentioning

confidence: 99%

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Mohammadian,

Ismail

2024

Phys. Scr.

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“…Numerical solutions of vibration of microshells of revolution [55] and thin shallow microshells [56] have been studied based on CPT and MCST and using finite element model. Large deformation and stability characteristics of microbeam on the basis of Euler-Bernoulli assumptions and MCST under a tip-concentrated nonconservative load [57] have been investigated. Numerical solutions of nonlinear snap-through instability of piezo-FGM sandwich microarches [58] based on the Timoshenko hypothesis and MCST under thermo-mechanical and electrical loads using the two-step perturbation have been investigated.…”

Section: Introductionmentioning

confidence: 99%

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

et al. 2023

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Using modified couple stress plate and Mindlin theories, the present study is a parametric study for revealing the effect of length scale parameter on postbuckling of saturated poroelastic rectangular microplates with pore distribution being functionally graded across thickness. The microplate postbuckling is a nonlinear eigenvalue problem with coupled partial differential equations of equilibrium. In order to find the mode shapes, the eigenfunctions have been approximated by some complete polynomial series expansions in accordance with the conventional Ritz approximation technique. After discretizing the governing equations throughout the microplate grid points, the assembled difference equations construct a nonlinear eigenvalue problem with coupled algebraic equations. The nontrivial coefficients of the expansions were calculated such that the eigenfunctions extremize the microplate potential energy for satisfying the equilibrium homogeneous equations. Variation of the potential energy have been derived with respect to the expansions coefficients from the vantage of using Maple software. By gradual reduction in the initial end shortening of the movable supports and solving the assembled difference equations via Newton-Raphson iterations, the critical postbuckling displacement imposed to the movable supports are found along with the nontrivial coefficients regarding eigenfunctions. The results of the parametric study have revealed how geometric parameters, pore distribution, the Skempton coefficient, porosity, and different boundary conditions modify the influence of length scale parameter on the microplate postbuckling.

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Size-dependent buckling and instability of a porous microplate under electrostatic fields and Casimir forces

Mojahedi,

Ayatollahi

2024

Arch Appl Mech

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On large deformation and stability of microcantilevers under follower load

Cited by 14 publications

References 78 publications

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Improved harmonic balance method for analyzing asymmetric restoring force functions in nonlinear vibration of mechanical systems

Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

Size-dependent buckling and instability of a porous microplate under electrostatic fields and Casimir forces

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