A homotopy perturbation analysis of nonlinear free vibration of Timoshenko microbeams

Moeenfard, Hamid; Mojahedi, Mahdi; Ahmadian, Mohammad Taghi

doi:10.1007/s12206-011-0130-8

Cited by 44 publications

(20 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Resonant microsensors, as one of the largest categories of these systems, are extensively used in different applications, such as signal filtering and chemical and mass sensing [7,8]. The building blocks of these sensors, which employ the same vibrational characteristics as those of sensing method, are microbeams and microplates [9][10][11][12][13]. They represent the major structural components of resonant microsensors because of the high stiffness and simplicity of the production procedure of fully clamped rectangular microplates [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Analytical determination of size-dependent natural frequencies of fully clamped rectangular microplates based on the modified couple stress theory

Askari

Tahani

2015

J Mech Sci Technol

View full text Add to dashboard Cite

This paper presents an analytical and size-dependent model for vibrational analysis of fully clamped rectangular microplates. Modified couple stress theory (MCST) and the Kirchhoff plate model are considered, and Hamilton's principle is employed to derive the sizedependent equation of motion that accounts for the effect of residual stresses. The natural frequencies of the microplate are extracted analytically by extended Kantorovich method. The present findings are validated with the available results in the literature, and an excellent agreement is observed between them. In addition, a parametric study is conducted to demonstrate the significant effects of couple stress components on the natural frequencies of fully clamped microplates. The ratio of MCST natural frequencies to those obtained with classical theory depends only on the Poisson's ratio of the plate and is independent of the aspect ratio of the plate for cases with no residual stresses.

show abstract

Section: Introductionmentioning

confidence: 99%

Analytical determination of size-dependent natural frequencies of fully clamped rectangular microplates based on the modified couple stress theory

Askari

Tahani

2015

J Mech Sci Technol

View full text Add to dashboard Cite

show abstract

“…Moeenfard et al (2011) also analyzed this problem by applying the homotopy perturbation method. Foda (1999) analyzed the same problem in macro-scale with perturbation methods considering the pinned boundary condi-tion.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis

Shahlaei-Far

Nabarrete

Balthazar

2016

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

This study analyzes the fourth-order nonlinear free vibration of a Timoshenko beam. We discretize the governing differential equation by Galerkin's procedure and then apply the homotopy analysis method (HAM) to the obtained ordinary differential equation of the generalized coordinate. We derive novel analytical solutions for the nonlinear natural frequency and displacement to investigate the effects of rotary inertia, shear deformation, pre-tensile loads and slenderness ratios on the beam. In comparison to results achieved by perturbation techniques, this study demonstrates that a first-order approximation of HAM leads to highly accurate solutions, valid for a wide range of amplitude vibrations, of a highorder strongly nonlinear problem.

show abstract

“…Qaisi (1993) determined the vibration modes of geometrically nonlinear beams under the various edge conditions by the harmonic balance principle. Moeenfard et al (2011) developed the homotopy perturbation method (HPM) to analyze the nonlinear free vibration of Timoshenko beams. They also converted the nonlinear partial differential governing equation to a non-linear ordinary differential equation using Galerkin's projection method.…”

Section: Introductionmentioning

confidence: 99%

Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams

Jafari

Rashidi

Johnson

2016

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of EulerBernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load.

show abstract

A homotopy perturbation analysis of nonlinear free vibration of Timoshenko microbeams

Cited by 44 publications

References 17 publications

Analytical determination of size-dependent natural frequencies of fully clamped rectangular microplates based on the modified couple stress theory

Analytical determination of size-dependent natural frequencies of fully clamped rectangular microplates based on the modified couple stress theory

Nonlinear Vibrations of Cantilever Timoshenko Beams: A Homotopy Analysis

Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams

Contact Info

Product

Resources

About