Double‐mode modeling of nonlinear flexural vibration analysis for a symmetric rectangular honeycomb sandwich thin panel by the homotopy analysis method

2020 ◽  
Vol 44 (1) ◽  
pp. 7-26
Author(s):  
Yongqiang Li ◽  
WenKai Yao
Keyword(s):  
Homotopy Analysis Method ◽  
Vibration Analysis ◽  
Flexural Vibration ◽  
Analysis Method ◽  
Honeycomb Sandwich ◽  
Homotopy Analysis ◽  
Thin Panel

Application of Homotopy Analysis Method for the Pull-In and Nonlinear Vibration Analysis of Nanobeams Using a Nonlocal Euler–Bernoulli Beam Model

2017 ◽  
Vol 72 (12) ◽  
pp. 1093-1104 ◽  
Author(s):  
F. Samadani ◽  
P. Moradweysi ◽  
R. Ansari ◽  
K. Hosseini ◽  
A. Darvizeh
Keyword(s):  
Differential Equation ◽  
Nonlinear Vibration ◽  
Homotopy Analysis Method ◽  
Vibration Analysis ◽  
Nonlocal Parameter ◽  
Beam Model ◽  
Analysis Method ◽  
Bernoulli Beam ◽  
Homotopy Analysis ◽  
Euler Bernoulli Beam

AbstractIn this investigation, the homotopy analysis method (HAM) is utilized for the pull-in and nonlinear vibration analysis of nanobeams based on the stress-driven model (SDM) of nonlocal elasticity theory. The physical properties of nanobeams are assumed not to vary through the thickness. The nonlinear equation of motion and the corresponding boundary condition are derived on the basis of the Euler–Bernoulli beam theory. For the solution purpose, the Galerkin method is employed for reducing the nonlinear partial differential equation to a nonlinear ordinary differential equation in the time domain, and then, the resulting equation is analytically solved using the HAM. In the results section, the influences of different parameters, including nonlocal parameter, electrostatic and intermolecular van der Waals forces and fringing field effect changes on the pull-in and nonlinear vibration response are investigated.

HOMOTOPY ANALYSIS METHOD TO SOLVE BOUSSINESQ EQUATIONS

2015 ◽  
Vol 10 (3) ◽  
pp. 2825-2833
Author(s):  
Achala Nargund ◽  
R Madhusudhan ◽  
S B Sathyanarayana
Keyword(s):  
Homotopy Analysis Method ◽  
Degrees Of Freedom ◽  
Initial Approximation ◽  
Boussinesq Equations ◽  
Convergent Series ◽  
Boussinesq System ◽  
Analysis Method ◽  
Analytical Technique ◽  
Homotopy Analysis ◽  
Region Of Convergence

In this paper, Homotopy analysis method is applied to the nonlinear coupleddifferential equations of classical Boussinesq system. We have applied Homotopy analysis method (HAM) for the application problems in [1, 2, 3, 4]. We have also plotted Domb-Sykes plot for the region of convergence. We have applied Pade for the HAM series to identify the singularity and reflect it in the graph. The HAM is a analytical technique which is used to solve non-linear problems to generate a convergent series. HAM gives complete freedom to choose the initial approximation of the solution, it is the auxiliary parameter h which gives us a convenient way to guarantee the convergence of homotopy series solution. It seems that moreartificial degrees of freedom implies larger possibility to gain better approximations by HAM.

scholarly journals Dynamics with Cattaneo–Christov heat and mass flux theory of bioconvection Oldroyd-B nanofluid

2020 ◽  
Vol 12 (8) ◽  
pp. 168781402093046 ◽  
Author(s):  
Noor Saeed Khan ◽  
Qayyum Shah ◽  
Arif Sohail
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Mass Flux ◽  
Homotopy Analysis Method ◽  
Two Dimensional ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Transfer Flow ◽  
Insight Into

Entropy generation in bioconvection two-dimensional steady incompressible non-Newtonian Oldroyd-B nanofluid with Cattaneo–Christov heat and mass flux theory is investigated. The Darcy–Forchheimer law is used to study heat and mass transfer flow and microorganisms motion in porous media. Using appropriate similarity variables, the partial differential equations are transformed into ordinary differential equations which are then solved by homotopy analysis method. For an insight into the problem, the effects of various parameters on different profiles are shown in different graphs.

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