scholarly journals Analytical Expressions for Frequency and Buckling of Large Amplitude Vibration of Multilayered Composite Beams

2011 ◽  
Vol 2011 ◽  
pp. 1-9
Author(s):  
R. A. Jafari-Talookolaei ◽  
M. H. Kargarnovin ◽  
M. T. Ahmadian ◽  
M. Abedi
Keyword(s):  
Shear Deformation ◽  
Natural Frequency ◽  
Large Amplitude ◽  
Composite Beam ◽  
Numerical Study ◽  
Harmonic Balance Method ◽  
Rotary Inertia ◽  
Displacement Fields ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

The aim of this paper is to present analytical and exact expressions for the frequency and buckling of large amplitude vibration of the symmetrical laminated composite beam (LCB) with simple and clamped end conditions. The equations of motion are derived by using Hamilton's principle. The influences of axial force, Poisson effect, shear deformation, and rotary inertia are taken into account in the formulation. First, the geometric nonlinearity based on the von Karman's assumptions is incorporated in the formulation while retaining the linear behavior for the material. Then, the displacement fields used for the analysis are coupled using the equilibrium equations of the composite beam. Substituting this coupled displacement fields in the potential and kinetic energies and using harmonic balance method, we obtain the ordinary differential equation in time domain. Finally, applying first order of homotopy analysis method (HAM), we get the closed form solutions for the natural frequency and deflection of the LCB. A detailed numerical study is carried out to highlight the influences of amplitude of vibration, shear deformation and rotary inertia, slenderness ratios, and layup in the case of laminates on the natural frequency and buckling load.

Effects of Rotary Inertia and Shear Deformation on Nonlinear Free Vibration of Microbeams

2006 ◽  
Vol 128 (5) ◽  
pp. 611-615 ◽  
Author(s):  
Asghar Ramezani ◽  
Aria Alasty ◽  
Javad Akbari
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Free Vibration ◽  
Shear Deformation ◽  
Large Amplitude ◽  
Multiple Scales ◽  
Rotary Inertia ◽  
Partial Differential ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

In this paper, the large amplitude free vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton’s principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin’s method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second-order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the doubly clamped microbeam. Shear deformation and rotary inertia have significant effects on the large amplitude vibration of thick and short microbeams.

Effects of Rotary Inertia and Shear Deformation on Nonlinear Vibration of Micro/Nano-Beam Resonators

2005 ◽  
Author(s):  
Asghar Ramezani ◽  
Aria Alasty
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Shear Deformation ◽  
Large Amplitude ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Rotary Inertia ◽  
Partial Differential ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

In this paper, the large amplitude free vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton’s principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin’s method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the doubly clamped microbeam. Shear deformation and rotary inertia have significant effects on the large amplitude vibration of thick and short microbeams.

Nonlocal large-amplitude vibration of embedded higher-order shear deformable multiferroic composite rectangular nanoplates with different edge conditions

2017 ◽  
Vol 29 (5) ◽  
pp. 944-968 ◽  
Author(s):  
R Gholami ◽  
R Ansari ◽  
Y Gholami
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Large Amplitude ◽  
Higher Order ◽  
Small Scale ◽  
Nonlinear Frequency ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Multiferroic Composite ◽  
Shear Deformable

Based on the nonlocal elasticity theory, a unified nonlocal, nonlinear, higher-order shear deformable nanoplate model is developed to investigate the size-dependent, large-amplitude, nonlinear vibration of multiferroic composite rectangular nanoplates with different boundary conditions resting on an elastic foundation. By considering a unified displacement vector and using von Kármán’s strain tensor, the strain–displacement components are obtained. Using coupled nonlocal constitutive relations, the coupled ferroelastic, ferroelectric, ferromagnetic, and thermal properties of multiferroic composite materials and small-scale effect are taken into account. The electric and magnetic potential distributions in the nanoplate are calculated via Maxwell’s electromagnetic equations. Furthermore, Hamilton’s principle is utilized to obtain the mathematical formulation associated with the coupled governing equations of motions and boundary conditions. The developed model enables us to consider the effects of rotary inertia and transverse shear deformation without using any shear correction factor. Also, it can be degenerated to the models based on the Kirchhoff and existing shear deformation plate theories. To solve the large-amplitude vibration problem, an efficient multistep numerical solution approach is utilized. Effects of various important parameters such as the type of the plate theory, and parameters of nonlocality and coupled fields on the nonlinear frequency response are investigated.

Large Amplitude Vibration Analysis of Composite Beams under Thermal Stresses: Closed-Form Solutions

2012 ◽  
Vol 245 ◽  
pp. 144-149 ◽  
Author(s):  
Ali Reza Daneshmehr ◽  
Mostafa Mohammad Abadi ◽  
Meisam Soleimani
Keyword(s):  
Closed Form ◽  
Large Amplitude ◽  
Composite Beam ◽  
Vibration Analysis ◽  
Thermal Stresses ◽  
Method Comparison ◽  
Laminated Composite ◽  
Closed Form Solutions ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

In This study , the large amplitude vibration analysis of laminated composite beam under thermal stress with axially fixed ends is investigated with symmetric and asymmetric layup orientations by using the Rayleigh–Ritz (R–R) method. An exhaustive set of beam boundary condition are studied, namely, hinged-hinged, clamped-clamped, hinged- clamped, hinged-guided and clamped-guided beam in order to prove the efficacy of the present formulation. The composite beam is studied in this paper based on Euler-Bernoulli assumption together with von-Karman’s strain-displacement relation. The simple and efficient closed-form solutions are obtained for the nonlinear harmonic radian frequency as function of central amplitude of the beam using the R–R method. Comparison between results of the present study and those available in literature shows the accuracy of presented closed-form solutions.

Large Amplitude Elliptical Plate Vibration With Transverse Shear and Rotatory Inertia Effects

1982 ◽  
Vol 104 (2) ◽  
pp. 426-431 ◽  
Author(s):  
M. Sathyamoorthy
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Large Amplitude ◽  
Mode Analysis ◽  
Transverse Shear Deformation ◽  
Rotatory Inertia ◽  
Semi Major Axis ◽  
Nonlinear Bending ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

An improved nonlinear vibration theory is used in the present analysis to study the effects of transverse shear deformation and rotatory inertia on the large amplitude vibration behavior of isotropic elliptical plates. When these effects are negligible the differential equations given here readily reduce to the well-known dynamic von Ka´rma´n equations. Based on a single-mode analysis, solutions to the governing equations are presented for immovably clamped elliptical plates by use of Galerkin’s method and the numerical Runge-Kutta procedure. An excellent agreement is found between the present results and those available for nonlinear bending and large amplitude vibration of elliptical plates. The present results for moderately thick elliptical plates indicate significant influences of the transverse shear deformation, axes ratio, and semi-major axis-to-thickness ratio on the large amplitude vibration of elliptical plates.

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