An analytical approach for vibration analysis of laminated orthotropic beam based on nonlocal theory

Moshir, Saeed Khadem; Eipakchi, Hamidreza

doi:10.1177/0954406218820048

Cited by 5 publications

(2 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The present research is devoted to nonlinear dynamic lateral deflection and impact analysis of the particle-reinforced FG hyperelastic plates based on the accurate plate theory recently proposed by Shariyat [22,23], taking into account the thickness variations during the loading, even in the element scale. Only a limited number of articles have analyzed the vibration of the structures in the time-domain [24][25][26][27][28][29][30]. The governing equations are developed based on the principle of minimum total potential energy.…”

Section: Introductionmentioning

confidence: 99%

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

Shariyat

Abedi

2022

Z Angew Math Mech

View full text Add to dashboard Cite

The current article is devoted to the nonlinear dynamic and impact response analyses of rectangular incompressible neo‐Hookean hyperelastic plates with uniform/nonuniform transverse distributions of stiff elastic reinforcing particles. The nonlinear finite element governing equations are derived by using the principle of minimum total potential energy and solved by an updating scheme that uses the Runge‐Kutta time integration and penalty methods. The impact energy expressions are written for the integrated plate‐indenter system. The novelties of the article are: (i) realistic modeling the energy absorption of a particle‐reinforced nonlinear hyperelastic matrix based on the volume fractions of the constituent phases instead of using wrong Voigt‐type models or impractical predefined gradation coefficients, (ii) considering non‐uniform distributions of the reinforcing particles, (iii) using a highly accurate asymmetric (all the available theories are symmetric) infinite‐order plate theory, (iv) including the inherent hyperelastic nature of the material in the definition of the parameters of the plate theory, (v) considering the thickness changes of the plate, (vi) including von Karman's kinematic nonlinearity, (vii) analyzing both the dynamic and impact behaviors, (viii) proposing an adaptive algorithm to match the description of the displacement field with the load/stress variations, (ix) updating not only the stiffness but also the mass matrix within the time steps, (x) incorporation of the nonlinear boundary conditions by the penalty method, and (xi) performing time‐dependent analyses instead of the natural frequency analyses. Results reveal the drastic effects of the volume fraction of the reinforcing particles on the dynamic responses and report the impact responses of the FG hyperelastic plates, for the first time.

show abstract

Section: Introductionmentioning

confidence: 99%

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

Shariyat

Abedi

2022

Z Angew Math Mech

View full text Add to dashboard Cite

show abstract

“…54 proposed a simple nonlocal shear deformation model for vibration analysis of nanobeams and presented analytical solutions of natural frequencies for different boundary conditions. Moshir and Eipakchi 55 investigated the dynamic response and free vibration of laminated nanobeams subjected to harmonic and transient loading by using an analytical approach. Faraji-Oskouie et al.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent vibration of functionally graded rotating nanobeams with different boundary conditions based on nonlocal elasticity theory

Fang

Yin

Zhang

et al. 2021

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

The free vibration of rotating functionally graded nanobeams under different boundary conditions is studied based on nonlocal elasticity theory within the framework of Euler-Bernoulli and Timoshenko beam theories. The thickness-wise material gradient variation of the nanobeam is considered. By introducing a second-order axial shortening term into the displacement field, the governing equations of motion of the present new nonlocal model of rotating nanobeams are derived by the Hamilton’s principle. The nonlocal differential equations are solved through the Galerkin method. The present nonlocal models are validated through the convergence and comparison studies. Numerical results are presented to investigate the influences of the nonlocal parameter, angular velocity, material gradient variation together with slenderness ratio on the vibration of rotating FG nanobeams with different boundary conditions. Totally different from stationary nanobeams, the rotating nanobeams with relatively high angular velocity could produce larger fundamental frequencies than local counterparts. Additionally, the axial stretching-transverse bending coupled vibration is perfectly shown through the frequency loci veering and modal conversion.

show abstract

State-of-the-Art of Vibration Analysis of Small-Sized Structures by using Nonclassical Continuum Theories of Elasticity

Nuhu

Safaei

2022

Arch Computat Methods Eng

View full text Add to dashboard Cite

An analytical approach for vibration analysis of laminated orthotropic beam based on nonlocal theory

Cited by 5 publications

References 43 publications

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

An accurate hyperelasticity‐based plate theory and nonlinear energy‐based micromechanics for impact and shock analyses of compliant particle‐reinforced FG hyperelastic plates

Size-dependent vibration of functionally graded rotating nanobeams with different boundary conditions based on nonlocal elasticity theory

State-of-the-Art of Vibration Analysis of Small-Sized Structures by using Nonclassical Continuum Theories of Elasticity

Contact Info

Product

Resources

About