Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities

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A review of continuum mechanics models for size-dependent analysis of beams and plates

Flexural vibration analysis of beams made of functionally graded materials (FGMs) with various boundary conditions is considered in this paper. Due to technical problems during FGM fabrication, porosities and micro-voids can be created inside FGM samples which may lead to the reduction in density and strength of materials. In this investigation, the FGM beams are assumed to have even and uneven distributions of porosities over the beam cross-section. The modified rule of mixture is used to approximate material properties of the FGM beams including the porosity volume fraction. In order to cover the effects of shear deformation, axial and rotary inertia, the Timoshenko beam theory is used to form the coupled equations of motion for describing dynamic behavior of the beams. To solve such a problem, Chebyshev collocation method is employed to find natural frequencies of the beams supported by different end conditions. Based on numerical results, it is revealed that FGM beams with even distribution of porosities have more significant impact on natural frequencies than FGM beams with uneven porosity distribution.

Flexural vibration of imperfect functionally graded beams based on Timoshenko beam theory: Chebyshev collocation method

Nonlinear instability of axially loaded functionally graded multilayer graphene platelet-reinforced nanoshells based on nonlocal strain gradient elasticity theory

This paper presents the free vibration and buckling analyses of functionally graded carbon nanotube-reinforced (FG-CNTR) laminated non-rectangular plates, i.e., quadrilateral and skew plates, using a four-nodded straight-sided transformation method. At first, the related equations of motion and buckling of quadrilateral plate have been given, and then, these equations are transformed from the irregular physical domain into a square computational domain using the geometric transformation formulation via discrete singular convolution (DSC). The discretization of these equations is obtained via two-different regularized kernel, i.e., regularized Shannon’s delta (RSD) and Lagrange-delta sequence (LDS) kernels in conjunctions with the discrete singular convolution numerical integration. Convergence and accuracy of the present DSC transformation are verified via existing literature results for different cases. Detailed numerical solutions are performed, and obtained parametric results are presented to show the effects of carbon nanotube (CNT) volume fraction, CNT distribution pattern, geometry of skew and quadrilateral plate, lamination layup, skew and corner angle, thickness-to-length ratio on the vibration, and buckling analyses of FG-CNTR-laminated composite non-rectangular plates with different boundary conditions. Some detailed results related to critical buckling and frequency of FG-CNTR non-rectangular plates have been reported which can serve as benchmark solutions for future investigations.

Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method

Free vibration analysis of non-rotating and rotating Timoshenko beams with damaged boundaries using the Chebyshev collocation method

Natural frequencies and critical loads of beams and columns with damaged boundaries using Chebyshev polynomials

Frequency and mode veering phenomena of axially functionally graded non-uniform beams with nonlocal residuals

Laminar forced convection of gaseous slip flow in a circular micro-channel filled with porous media under local thermal equilibrium condition is studied numer- ically using the finite difference technique. Hydrodynamically fully developed flow is considered and the Darcy-Brinkman-Forchheimer model is used to model the flow inside the porous domain. The present study reports the effect of several operating parameters (Knudsen number (Kn), Darcy number (Da), Forchhiemer number (�) , and modified Reynolds number (Re ∗ )) on the velocity slip and temperature jump at the wall. Results are given in terms of the velocity distribution, temperature distri- bution, skin friction (CfRe ∗ ), and the Nusselt number (Nu). It is found that the skin friction is increased by (1) decreasing Knudsen number, (2) increasing Darcy number, and (3) decreasing Forchheimer number. Heat transfer is found to (1) decrease as the Knudsen number, or Forchheimer number increase, (2) increase as the Peclet number or Darcy number increase. Nomenclature C Coefficient in the Forchheimer term Cf Skin friction coefficient Cp Constant pressure specific heat Cv Constant volume specific heat D Diameter of the circular channel Da Darcy number (K/er 2 ) h Local heat transfer coefficient K Intrinsic permeability of the porous medium Kn Knudsen number (λ/r0)

Ma’en S. Sari

Papers

Free vibration analysis of non-rotating and rotating Timoshenko beams with damaged boundaries using the Chebyshev collocation method

Natural frequencies and critical loads of beams and columns with damaged boundaries using Chebyshev polynomials

Frequency and mode veering phenomena of axially functionally graded non-uniform beams with nonlocal residuals

Forced convection gaseous slip flow in circular porous micro-channels

Vibration analysis of non-uniform orthotropic Kirchhoff plates resting on elastic foundation based on nonlocal elasticity theory