Abstract
In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.
Highlights
Free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal eld, uniform, linear, and sinusoidal, are studied using a Re ned Higher-order shear Deformation eory. e present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. e stress-free boundary conditions are satis ed on the upper and lower surfaces of the beam without using any shear correction factor. e material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modi ed power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered
Graded Materials (FGMs) have been proposed, because the mixture ratio of their constituents varies smoothly, and the material characteristics continually change along some preferred direction. is largely avoids the stress concentration, induced by the material property discontinuities, typically observed in laminated and ber-reinforced composites
Mechanical Properties of P-FGB. e P-FGB examined here is made of a mixture of ceramic and metal, whose compositions vary from the top to the bottom surfaces. e top surface ( = +h/2) of the beam is ceramic-rich, whereas the bottom surface ( = −h/2) is metal-rich. e e ective material property (e.g., Young’s modulus, mass density, thermal expansion coe cient, and Poisson’s ratio ) is assumed to vary through the beam thickness as a function of the volume fraction, the properties of the constituent materials and the porosity volume fraction ( ≪ 1)
Summary
E P-FGB examined here is made of a mixture of ceramic and metal, whose compositions vary from the top to the bottom surfaces. E top surface ( = +h/2) of the beam is ceramic-rich, whereas the bottom surface ( = −h/2) is metal-rich. E e ective material property (e.g., Young’s modulus , mass density , thermal expansion coe cient , and Poisson’s ratio ) is assumed to vary through the beam thickness as a function of the volume fraction, the properties of the constituent materials and the porosity volume fraction ( ≪ 1). Two kinds of porosity distribution, uniform, and nonuniform through the crosssection area of the beam, between the top and bottom surfaces, are considered in this study. If the porosity distribution is assumed to be uniform, the rule of mixture is modi ed as follows [52]:.
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