Free vibration analysis of porous beams with gradually varying mechanical properties

Abstract

This work is aimed to present analysis on free vibration behavior of porous beams with gradually varying mechanical properties based on a robust finite beam element. The governing equations are developed using a mixed variational formulation considering high-order displacement distribution. A new parabolic distribution of the transverse shear strains is introduced and the zero condition of the shear stresses at the upper and bottom surfaces of the beam is satisfied. The porosity can be spread into the beam with evenly and unevenly distributions. According to a modified power function, the material properties are varying along the thickness direction of the FGM porous beam. The presented results show the effect of gradient index, porosity coefficient and forms, boundary conditions, and geometrical parameters on the vibration of FGM beams. It is found that porous beams can be useful as a passive method for control of vibration for structural components.

Mathematical Analysis on Dispersion Relation of Rayleigh Wave for an Initially Stressed Magneto-Poroelastic Material with Corrugated and Impedance Boundary

“…Consequently, some authors have made contributions to this concepts of impedance and corrugated boundaries, and other related wave propagation phenomena (Singh et al, 2008(Singh et al, , 2015(Singh et al, , 2018Das et al, 1992;Abd-Alla et al 2016;Chattopadhyay et al, 1975;Roy et al, 2017;Singh et al, 2011;Gupta et al, 2014;Anya et al, 2018Anya et al, , 2020Sunita et al, 2019;Dey et al, 1977;Nunziato et al, 1979;and Puri et al, 1975), as an individual or part considerations of the interacting physical quantities rather than in combined effect as presented in this investigation. Also, Zghal et al (2021), dealt on free vibration analysis of porous beams with gradually varying mechanical properties. Also, Kundu et al (2019), contributed to field by investigating the effect of initial stress on the propagation and attenuation characteristics of Rayleigh waves on a media.…”

Higher-Order Free Vibration Analysis of Porous Functionally Graded Plates

“…Starting with the basic idea from [21], we propose a four-variable refined plate theory to handle the problem without any use of shear correction factors, whose accuracy is verified against other higher-order formulations available from literature involving more variables. The potential of the proposed theoretical formulation for FG sandwich plates reinforced with carbon nanotubes (CNTs) would be of particular interest for different plate components, as commonly encountered in many aerospace, marine and automobile structures [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63], and can be extended to more complicated shell components under different boundary conditions.…”