• Steel and Composite Structures
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• v.42 no.3
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• pp.375-388
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• 2022

In this work, limit elastic speed analysis of functionally graded porous rotating disks has been reported. The work proposes an effective approach for modeling the mechanical properties of a porous functionally graded rotating disk. Four different types of porosity models namely: uniform, symmetric, inner maximum, and outer maximum distribution are considered. The approach used is the variational principle, and the solution has been achieved using Galerkin's error minimization theory. The study aims to investigate the effect of grading indices, aspect ratio, porosity volume fraction, and porosity types on limit angular speed for uniform and variable disk geometries of constant mass. To validate the current study, finite element analysis has been used, and there is good agreement between the two methods. The study yielded a decrease in limit speed as grading indices and aspect ratio increase. The porosity volume fraction is found to be more significant than the aspect ratio effect. The research demonstrates a range of operable speeds for porous and non-porous disk profiles that can be used in industries as design data. The results show a significant increase in limit speed for an exponential disk when compared to other disk profiles, and thus, the study demonstrates a range of FG-based structures for applications in industries that will not only save material (lightweight structures) but also improve overall performance.

• Computers and Concrete
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• v.26 no.1
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• pp.63-74
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• 2020

In this investigation, study of the bending response of functionally graded (FG) porous plates is presented using a cubic shear deformation theory. The properties of the FG-plate vary according to a power-law distribution which is modified to approximate material characteristics for considering the effect of porosities. The equilibrium equations are derived by using the principle of virtual work and solved by using Navier's procedure. Various numerical results are discussed to demonstrate the influence of the variation of the power index, the porosity parameter and the geometric ratios on the bending response of FG porous plates.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.225-238
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• 2020

This work treats the axisymmetric buckling of functionally graded (FG) porous annular/circular nanoplates based on modified couple stress theory (MCST). The nanoplate is located at the elastic medium which is simulated by Kerr foundation with two spring and one shear layer. The material properties of the porous FG nanostructure are assumed to vary through the nanoplate thickness based on power-law rule. Based on two variables refined plate theory, the governing equations are derived by utilizing Hamilton's principle. Applying generalized differential quadrature method (GDQM), the buckling load of the annular/circular nanoplates is obtained for different boundary conditions. The influences of different involved parameters such as boundary conditions, Kerr medium, material length scale parameter, geometrical parameters of the nanoplate, FG power index and porosity are demonstrated on the nonlinear buckling load of the annular/circular nanoplates. The results indicate that with increasing the porosity of the nanoplate, the nonlinear buckling load is decreased. In addition, with increasing the material length scale parameter to thickness ratio, the effect of spring constant of Kerr foundation on the buckling load becomes more prominent. The present results are compared with those available in the literature to validate the accuracy and reliability. A good agreement is observed between the two sets of the results.

• Structural Engineering and Mechanics
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• v.83 no.6
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• pp.771-788
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• 2022

This research investigates the free vibration of porous advanced composite plates resting on Winkler/Pasternak/ Kerr foundations by using a new hyperbolic quasi three dimensional (quasi-3D) shear deformation theory. The present theory, which does not require shear correction factor, accounts for shear deformation and thickness stretching effects by parabolic variation of all displacements across the thickness, and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate. In this work, we consider imperfect FG plates with porosities embedded within elastic Winkler, Pasternak or Kerr foundations. Implementing an analytical approach, the obtained governing equations from Hamilton's principle according to FG plates are derived. The closed form solutions are obtained by using Navier technique, and natural frequencies of FG plates are found, for simply supported plates, by solving the results of eigenvalue problems. A comprehensive parametric study is presented to evaluate effects of the geometry of material, mode numbers, porosity volume fraction, Power-law index and stiffness of foundations parameters on free vibration characteristics of FG plates.

• Advances in nano research
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• v.8 no.2
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• pp.149-156
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• 2020

The present paper explores forced vibrational properties of porosity-dependent functionally graded (FG) cylindrical nanoshells exposed to linear-type or triangular-type impulse load via classical shell theory (CST) and nonlocal strain gradient theory (NSGT). Employing such scale-dependent theory, two scale factors accounting for stiffness softening and hardening effects are incorporated in modeling of the nanoshell. Two sorts of porosity distributions called even and uneven have been taken into account. Governing equations obtained for porous nanoshell have been solved through inverse Laplace transforms technique to derive dynamical deflections. It is shown that transient responses of a nanoshell are affected by the form and position of impulse loading, amount of porosities, porosities dispensation, nonlocal and strain gradient factors.

• Advances in nano research
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• v.7 no.2
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• pp.135-143
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• 2019

The important effect of porosity on the mechanical behaviors of a continua makes it necessary to account for such an effect while analyzing a structure. motivated by this fact, a new two-step porosity dependent homogenization scheme is presented in this article to investigate the wave propagation responses of functionally graded (FG) porous nanobeams. In the introduced homogenization method, which is a modified form of the power-law model, the effects of porosity distributions are considered. Based on Hamilton's principle, the Navier equations are developed using the Euler-Bernoulli beam model. Thereafter, the constitutive equations are obtained employing the nonlocal elasticity theory of Eringen. Next, the governing equations are solved in order to reach the wave frequency. Once the validity of presented methodology is proved, a set of parametric studies are adapted to put emphasis on the role of each variant on the wave dispersion behaviors of porous FG nanobeams.

• Steel and Composite Structures
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• v.46 no.2
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• pp.203-210
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• 2023

In the present research, dynamic deflections of a sandwich beam having functionally graded (FG) porous core have been investigated assuming that the sandwich beam is exposed to a pulse load of blast type. The two layers of sandwich beam have been made of a polymeric matrix reinforced by graphene oxide powder (GOP). The micromechanical formulation of the layers has been done via Halpin-Tsai model. The solution method is chosen to be Ritz method which is an efficient method to solve the system of equations of beams modeled based on a higher-order theory. To derive the time history of sandwich beam under pulse load, Laplace method has been used. The porosity content of the core, the GOP content of the layers, thickness of the layer and also duration of the applied load have great influences of the responses of sandwich beam.

• Steel and Composite Structures
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• v.44 no.6
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• pp.829-843
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• 2022

This manuscript work presents a comprehensive continuum model capable to investigate the effect of porosity on vibro-acoustic behaviour of functionally graded (FG) beams resting on an elastic foundation subjected to thermal and mechanical loadings. Effects of uniform temperature rise and edge compressive load on the sound radiation characteristics are studied in a comparative manner. The numerical analysis is carried out by combining finite element method with Rayleigh's integral. Detailed parametric studies are accomplished, and influences of power law index, porosity volume, porosity distribution and boundary conditions on the vibro-acoustic response characteristics are analyzed. It is found that the vibro-acoustic response under mechanical edge compression is entirely different compared to from that under the thermal load. Furthermore, nature of grading of porosity affects the sound radiation behaviour for both the loads. The proposed model can be used to obtain the suppression performance of vibration and noise FG porous beams under thermal and mechanical loads.

• Advances in nano research
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• v.13 no.5
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• pp.453-463
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• 2022

This paper aims to investigate the vibration analysis of functionally graded porous (FGP) beams using State-space approach with several classical and non-classical boundary conditions. The materials properties of the porous FG beams are considered to have even and uneven distributions profiles along the thickness direction. The equation of motion for FGP beams with various boundary conditions is obtained through Hamilton's principle. State-space approach is used to obtain the governing equation of porous FG beam. The comparison of the results of this study with those in the literature validates the present analysis. The effects of span-to-depth ratio (L/h), of distribution shape of porosity and others parameters on the dynamic behavior of the beams are described. The results show that the boundary conditions, the geometry of the beams and the distribution shape of porosity affect the fundamental frequencies of the beams.

• Computers and Concrete
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• v.25 no.1
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• pp.37-57
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• 2020

This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.