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

Wattanasakulpong, Nuttawit; Ungbhakorn, Variddhi

doi:10.1016/j.ast.2013.12.002

Cited by 397 publications

(109 citation statements)

References 31 publications

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“…An improved third-order shear deformation theory was employed by Wattanasakulpong et al [30] to formulate the governing equations for the free vibrations of functionally graded beams including porosities. The same analyses were performed by Wattanasakulpong and Ungbhakorn [31], including the effect of nonlinearities on the structural response. In their paper, the influence of porosities on the structural response was proven through a set of experimental analyses.…”

Section: Introductionmentioning

confidence: 89%

“…For this purpose, the well-known rule of mixture has been modified to deal with porosities. Since this approach has been validated by other authors, as illustrated in [30][31][32][33][34][35], the same empirical scheme is employed in the present paper to deal with FGM structures. The methodology in hand is also extended to the case of shell structures, since the previous studies are mainly focused on beams and plates with porosities.…”

Section: Introductionmentioning

confidence: 99%

“…As can be noted from Equations (9)- (11), the overall mechanical properties of the composite are computed through the well-known rule of mixture, which has been properly modified to take into account the porosity of the medium [31]. The same empirical approach has been recently employed and validated by many authors to describe the porous phase of FGMs [30][31][32][33][34][35]. To the best of the authors' knowledge, the rule of mixture represents a simple homogenization technique that allows us to evaluate in an efficient manner the elastic properties of a graded composite.…”

Section: Functionally Graded Materialsmentioning

confidence: 99%

“…For this purpose, various hierarchical refined exponential, polynomial, and trigonometric higher-order beam theories were developed in a generalized manner. An empirical approach has been used in all the aforementioned papers concerning porous and imperfect media to evaluate the overall mechanical properties of the composites at issue [30][31][32][33][34][35]. For this purpose, the well-known rule of mixture has been modified to deal with porosities.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

et al. 2017

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Due to some technical issues that can appear during the manufacturing process of Functionally Graded Materials (FGMs), it can be extremely difficult to produce perfect materials. Indeed, one of the biggest problems is the presence of porosities. For this purpose, the vibrational behavior of doubly-curved shells made of FGM including porosities is investigated in this paper. With respect to previous research, the porosity has been added to the mechanical model that characterizes the through-the-thickness distribution of the graded constituents and applied to doubly-curved shell structures. Few papers have been published on this topic. In fact, it is easier to find works related to one-dimensional structures and beam models that take account the effect of porosities. The First-order Shear Deformation Theory (FSDT) is considered as the theoretical framework. In addition, the mechanical properties of the constituents vary along the thickness direction. For this purpose, two power-law distributions are employed to characterize their volume fraction. Strain components are established in an orthogonal curvilinear coordinate system and the governing equations are derived according to the Hamilton's principle. Finally, Navier's solution method is used and the numerical results concerning three different types of shell structures are presented.

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Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Functionally Graded Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

et al. 2017

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“…Wattanasakulpong and Ungbhakorn investigated linear and nonlinear vibration responses of the functionally graded beams with the elastically restrained ends by taking into account the porosities which occur during fabrication. 13 The differential transformation method (DTM) is used to solve linear and nonlinear vibration responses of FG beams. Duy et al investigated free vibration response of a FG beam having an elastic foundation and spring supports.…”

Section: Introductionmentioning

confidence: 99%

Vibration Analysis of a Spring Supported FG Beam Under Harmonic Force

Demir¹,

Altinoz²

2018

IJAV

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The harmonic response and resonance frequency behavior of the spring supported FGM beam against the lateral motion for the various values of support stiffness at the ends are analyzed by using the force transmissibility parameter with the finite-element method and Lagrange's equations. The steady-state responses to a sinusoidal varying force are determined for the support reactions in a frequency domain. The problem is solved within the framework of the Timoshenko beam theory. For the convergence study, some of the results are compared with previous works' values, and a good agreement can be seen. The study concludes that the support stiffness, volume fraction coefficient and the ratio of young module level all strongly affect the natural frequencies and the force transmissibility. For some values of spring stiffness of support, the rigid body motion of the beam occurs and reduces the effect of volume fraction coefficient on the natural frequencies.

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Thermal nonlinear stability of functionally graded porous material nearly cylindrical shells with surrounding elastic media and tangentially restrained edges

Trang

Tung

2022

Math Methods in App Sciences

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This paper aims to investigate the influences of surrounding elastic media and tangential edge constraints on the buckling and postbucking behaviors of nearly cylindrical shell (NCS) made of functionally graded porous material (FGPM) and subjected to uniform temperature rise. Three different types of porosity distributions are considered and assumed to be in forms of cosine functions of thickness variable. The volume fractions of material constituents are assumed to vary through the shell thickness according to power‐law functions. Temperature‐dependent material properties and elasticity of tangential constraints of boundary edges are included. Governing equations are established within the framework of classical shell theory taking into account von Kármán–Donnell nonlinearity and interactive pressure from surrounding elastic media. Multiterm analytical solutions for simply supported NCSs are assumed and Galerkin procedure is utilized to derive expressions of buckling load and nonlinear load–deflection relation. An iteration process is adopted to determine critical thermal loads and postbuckling temperature–deflection paths. Numerous parametric studies are carried out to assess many different effects on thermal buckling resistance and postbuckling load carrying capabilities. The study reveals that porosity and tangential edge constraint have beneficial and deteriorative influences on the thermal stability of the NCSs, respectively. Furthermore, the obtained results demonstrate that surrounding elastic media have significantly beneficial influences on the thermal nonlinear stability of FGPM NCSs.

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

Cited by 397 publications

References 31 publications

Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

Free Vibration Analysis of Functionally Graded Porous Doubly-Curved Shells Based on the First-Order Shear Deformation Theory

Vibration Analysis of a Spring Supported FG Beam Under Harmonic Force

Thermal nonlinear stability of functionally graded porous material nearly cylindrical shells with surrounding elastic media and tangentially restrained edges

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