A Mechanical-Based Solution for Axially Functionally Graded Tapered Euler-Bernoulli Beams

Shahba, Ahmad; Attarnejad, Reza; Hajilar, Shahin

doi:10.1080/15376494.2011.640971

Cited by 45 publications

(23 citation statements)

References 33 publications

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“…It is observed from the table that the results obtained using PSM is slightly lower than that of [21]. The results presented in [21] were calculated utilizing 20 elements to model the bar for a taper ratio of = 0.1 and higher number of elements for other taper ratios. Moreover, it is observed from literature [21], that the stiffness method generally provides results that are higher than the exact ones.…”

Section: First Overtonementioning

confidence: 92%

“…In the second example we consider a functionally graded tapered axial bar with ( ) = (1 − ); ( ) = and ( ) = where is the taper ratio. For such an FG axial bar Shahba et al [21] computed the nondimensional frequencies = ⁄ , ( = 1,2,3) using Finite element method by introducing the concept of basic displacement functions. The pseudospectral method is used in the present work to compute the first three non-dimensional frequencies of the axial bar with = 16 under fixed-fixed, fixed-free boundary conditions.…”

Section: First Overtonementioning

confidence: 99%

“…The pseudospectral method is used in the present work to compute the first three non-dimensional frequencies of the axial bar with = 16 under fixed-fixed, fixed-free boundary conditions. The results obtained using the present method are compared with those presented in [21] in Table 13. It is observed from the table that the results obtained using PSM is slightly lower than that of [21].…”

Section: First Overtonementioning

confidence: 99%

“…The results obtained using the present method are compared with those presented in [21] in Table 13. It is observed from the table that the results obtained using PSM is slightly lower than that of [21]. The results presented in [21] were calculated utilizing 20 elements to model the bar for a taper ratio of = 0.1 and higher number of elements for other taper ratios.…”

Section: First Overtonementioning

confidence: 99%

“…Two new approaches based on Differential Transformation Method (DTM), namely Differential Transform Element Method (DTEM) and Differential Quadrature Element method of Lowest order (DQEL) were introduced by them to numerically study the free longitudinal vibration of tapered functionally graded (FG) rods. Further, in [21], the longitudinal vibrations of a linearly tapered axial bar with exponential variation in mass density and modulus of elasticity was investigated using Finite Element Method (FEM) by proposing a new element that could be derived by using the basic principles of structural mechanics.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

Pillutla¹,

Sudheer²,

Yerikalapudy³

2018

J. vibroeng.

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In this work, the problem of free longitudinal vibration of rods with variable cross-sectional area and material properties is investigated using the pseudospectral method. With the gradation of material properties like modulus of elasticity and mass density in the axial direction, the results corresponding to a functionally graded axial bar are obtained using the proposed pseudospectral formulation. The pseudospectral formulation used is relatively easy to implement and powerful in analyzing vibration problems. With the help of several numerical examples, the non-dimensional natural frequencies of rods obtained using the pseudospectral method are compared with those obtained by the analytical solution, generalized finite element method, the discrete singular convolution method and differential transformation method. The numerical results obtained show that the proposed technique allows boundary conditions to be incorporated easily and yields results with good accuracy and faster convergence rates than other methods.

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Section: First Overtonementioning

confidence: 92%

Section: First Overtonementioning

confidence: 99%

Section: First Overtonementioning

confidence: 99%

Section: First Overtonementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

Pillutla¹,

Sudheer²,

Yerikalapudy³

2018

J. vibroeng.

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show abstract

A novel finite element for the vibration analysis of tapered laminated plates

Hosseinian,

Attarnejad

2024

Polymer Composites

Self Cite

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In the present study, a new tapered finite element is developed by incorporating the in‐plane effect in our recently introduced element for the vibration analysis of internally tapered laminated plates. Stress and strain fields for a laminated plate with varying thickness along two orthogonal directions are expressed through extending classical laminated plate theory. Shape functions regarding bending and membrane behavior are extracted from the bending and axial basic displacement functions of the Euler‐Bernoulli beam, respectively. Several laminated plates with different taper configurations have been studied, and the results obtained from vibration analysis are compared with those of the literature. Since the element can capture the exact form of variation in thickness, the solution has shown to be competitively accurate with considerably fewer total degrees of freedom and elements in comparison with conventional finite elements.Highlight A new finite element for thin, tapered, laminated plates is introduced. Laminates' stiffness matrix is obtained for arbitrary thickness variation. A novel method is adopted to derive in‐plane shape functions. C1 continuity is guaranteed along the edges of elements. Calculation cost is considerably reduced.

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Vibrations of Size-Dependent Beams Under Topologic Optimization and Temperature Field

Awrejcewicz

Krysko

Zhigalov

et al. 2020

Advanced Structured Materials

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A Mechanical-Based Solution for Axially Functionally Graded Tapered Euler-Bernoulli Beams

Cited by 45 publications

References 33 publications

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

Free longitudinal vibrations of functionally graded tapered axial bars by pseudospectral method

A novel finite element for the vibration analysis of tapered laminated plates

Vibrations of Size-Dependent Beams Under Topologic Optimization and Temperature Field

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