Free vibration analysis of circular plates by differential transformation method

Yalçın, Hülya; Arıkoğlu, Aytaç; Özkol, İbrahim

doi:10.1016/j.amc.2009.02.032

Cited by 71 publications

(45 citation statements)

References 10 publications

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“…[1,6,9,10,16]. The numerical results for plates with sliding supports are shown in Table 5 with comparison to Refs.…”

Section: Numerical Resultsmentioning

confidence: 93%

“…Ebrahimi and Rastgo [8] investigated the natural vibration behavior of circular functionally graded plates with clamped edges based on classical plate theory. Yalcin et al [9] have studied free vibration of circular plates by using differential transformation method (DTM). Zhou et al [10] applied the Hamiltonian approach to a solution of the free vibration problem of circular and annular thin plates.…”

Section: Introductionmentioning

confidence: 99%

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Green’s function approach to frequency analysis of thin circular plates

Żur¹

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract.The free vibration analysis of homogeneous and isotropic circular thin plates by using the Green's functions is considered. The formulae for construction of the influence function for all nodal diameters are presented in a closed form. The limited independent solutions of differential Euler equations were expanded in the Neumann power series using the method of successive approximation. This approach allows to obtain the analytical frequency equations as power series rapidly convergent to exact eigenvalues for different number of nodal diameters.

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“…[1,6,9,10,16]. The numerical results for plates with sliding supports are shown in Table 5 with comparison to Refs.…”

Section: Numerical Resultsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Green’s function approach to frequency analysis of thin circular plates

Żur¹

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…The method captures the exact solution in terms of a Taylor series expansion. This method has been successfully implemented in engineering applications [19][20][21][22][23][24][25]. Ndlovu and Moitsheki [26] derived approximate analytical solutions for the temperature distribution in a longitudinal rectangular and convex parabolic fin with temperature dependent thermal conductivity and heat transfer coefficients.…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions

Jooma

Harley

2017

Advances in Mathematical Physics

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A time dependent nonlinear partial differential equation modelling heat transfer in a porous radial fin is considered. The Differential Transformation Method is employed in order to account for the steady state case. These solutions are then used as a means of assessing the validity of the numerical solutions obtained via the Crank-Nicolson finite difference method. In order to engage in the stability of this scheme we conduct a stability and dynamical systems analysis. These provide us with an assessment of the impact of the nonlinear sink terms on the stability of the numerical scheme employed and on the dynamics of the solutions.

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“…Indeed, this fact can be seen in Section 4, where the concept of differential transforms is briefly described. It may be pointed out that, later, this method has been successfully used in a series of literature [15][16][17][18][19][20][21] dealing with many engineering problems.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

Torabi

Yaghoobi

Colantoni

et al. 2013

Chinese Journal of Engineering

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Radiative radial fin with temperature-dependent thermal conductivity is analyzed. The calculations are carried out by using differential transformation method (DTM), which is a seminumerical-analytical solution technique that can be applied to various types of differential equations, as well as the Boubaker polynomials expansion scheme (BPES). By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related boundary conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced and then applied to the aforementioned equations. Solutions are subsequently obtained by a process of inverse transformation. The current results are then compared with previously obtained results using variational iteration method (VIM), Adomian decomposition method (ADM), homotopy analysis method (HAM), and numerical solution (NS) in order to verify the accuracy of the proposed method. The findings reveal that both BPES and DTM can achieve suitable results in predicting the solution of such problems. After these verifications, we analyze fin efficiency and the effects of some physically applicable parameters in this problem such as radiation-conduction fin parameter, radiation sink temperature, heat generation, and thermal conductivity parameters.

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Free vibration analysis of circular plates by differential transformation method

Cited by 71 publications

References 10 publications

Green’s function approach to frequency analysis of thin circular plates

Green’s function approach to frequency analysis of thin circular plates

Heat Transfer in a Porous Radial Fin: Analysis of Numerically Obtained Solutions

Analysis of Radiative Radial Fin with Temperature-Dependent Thermal Conductivity Using Nonlinear Differential Transformation Methods

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