Analytical and Semi-Analytical Methods for the Evaluation of Dynamic Thermo-Elastic Behavior of Structures Resting on a Pasternak Foundation

Liang, Xu; Cao, Zeng; Sun, Honglei; Zha, Xing; Leng, Jianxing

doi:10.1115/1.4038724

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…Durbin proposed the numerical inversion of the Laplace transform. This kind of method, which has been widely used in various engineering fields, can obtain almost the same solutions as that given by analytical inversion in a shorter time [34,35]. In that case, it can be defined by:…”

Section: Laplace Numerical Inversionmentioning

confidence: 99%

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

et al. 2019

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The primary objective of this article is to present a semi-analytical algorithm for the transient behaviors of Functionally Graded Materials plates (FGM plates) considering both the influence of in-plane displacements and the influence of temperature changes. Based on the classical plate theory considering the effect of in-plane displacements, the equilibrium equations of the motion system are derived by Hamilton’s principle. Here, we propose a novel, accurate, and efficient semi-analytical method that incorporates the Fourier series expansion, the Laplace transforms, and its numerical inversion and the Differential Quadrature Method (DQM) to simulate the transient behaviors. This paper validates the proposed method by comparisons with semi-analytical natural frequency results and those from the literature. Expressly, the results of dynamic response also agree well with those generated by the Navier’s method and Finite Element Method (FEM). A convergence study that utilizes the different numbers of sampling points shows that the process can converge quickly, and a few sampling points can achieve high accuracy. The effects of various boundary conditions at the ends, material graded index, and temperature change are further investigated. From the detailed parametric study, it is seen that the peak displacement increases as the edge degrees of freedom, the gradient index of the material, and temperature change increase.

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Section: Laplace Numerical Inversionmentioning

confidence: 99%

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

et al. 2019

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“…Generalized integral transform technique (GITT) solution is a semi-analytical method that has been widely applied in solving heat and fluid flow problems [15]. GITT was further applied to solve the dynamic behavior of Euler-Bernoulli beams [16], the dynamic behavior of pipes conveying twophase flow [1], problems of functionally graded material annular sector plate [17][18][19], and dynamic behavior of a fluid-conveying vertical or horizontal pipe [20][21][22]. However, GITT has not been employed before in the analysis of the dynamic behavior of a curved pipe conveying fluid problem.…”

Section: Introductionmentioning

confidence: 99%

In-plane and out-of-plane dynamics of curved pipes conveying fluid by integral transform method

Duan

et al. 2019

J Braz. Soc. Mech. Sci. Eng.

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This study presents a new solution for the dynamic behavior of in-plane and out-of-plane motion of a curved pipe conveying fluid, using the generalized integral transform technique (GITT). The system of sixth-and fourth-order partial differential equations governing three-dimensional motion of the curved pipe is integral transformed into three coupled systems of second-order ordinary differential equations, which are solved numerically by using the NDSolve routine of Mathematica. Excellent convergence behavior of the GITT solution is shown by comparing the vibration deflections at different points along the curved pipe centerline obtained with of different truncation orders. The results of natural frequencies and vibration responses compare well with available results in the literature obtained by other methods. Furthermore, we investigate the dynamic behavior of the curved pipe with different axial forces, flow velocities and other vibration parameters. A relationship between boundary conditions and axial forces is provided, and a series of vibration displacement and velocity trajectories is obtained. It is shown that the GITT is a convenient and effective mathematical method for vibration analysis of the curved pipe conveying fluid and can be used for further study of the dynamics of variable-curvature curved pipes. Keywords Curved pipe conveying fluid • Generalized integral transform technique • Dynamic behavior • In-plane and outof-plane vibration • Natural frequency * Chen An

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Elastic and viscoelastic foundations: a review on linear and nonlinear vibration modeling and applications

et al. 2019

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Analytical and Semi-Analytical Methods for the Evaluation of Dynamic Thermo-Elastic Behavior of Structures Resting on a Pasternak Foundation

Cited by 4 publications

References 23 publications

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

Novel Semi-Analytical Solutions for the Transient Behaviors of Functionally Graded Material Plates in the Thermal Environment

In-plane and out-of-plane dynamics of curved pipes conveying fluid by integral transform method

Elastic and viscoelastic foundations: a review on linear and nonlinear vibration modeling and applications

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