A convenient analytical method for solution of dynamic problems in one-dimensional distributed-parameters systems

Multibody distributed dynamic systems are seen in many engineering applications. Developed in this investigation is a new analytical method for a class of branched multibody distributed systems, which is called the augmented distributed transfer function (DTFM). This method adopts an augmented state formulation to describe the interactions among multiple distributed and lumped bodies, which resolves the problems with conventional transfer function methods in modeling and analysis of multibody distributed systems. As can be seen, the augmented DTFM, without the need for orthogonal system eigenfunctions, produces exact and closed-form solutions of various dynamic problems, in both frequency and time domains.

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An Analytical Method for the Response of Coated Plates Subjected to One-Dimensional Underwater Weak Shock Wave

Shock and Vibration ◽

10.1155/2014/803751 ◽

2014 ◽

Vol 2014 ◽

pp. 1-13 ◽

Cited By ~ 3

Author(s):

Zeyu Jin ◽

Caiyu Yin ◽

Yong Chen ◽

Xiuchang Huang ◽

Hongxing Hua

Keyword(s):

Shock Wave ◽

Analytical Method ◽

Weak Shock ◽

Wave Theory ◽

Time Sequence ◽

Weak Shock Wave ◽

One Dimensional ◽

Coated Plate ◽

Pressure Increment ◽

Good Agreement

An analytical method based on the wave theory is proposed to calculate the pressure at the interfaces of coated plate subjected to underwater weak shock wave. The method is carried out to give analytical results by summing up the pressure increment, which can be calculated analytically, in time sequence. The results are in very good agreement with the finite element (FE) predictions for the coating case and Taylor’s results for the noncoating case, which validate the method that is suitable for underwater weak shock problem. On the other hand, Taylor’s results for the coating case are invalid, which indicates a potential application field for the method. The extension of the analytical method to q-layer systems and dissipation case is also outlined.

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Numerical methods of solving one-dimensional non-stationary gas-dynamic problems

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(76)90047-1 ◽

1976 ◽

Vol 16 (6) ◽

pp. 120-136 ◽

Cited By ~ 1

Author(s):

Yu.P. Popov ◽

A.A. Samarskii

Keyword(s):

Numerical Methods ◽

Dynamic Problems ◽

One Dimensional ◽

Gas Dynamic

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Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation

Journal of Function Spaces ◽

10.1155/2021/6613619 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Hassan Eltayeb ◽

Said Mesloub

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Analytical Method ◽

Decomposition Method ◽

Nonlinear Partial Differential Equations ◽

One Dimensional ◽

Burger's Equation ◽

Burger’S Equation ◽

Sumudu Transform ◽

Linear And Nonlinear

The conformable double Sumudu decomposition method (CDSDM) is a combination of decomposition method (DM) and a conformable double Sumudu transform. It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. Two examples are used to illustrate the method.

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