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Research Papers

A Finite Volume Time Domain Method for In-Plane Vibration on Mixed Grids

[+] Author and Article Information
Ling-kuan Xuan

e-mail: xuanlingkuan@163.com

Ping-jian Ming

e-mail: pingjianming@hrbeu.edu.cn

Jing-feng Gong, Wen-ping Zhang

College of Power and Energy Engineering,
Harbin Engineering University,
Harbin 150001, China

Da-yuan Zheng

Luoyang Ship Material Research Institute,
Luoyang 471000, China

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 15, 2011; final manuscript received August 20, 2013; published online October 3, 2013. Assoc. Editor: Liang-Wu Cai.

J. Vib. Acoust 136(1), 011003 (Oct 03, 2013) (9 pages) Paper No: VIB-11-1245; doi: 10.1115/1.4025398 History: Received October 15, 2011; Revised August 20, 2013

A finite volume time domain method is developed for in-plane vibration based on mixed triangular and quadrilateral elements. Here the linear quadrilateral element shape function is introduced instead of the constant one to improve the accuracy of the present method. The improvement is validated to be vital to avoid violent numerical oscillation of displacement fields when applying to the point–source problem. The present method is proposed to analyze the transient responses and the natural characteristics of several in-plane problems. The results show good agreement with the commercial code solutions and the analytical solutions. In order to demonstrate the capability of the present method for multiexcitation problems, an example with sources containing different frequencies and phase angles, concentrated and uniform distributions, and impulse and continuous forms is analyzed.

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Figures

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Fig. 1

The scheme of control volume

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Fig. 2

Time marching scheme

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Fig. 3

Any quadrilateral element: (a) global coordinate and (b) local coordinate

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Fig. 4

An elliptic membrane: (a) geometry and boundary conditions and (b) mesh a with 24 quadrilateral elements and mesh b with 384 quadrilateral elements

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Fig. 5

Transient responses of displacement ux at point A: (a) mesh a and (b) mesh b

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Fig. 6

Contours from the method before improvement at t = 2 × 10−5 s: (a) displacement ux and (b) displacement uy

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Fig. 7

Contours from the method after improvement at t = 2 × 10−5 s: (a) displacement ux and (b) displacement uy

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Fig. 8

Comparison of displacement curves at t = 1.6 × 10−5 s: (a) displacement ux along y = 0 m and (b) displacement uy along y = 0.02 m

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Fig. 9

Sketch of a square plate with a hole

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Fig. 10

Transient responses at point A for different cases: (a) displacement uy and (b) stress σyy

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Fig. 11

Sketch map of rectangular membrane

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Fig. 12

Comparison of nodal displacement ux

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Fig. 13

Comparisons between FVM and FEM: (a) displacement ux at node 2 and (b) stress σxx at node 1

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Fig. 14

Contours of stress σxx at t = 0.002 s: (a) FVM and (b) FEM

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Fig. 15

Transient responses at node 4: (a) displacement uy and (b) stress σxx

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Fig. 16

Displacements at node 2: (a) transient responses and (b) spectrums

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