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Research Papers

Dynamic Behavior of Finite Coupled Mindlin Plates With a Blocking Mass

[+] Author and Article Information
XianZhong Wang

Key Laboratory of High Performance Ship
Technology of Ministry of Education;
Departments of Naval Architecture,
Ocean and Structural Engineering,
School of Transportation,
Wuhan University of Technology,
Hubei 430063, China
e-mails: xianzhongwang00@gmail.com;
xianzhongwang00@163.com

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received October 20, 2015; final manuscript received July 6, 2016; published online August 16, 2016. Assoc. Editor: Nicole Kessissoglou.

J. Vib. Acoust 138(6), 061008 (Aug 16, 2016) (10 pages) Paper No: VIB-15-1448; doi: 10.1115/1.4034251 History: Received October 20, 2015; Revised July 06, 2016

A power flow analysis of finite coupled Mindlin plates with a blocking mass at the junction of the coupled plates is investigated using the method of reverberation-ray matrix (MRRM). An exact solution is derived by the plate equations of motion to satisfy the boundary condition. The wave amplitude coefficients are obtained from the continuity conditions at driving force locations, and the line junction of two plates connected at an arbitrary angle. The blocking mass located at the junction of the two plates is modeled as a Timoshenko beam. The dynamic responses of the finite coupled Mindlin plates are verified by comparing with finite element method (FEM) results. The effects of the connected angles, blocking mass, and structural damping on the input power and transmitted power are calculated and analyzed. Numerical simulations of the finite coupled Mindlin plates with a blocking mass show that the present method can predict the dynamic behavior.

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Figures

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Fig. 1

Schematic diagram of the coupled Mindlin plates with a beam at the junction

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Fig. 2

Dual local coordinates of coupled plates

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Fig. 3

Comparisons of displacement vector of finite coupled Mindlin plates: (a) the real part of the transverse displacement at position I, γ = π; (b) the imaginary part of the transverse displacement at position I, γ = π; (c) the real part of the angular displacement at position I, γ = π; (d) the imaginary part of the angular displacement at position I, γ = π; (e) the real part of the transverse displacement at position II, γ = π/2; (f) the imaginary part of the transverse displacement at position II, γ = π/2; (g) the real part of the angular displacement at position II, γ = π/2; (h) the imaginary part of the angular displacement at position II, γ = π/2; (i) the real part of in-plane displacement u at position III, γ = π/2; and (j) the imaginary part of in-plane displacement u at position III, γ = π/2

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Fig. 4

Vibration responses distribution of finite coupled plates (γ = π) calculated by the present method: (a) f = 66 Hz, (b) f = 78 Hz, and (c) f = 115 Hz

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Fig. 5

Vibration responses distribution of finite coupled plates (γ = π) calculated by FEM: (a) f = 66.13 Hz, (b) f = 78.16 Hz, and (c) f = 114.28 Hz

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Fig. 6

Vibration responses distribution of finite coupled plates (γ = π/2) calculated by the present method: (a) f = 76 Hz, (b) f = 153 Hz, and (c) f = 254 Hz

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Fig. 7

Vibration responses distribution of finite coupled plates (γ = π/2) calculated by FEM: (a) f = 76.15 Hz, (b) f = 153.31 Hz, and (c) f = 253.51 Hz

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Fig. 8

The comparison of power flow with Ref. [5] and the present method

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Fig. 9

The comparison of power flow with different connected angles: (a) input power, (b)power transmitted across xHJ= 0, (c) power transmitted across xJK= 0, and (d) power transmitted across xJK= 0.25

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Fig. 10

The comparison of power flow of finite coupled plates (γ = π/2) with different blocking masses: (a) input power, (b) power transmitted across xHJ= 0, (c) power transmitted across xJK= 0, and (d) power transmitted across xJK= 0.25

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Fig. 11

The comparison of power flow of finite coupled plates (γ = π) with different blockingmasses: (a) input power, (b) power transmitted across xHJ= 0, (c) power transmitted acrossxJK= 0, and (d) power transmitted across xJK= 0.25

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Fig. 12

The comparison of the structure power including (a) γ = π/4, low-frequency range; (b) γ = π/4, high-frequency range; (c) γ = π/2, low-frequency range; (d) γ = π/2, high-frequency range; (e) γ = 3π/4, low-frequency range; (f) γ = 3π/4, high-frequency range; (g) γ = π, low-frequency range; and (h) γ = π, high-frequency range

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