Vibration Analysis of a Magnetoelectroelastic Rectangular Plate Based on a Higher-Order Shear Deformation Theory

Shooshtari, Alireza; Razavi, Soheil

doi:10.1590/1679-78251831

Alireza Shooshtari

Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran. Email: shooshta@basu.ac.ir

Soheil Razavi

Mechanical Engineering Department, Bu-Ali Sina University, Hamedan, Iran. Email: soheilrazavi@outlook.com

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Figure 1:
Schematic of a magnetoelectroelastic plate on an elastic foundation.

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Figure 2:
Effect of shear coefficient of foundation on the fundamental natural frequency of closed-circuit magnetoelectroelastic square plates (a/h = 25,

= 0).

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Figure 3:
Effect of length-to-thickness on the fundamental natural frequency of closed-circuit magnetoelectroelastic square plates (h = 1 mm,

=

= 0).

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Table 1:
Comparison of dimensionless fundamental frequency of asimply-supportedsquare plate (ν = 0.3).

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Table 2:
Comparison of dimensionless fundamental frequency of a simply-supportedrectangular plate (ν = 0.3, a/h=1000).

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Table 3:
First four dimensionless frequencies of square plates with different boundary conditions (ν = 0.3, a/h=1000).

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Table 4:
Dimensionless fundamental frequency of square isotropic plates resting on elastic foundation (ν = 0.3).

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Table 5:
Dimensionless frequencies of several square plates.

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Table 6:
Dimensionless fundamental frequencies of a magnetoelectroelastic rectangular plate(h = 1 mm, a/h = 10).

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Table 7:
Dimensionless frequencies of a magnetoelectroelastic square plate (h = 1 mm).

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Method	a/b
Method	0.4	2/3	1.0	1.5	2.5
Leissa (1973)Leissa, A.W. (1973). The free vibration of rectangular plates, Journal of Sound and Vibration 31(3): 257-293.	11.4487	14.2561	19.7392	32.0762	71.5564
Present study	11.4487	14.2561	19.7391	32.0760	71.5537

Method	SCSC			CCCC
Method	ω₁	ω₂	ω₃	ω₄	ω₁	ω₂	ω₃	ω₄
Kim et al. (1993)	2.9333	5.5466	7.0242	9.5833	3.6460	7.4362	7.4362	10.9644
Woo et al. (2003)Woo, K.S., Hong, C.H., Basu, P.K., Seo, C.G. (2003). Free vibration of skew Mindlin plates by p-version of FEM, Journal of Sound and Vibration 268(4): 637-656.	2.9306	5.5469	7.0208	9.5831	3.6448	7.4373	7.4374	10.9650
Eftekhari and Jafari (2013)Eftekhari, S.A., Jafari, A.A. (2013). Modified mixed Ritz-DQ formulation for free vibration of thick rectangular and skew plates with general boundary conditions, Applied Mathematical Modelling 37: 7398-7426.	2.9333	5.5466	7.0242	9.5833	3.6460	7.4362	7.4362	10.9643
Present study	2.9219	5.5643	7.0282	9.6122	3.6315	7.4615	7.4615	11.0383

(K_w,K_s)	Boundary condition	Method
(K_w,K_s)	Boundary condition	Lam et al. (2000)Lam, K.Y., Wang, C.M., He, X.Q. (2000). Canonical exact solutions for Levy-plates on two-parameter foundation using Green's functions, Engineering Structures 22: 364-378.	Hasani Baferani et al. (2011)Hasani Baferani, A., Saidi, A.R., Ehteshami, H. (2011). Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation, Composite Structures 93: 1842-1853.	Present study
(0,0)	SSSS	19.74	19.7374	19.7320
(0,0)	SCSC	28.95	28.9441	28.8274
(0,100)	SSSS	41.62	48.6149	48.6101
(0,100)	SCSC	54.68	54.6742	55.1384
(100,0)	SSSS	22.13	22.1261	22.1209
(100,0)	SCSC	30.63	30.6229	30.5123
(100,100)	SSSS	49.63	49.6327	49.6279
(100,100)	SCSC	55.59	55.5811	56.0377

Method	Mode (m,n)
	(1,1)			(2,1)
	B	F	Al	B	F	Al
Ribeiro (2005)Ribeiro, P. (2005). Nonlinear vibrations of simply-supported plates by the p-version finite element method, Finite Elements in Analysis and Design 41(9-10): 911-924.	-	-	19.7392	-	-	49.3480
Wu and Lu (2009)Wu, C.P., Lu, Y.C. (2009). A modified Pagano method for the 3D dynamic responses of functionally graded magneto-electro-elastic plates, Composite Structures 90: 363-372.	1.2523	1.0212	-	2.3003	1.9747	-
Moita et al. (2009)Moita, J.M.S., Soares, C.M.M., Soares, C.A.M. (2009). Analyses of magneto-electro-elastic plates using a higher order finite element model, Composite Structures 91(4): 421-426.	1.2629	1.1358	-	2.4649	2.1075	-
Present study	1.2349	1.1048	19.7384	2.2857	1.9571	49.3430

Boundary Condition	a/b	V₀ (10⁸ V)		Ω₀ (10⁶ A)
Boundary Condition	a/b	0	+1	0	+1
SSSS	0.5	0.343322939	0.343322938	0.343322939	0.343322939
	1.0	0.535860885	0.535860883	0.535860885	0.535860887
	2.0	1.233226423	1.233226400	1.233226423	1.233226453
SCSC	0.5	0.380853054	0.380853053	0.380853054	0.380853055
	1.0	0.774485196	0.774485191	0.774485196	0.774485204
	2.0	2.270502531	2.270502390	2.270502531	2.270502717
CCCC	0.5	0.675570089	0.675570085	0.675570089	0.675570094
	1.0	0.962062272	0.962062261	0.962062272	0.962062287
	2.0	2.342843729	2.342843576	2.342843729	2.342843931

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Vibration Analysis of a Magnetoelectroelastic Rectangular Plate Based on a Higher-Order Shear Deformation Theory

Abstract