Vibration of a Reissner–Mindlin–Timoshenko plate–beam system

Labuschagne, A.; Rensburg, N.F.J. van; Merwe, A. J. van der

doi:10.1016/j.mcm.2009.05.029

Cited by 7 publications

(5 citation statements)

References 12 publications

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“…The theories are characterised by an equivalent approximation degree known as the Reissner–Mindlin plate theory. Their comparison is discussed in [ 5 , 6 , 7 , 8 ], etc. Theoretical considerations can be found in [ 9 , 10 , 11 , 12 , 13 , 14 , 15 ] for higher-order shear deformation theories as well.…”

Section: Introductionmentioning

confidence: 99%

“…In [ 6 ], for Reissner, Mindlin and Reddy plate models, a solution to the rectangular transverse plate sinusoidally loaded and freely supported along all the edges is given. Vibrations in the plate–beam system, in which the Reissner–Mindlin plate model related to the Timoshenko beam model was applied, were analysed in [ 7 ]. In [ 11 , 16 ], it is shown that when the plate thickness is around zero, the solution for the Reissner–Mindlin plate becomes close to the solution within the Kirchhoff–Love plate theory (the so-called classical plate theory (CPT)).…”

Section: Introductionmentioning

confidence: 99%

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Effect of Membrane Components of Transverse Forces on Magnitudes of Total Transverse Forces in the Nonlinear Stability of Plate Structures

Kołakowski¹,

Jankowski²

2020

Materials

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For an isotropic square plate subject to unidirectional compression in the postbuckling state, components of transverse forces in bending, membrane transverse components and total components of transverse forces were determined within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), the classical plate theory (CPT) and the finite element method (FEM). Special attention was drawn to membrane components of transverse forces, which are expressed with the same formulas for the first three theories and do not depend on membrane deformations. These components are nonlinearly dependent on the plate deflection. The magnitudes of components of transverse forces for the four theories under consideration were compared.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Effect of Membrane Components of Transverse Forces on Magnitudes of Total Transverse Forces in the Nonlinear Stability of Plate Structures

Kołakowski¹,

Jankowski²

2020

Materials

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“…Many studies concerning dynamic analysis of plates on elastic foundation are performed. Labuschange et al [2] analyzed a plate-beam system in which Reissner-Mindlin plate model is combined with the Timoshenko beam model, and calculated natural frequencies and vibration modes for the system. Sapountzakis and Katsikadelis [3] presented an optimized model for the analysis of plates reinforced with beams.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Thick Plates Including Deep Beams on Elastic Foundations Using Modified Vlasov Model

Özgan

2013

Shock and Vibration

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Dynamic analysis of foundation plate-beam systems with transverse shear deformation is presented using modified Vlasov foundation model. Finite element formulation of the problem is derived by using an 8-node (PBQ8) finite element based on Mindlin plate theory for the plate and a 2-node Hughes element based on Timoshenko beam theory for the beam. Selective reduced integration technique is used to avoid shear locking problem for the evaluation of the stiffness matrices for both the elements. The effect of beam thickness, the aspect ratio of the plate and subsoil depth on the response of plate-beam-soil system is analyzed. Numerical examples show that the displacement, bending moments and shear forces are changed significantly by adding the beams.

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“…Many researchers have studied the free vibration for Mindlin plates [8][9][10][11][12][13][14][15][16][17][18][19][20]. Liew et al [9] used the boundary characteristic orthogonal polynomials to approximate the transverse displacement and rotational functions of Mindlin plates.…”

mentioning

confidence: 99%

“…Although much attention has been paid to the free vibration [8][9][10][11][12][13][14][15][16][17][18][19][20] and response in time domain [21,22] for Mindlin plates, few researchers have studied the dynamic response in frequency domain for finite Mindlin plates. Previous works on the vibratory power flow in finite Mindlin plates show that the shear and rotary inertia corrections only influence the power flow at high frequencies [30][31][32].…”

mentioning

confidence: 99%

The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges

Liu

Tao

et al. 2011

Acta Mech Sin

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In this paper, wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach. The dynamic responses, active and reactive power flow in the finite plate are calculated by the Mindlin plate theory (MPT) and classic plate theory (CPT). To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate, the near-field and far-field waves are entirely contained in the wave approach. The in-plane longitudinal and shear waves are also considered. The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated. From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies. Furthermore, the effects of structural damping on the active and reactive power flow at the junction are also analyzed.

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Vibration of a Reissner–Mindlin–Timoshenko plate–beam system

Cited by 7 publications

References 12 publications

Effect of Membrane Components of Transverse Forces on Magnitudes of Total Transverse Forces in the Nonlinear Stability of Plate Structures

Effect of Membrane Components of Transverse Forces on Magnitudes of Total Transverse Forces in the Nonlinear Stability of Plate Structures

Dynamic Analysis of Thick Plates Including Deep Beams on Elastic Foundations Using Modified Vlasov Model

The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges

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