Free Vibration Analysis of Rectangular Plates

Gorman, Daniel; Saunders, H.

doi:10.1115/1.3264295

Cited by 23 publications

(39 citation statements)

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“…The out-of-plane oscillation caused by transverse waves is closely related to bending stiffness of the plate, whereas the in-plane oscillation caused by longitudinal waves is related to its in-plane stiffness, i.e., tensile/compressive stiffness [10]. The out-of-plane oscillations are classified furthermore into three types: symmetric, antisymmetric, and complex (symmetric-antisymmetric) modes, depending on the symmetry of the oscillation shape [17] as well as the in-plane oscillations [18]. Figure 4a and b display the natural frequencies of some selected modes calculated for variations of Young's modulus E 1 , Poisson's ratio m 1 , and in-plane stress r 1 .…”

Section: Results Of Model Amentioning

confidence: 99%

Mechanical Characteristics of Electrolytes Assessed with Resonant Ultrasound Spectroscopy

et al. 2013

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Elastic properties and residual stresses are critical for the assessment of the reliability of ceramics components. The thin electrolyte layer of anode supported SOFCs is under a state of high compressive residual stress. In the present study, the elastic properties of this layer as well as the residual stress distribution induced in the anode‐supported planar SOFC cell were examined by using the resonant ultrasound spectroscopy (RUS). A modal analysis by finite element simulation demonstrated that the RUS has a great potential to determine these mechanical characteristics. The Young's modulus can be determined from the natural frequencies of the layered sample whilst the residual stress can be determined using the sample with a semi‐hole. Estimates of the Poisson's ratio are possible. In the experiment, various individual resonant oscillations were successfully identified using the present RUS system. Hence, by comparison of experimental results and simulations, the elastic properties as well as the residual stress were obtained. Although the proposed method is still experimentally challenging, it could be developed to become a powerful tool to simultaneously determine residual stresses and elastic constants of thin‐layered systems.

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Section: Results Of Model Amentioning

confidence: 99%

Mechanical Characteristics of Electrolytes Assessed with Resonant Ultrasound Spectroscopy

et al. 2013

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“…To formulate spectral element model for a thin plate by following the general procedure introduced in [4], firstly all the time-domain quantities in the governing equations (1) and (2) are transformed into the frequency-domain quantities by using the discrete Fourier transform (DFT) theory. For instance, the transverse displacement ( , , ) and the external force ( , , ) can be represented in the spectral forms as…”

Section: Spectral Element Model For a Finite Plate Elementmentioning

confidence: 99%

“…Although the subject of dynamic analysis of the plate has a long history which spans more than two centuries, most theoretical solutions to this classical problem are considered to be at best approximate because it is difficult to obtain exact closed-form solutions which simultaneously satisfy the governing differential equations and the associated boundary conditions, except for the Levy-type plates [1,2].…”

Section: Introductionmentioning

confidence: 99%

Transverse Vibration of the Thin Plates: Frequency-Domain Spectral Element Modeling and Analysis

Park

Lee

Park

2015

Mathematical Problems in Engineering

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It has been well known that exact closed-form solutions are not available for non-Levy-type plates. Thus, more accurate and efficient computational methods have been required for the plates subjected to arbitrary boundary conditions. This paper presents a frequency-domain spectral element model for the rectangular finite plate element. The spectral element model is developed by using two methods in combination: (1) the boundary splitting and (2) the super spectral element method in which the Kantorovich method-based finite strip element method and the frequency-domain waveguide method are utilized. The present spectral element model has nodes on four edges of the finite plate element, but no nodes inside. This can reduce the total number of degrees of freedom a lot to improve the computational efficiency significantly, when compared with the standard finite element method (FEM). The high solution accuracy and computational efficiency of the present spectral element model are evaluated by the comparison with exact solutions and the solutions by the standard FEM.

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“…shown in equation (13). It is shown that the weaker continuity condition of assumed refined rotation functions in an element has been satisfied.…”

Section: Refined Rotation Function Of the Elementmentioning

confidence: 99%

Refined triangular discrete Kirchhoff plate element for thin plate bending, vibration and buckling analysis

Wanji

Cheung

1998

Int. J. Numer. Meth. Engng.

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A refined triangular discrete Kirchhoff thin plate bending element RDKT which can be used to improve the original triangular discrete Kirchhoff thin plate bending element DKT is presented. In order to improve the accuracy of the analysis a simple explicit expression of a refined constant strain matrix with an adjustable constant can be introduced into its formulation. The new element displacement function can be used to formulate a mass matrix called combined mass matrix for calculation of the natural frequency and in the same way a combined geometric stiffness matrix can be obtained for buckling analysis. Numerical examples are presented to show that the present methods indeed, can improve the accuracy of thin plate bending, vibration and buckling analysis.

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Free Vibration Analysis of Rectangular Plates

Cited by 23 publications

References 0 publications

Mechanical Characteristics of Electrolytes Assessed with Resonant Ultrasound Spectroscopy

Mechanical Characteristics of Electrolytes Assessed with Resonant Ultrasound Spectroscopy

Transverse Vibration of the Thin Plates: Frequency-Domain Spectral Element Modeling and Analysis

Refined triangular discrete Kirchhoff plate element for thin plate bending, vibration and buckling analysis

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