Free Vibration Analysis of Rectangular Fgm Plates with a Cutout

Zhang, Jun; Li, Tianyun; Zhu, Xiang

doi:10.1088/1755-1315/283/1/012037

Cited by 4 publications

(7 citation statements)

References 9 publications

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“…In Table 4, the first fix non-dimensional frequency parameters are obtained. It is observed that the frequencies are in excellent agreement with those given in [38], which verifies the accuracy and efficiency of the proposed model. The effect of gradient index on the frequency parameters of structure with cutout is consistent with that structure without cutout also can be concluded from the table below.…”

Section: Convergence Of the Methodssupporting

confidence: 79%

“…The truncated number of admissible displacement function components in Fourier series expansion is expressed as M × N × Q, and the truncated number of this paper is from 3 to 10. It can be observed that the maximum error with [38] is 1.7898%, and the main reason of the error is that the first order shear theory is adopted by [38]. It can be concluded that the proposed method has fast convergence and good stability, and the truncation numbers will be set as M = N = Q = 10 in the following studies.…”

Section: Convergence Of the Methodsmentioning

confidence: 99%

“…Convergence property for the free vibration analysis of FGMs plate with circular cutout is examined in terms of the limited number of terms in the displacement expressions in actual calculation to verify the accuracy and efficiency of the proposed method. Table 2 shows the convergence studies of the first six non-dimensional frequency parameters of a FGMs square plate with a central circular cutout with different truncated numbers, and the data of [38] are also given out in Table 2. The truncated number of admissible displacement function components in Fourier series expansion is expressed as M × N × Q, and the truncated number of this paper is from 3 to 10.…”

Section: Convergence Of the Methodsmentioning

confidence: 99%

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Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions

Huang

Xue

2021

Materials

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Functionally graded materials (FGMs) structures are increasingly used in engineering due to their superior mechanical and material properties, and the FGMs plate with cutouts is a common structural form, but research on the vibration characteristics of FGMs plate with cutouts is relatively limited. In this paper, the three-dimensional exact solution for the vibration analysis of FGMs rectangular plate with circular cutouts subjected to general boundary conditions is presented based on the three-dimensional elasticity theory. The displacement field functions are expressed as standard cosine Fourier series plus auxiliary cosine series terms satisfying the boundary conditions in the global coordinate system. The plate with circular cutout is discretized into four curve quadrilateral sub-domains using the p-version method, and then the blending function method is applied to map the closed quadrilateral region to the computational space. The characteristic equation is obtained based on the Lagrangian energy principle and Rayleigh–Ritz method. The efficiency and reliability of proposed method are verified by comparing the present results with those available in the literature and FEM methods. Finally, a parametric study is investigated including the cutout sizes, the cutout positions, and the cutout numbers from the free vibration characteristic analysis and the harmonic analysis. The results can serve as benchmark data for other research on the vibration of FGMs plates with cutouts.

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Section: Convergence Of the Methodssupporting

confidence: 79%

Section: Convergence Of the Methodsmentioning

confidence: 99%

Section: Convergence Of the Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions

Huang

Xue

2021

Materials

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“…e number and size of cutouts have a great influence on the transverse vibration characteristics of the plate structures [1][2][3][4][5][6][7][8][9]. e rigidity of the structure with cutouts is mostly dependent on the number of cutouts.…”

Section: Introductionmentioning

confidence: 99%

“…Lu [5] proposed an analytical solution of an elastic infinite plate containing an ellipse hole and a circle hole subjected to internal tractions and shears at infinity. e investigations on the effects of the cutout size are focused on the cutouts located in the center of the flexible plate [6][7][8][9]. Takahashi [6] used the Ritz method to analyze the rectangular plate with a central circular hole.…”

Section: Introductionmentioning

confidence: 99%

In‐Plane Vibration Analysis of Square Plate with Multiple Cutouts

Shi

Zhang

et al. 2021

Shock and Vibration

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A theoretical solution method for the in-plane vibration characteristics of the plate with cutouts is proposed in this paper. The energy principle in conjunction with the Rayleigh–Ritz solution technique is adopted for the theoretical modeling of the in-plane vibration of the structure. The energy functions for the plate with cutouts are established by subtracting the energies of the cutout domains from the total energies of the whole plate. To ensure continuity over the entire solution domain, the in-plane displacements are composed of two-dimensional standard Fourier series and supplementary functions. The in-plane eigenmodes of the plates with different square cutouts are compared with the results obtained from the finite element method (FEM), with good agreements. The influences of the cutouts on the in-plane vibration characteristics of the plates with cutouts are investigated by varying the number, size, and position of the cutouts.

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Dynamic Modeling and Analysis of Boundary Effects in Vibration Modes of Rectangular Plates with Periodic Boundary Constraints Based on the Variational Principle of Mixed Variables

2023

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The modal and vibration-noise response characteristics of plate structures are closely related to their boundary effects, and the analytical modeling and solution of the dynamics of plate structures with complex boundary conditions can reveal mechanisms of the influence of the boundary structure parameters on the modal characteristics. This paper proposes a new method for dynamic modeling of rectangular plates with periodic boundary conditions based on the energy equivalence principle (mixed-variable variational principle) of equating complex boundary “geometric constraints” to “mathematical physical constraints”, taking a rectangular plate structure with periodic boundaries commonly used in engineering as the object. First, the boundary external potential energy of the periodic boundary rectangular plate is obtained by equating the bending moment and deflection to the boundary conditions. Next, we establish the total potential energy model, the amplitude boundary equation, as well as the frequency equation of the periodic boundary rectangular plate in turn. Solving by numerical method, the natural frequency of the theoretical model is obtained. The validity of the theoretical model is then verified by modal test experiments. Finally, the law of the parameters such as the form of boundary constraint, the number of periods, and the clamp support ratio on the natural frequency of the rectangular plate is investigated. The results show that the natural frequency of the rectangular plate is closely related to the boundary form and period distribution of the plate. The modal frequencies of the plate structure can be tuned by the design of the boundary conditions for a certain size of the plate structure. The research in this paper provides a theoretical and technical basis for the vibration noise control of complex boundary plate structures.

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Free Vibration Analysis of Rectangular Fgm Plates with a Cutout

Cited by 4 publications

References 9 publications

Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions

Three-Dimensional Solution for the Vibration Analysis of Functionally Graded Rectangular Plate with/without Cutouts Subject to General Boundary Conditions

In‐Plane Vibration Analysis of Square Plate with Multiple Cutouts

Dynamic Modeling and Analysis of Boundary Effects in Vibration Modes of Rectangular Plates with Periodic Boundary Constraints Based on the Variational Principle of Mixed Variables

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