Free in-plane vibration analysis of elastically restrained annular panels made of functionally graded material

Lyu, Peng; Du, Jingtao; Liu, Zhigang; Zhang, Peng

doi:10.1016/j.compstruct.2017.06.065

Cited by 19 publications

(4 citation statements)

References 32 publications

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“…In addition to the homogeneous material cases, with the development of material science and engineering, in-plane vibration of annular plates made of various novel composite materials is also investigated to obtain a deep understanding on dynamic characteristics of this vibration form. For example, Hosseini-Hashemi et al and Lyu et al [9,21] explored the in-plane vibration of annular panels made of the functional gradient materials. Moreover, circular/annular plates are frequently encountered in various rotating machinery, and many research efforts are also made for the in-plane vibration analysis of rotating annular plate, such as the works by Chen and Jhu, Hamidzadeh, and Lyu et al [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

A Semianalytical Solution for In-Plane Vibration Analysis of Annular Panels with Arbitrary Distribution of Internal Point Constraints

Lyu

Liu

2020

Mathematical Problems in Engineering

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In this paper, a semianalytical solution for the in-plane vibration analysis of annular panel with arbitrary distribution of internal point constraints is established for the first time. In-plane dynamic behavior of such panel structure is described via energy principle. A modified version of Fourier series is constructed for the in-plane vibration displacement expansion supplemented with the boundary smoothed terms, and the arbitrarily concentrated constraint in each field point is described in conjunction with Dirac delta function. A standard matrix eigenvalue problem containing various in-plane modal information of such annular panel is derived and solved through Rayleigh–Ritz procedure. Several numerical examples are presented to demonstrate the correctness and effectiveness of the proposed model by comparing the results with those from other approaches. Three representative types of point constraints, including point, line, and area configurations, are considered by collection of point constraints, and it is shown that the current model can make an accurate and efficient modal parameter prediction for annular panel with such most general case of point constraints.

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Section: Introductionmentioning

confidence: 99%

A Semianalytical Solution for In-Plane Vibration Analysis of Annular Panels with Arbitrary Distribution of Internal Point Constraints

Lyu

Liu

2020

Mathematical Problems in Engineering

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“…At the same time, other numerical techniques such as the differential quadrature method (Sharma et al, 2012), the meshfree Hermite radial basis collocation technique (Chu et al, 2014), the Chebyshev collocation approach in conjunction with the differential quadrature method (Kumar, 2015), the finite Taylor series expansion approach (Boreyri et al, 2016), the Fourier series combined with the boundary smoothed auxiliary polynomials (Lyu et al, 2017), two dimensional Chebyshev spectral approach (Huang et al, 2019), the pseudo spectral approach (Heshmati and Jalali, 2019), and so on were applied to gain the vibration frequencies and mode shapes of in-plane functionally graded plates under various boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of functionally graded magneto-electro-elastic plates with in-plane material heterogeneity

Zhang

Fang

et al. 2020

Journal of Intelligent Material Systems and Structures

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A three dimensional elasticity analysis for the transverse free vibration characteristics of functionally graded magneto-electro-elastic plates based on the scaled boundary finite element method (SBFEM) incorporated with the precise integration algorithm (PIA) is presented. The material properties of magneto-electro-elastic plates are changing along the in-plane direction with arbitrary mathematical functions. In the proposed methodology, the strategies of only discretizing the in-plane surface and utilizing the two-dimensional spectral elements to construct diagonal coefficient matrices are adopted, which contributes to decreasing the calculation effort. The derivation process begins with the three dimensional governing equations of magneto-electro-elastic materials. Neither the plate mechanical kinematics nor invoking assumptions on the spatial distributions of electric and magnetic quantities are adopted. Built upon the introduced scaled boundary coordinates, the principle of virtual work and the technique of dual vectors, a first order ordinary differential SBFEM matrix equation for the in-plane functionally graded magneto-electro-elastic plates is obtained. Its general solution is analytically denoted as the matrix exponent. To improve the computation accuracy of the matrix exponent, the PIA is utilized to form the stiffness matrix. By virtue of the kinetic energy technique, it is convenient to construct the mass matrix of the in-plane functionally graded magneto-electro-elastic plates based on the SBFEM for the first time. Finally, comparisons of flexural frequency parameters with those from exact solutions and other numerical methods are provided. The accuracy, effectiveness, and versatility of the employed technique are validated. Moreover, additional numerical exercises are conducted to exhibit the influences of boundary conditions, material gradation functions, and aspect ratios on the free vibration behaviors of in-plane functionally graded magneto-electro-elastic rectangular, circular, and perforated plates.

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“…A thermal buckling analysis of a functionally graded circular plate has been presented by Farhatnia et al (2017) using a differential transform method and von Ka´rma´n assumptions. Lyu et al (2017) investigated the free in-plane vibrations of elastically restrained annular panels, employing an admissible functionsbased Fourier series method and a Rayleigh-Ritz procedure. The axisymmetric vibrations of functionally graded circular plates have been analyzed by Z _ ur using quasi-Green's function method (Z _ ur, 2018) and a Neumann series method (Z _ ur, 2019) on the basis of classical plate theory.…”

Section: Introductionmentioning

confidence: 99%

“…(2017) using a differential transform method and von Kármán assumptions. Lyu et al. (2017) investigated the free in-plane vibrations of elastically restrained annular panels, employing an admissible functions-based Fourier series method and a Rayleigh–Ritz procedure.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method

Lal

Saini

2019

Journal of Vibration and Control

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The vibration of functionally graded circular plates of variable thickness under a thermal environment is analyzed when the nodal lines are concentric circles by using the generalized differential quadrature method for the nonlinear temperature distribution in the thickness direction. The parabolic variation in thickness along the radial direction is controlled by a taper constant. The plate material is graded in the transverse direction and its mechanical properties are temperature-dependent. The thermal environment over the top and bottom surfaces of the plate is assumed to be uniform. Hamilton's principle has been used in obtaining the governing differential equations for thermo-elastic equilibrium and axisymmetric motion for such a plate model employing Kirchhoff plate theory. Numerical results for thermal displacements and natural frequencies of clamped and simply supported plates have been obtained using MATLAB. The effect of the taper constant, volume fraction index, and temperature difference on the vibration characteristics has been analyzed for the lowest three modes of vibration. A study in which the plate material has temperature-independent properties has also been performed. The accuracy of the present technique is verified by comparing the results with those available in the literature.

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Free in-plane vibration analysis of elastically restrained annular panels made of functionally graded material

Cited by 19 publications

References 32 publications

A Semianalytical Solution for In-Plane Vibration Analysis of Annular Panels with Arbitrary Distribution of Internal Point Constraints

A Semianalytical Solution for In-Plane Vibration Analysis of Annular Panels with Arbitrary Distribution of Internal Point Constraints

Free vibration analysis of functionally graded magneto-electro-elastic plates with in-plane material heterogeneity

Vibration analysis of functionally graded circular plates of variable thickness under thermal environment by generalized differential quadrature method

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