Inherent characteristic analysis of a precast concrete vibrating table based on the Rayleigh-Ritz method

Abstract The first natural frequency of oscillations of the vibrations of a discrete-continuous interresonant vibrating table plate was found using the functions of the Krylov-Duncan. The continuous member, presented in a plate hinged at four points, is used as a reactive mass with distributed parameters to create an inter-resonance vibrating table with an electromagnetic drive. For this purpose, the plate was considered as a rod on hinged supports. The justification of this approach is confirmed by simulation in the Ansys software. The results were confirmed using the approximate Rayleigh-Ritz method. The geometric shape of the plate is reduced to a section of a hyperboloidal surface. The results of simulation of the first natural frequency were verified experimentally.

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Free Vibration Analysis of Rotating Pretwisted Functionally Graded Sandwich Blades

International Journal of Aerospace Engineering ◽

10.1155/2018/2727452 ◽

2018 ◽

Vol 2018 ◽

pp. 1-18 ◽

Cited By ~ 3

Author(s):

L. T. Liu ◽

Y. X. Hao ◽

W. Zhang ◽

J. Chen

Keyword(s):

Free Vibration ◽

Volume Fraction ◽

Ritz Method ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Thickness Ratio ◽

Mode Shapes ◽

Homogeneous Material ◽

Characteristic Analysis ◽

Structural Dynamic

A new structural dynamic model for the free vibration characteristic analysis of rotating pretwisted functionally graded (FG) sandwich blades is developed. The sandwich blade is made up of two functionally graded skins and a homogeneous material core. The thick shell theory is applied to derive the basic equations of motion of the rotating FG sandwich blade by considering the effects of centrifugal and Coriolis forces. The mode shapes are expanded in terms of two-dimensional algebraic polynomials in the Rayleigh–Ritz method, and the static and dynamic natural frequencies of the blade are obtained. The convergence analysis is studied, and the accuracy of the proposed model is verified by comparing with the literature results and ANSYS data. The effects of frequency parameters such as the twist angle, the thickness ratio, the aspect ratio, the layer thickness ratio, the scalar parameter of volume fraction, the stagger angle, and the rotation velocity on the vibration characteristics for pretwist FG sandwich blade are investigated in detail. In addition, the phenomena of frequency locus veering and mode shape exchanging occur in the static and dynamic states. Frequency locus veering is essentially caused by the coupling between different modes.

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

Materials ◽

10.3390/ma14227088 ◽

2021 ◽

Vol 14 (22) ◽

pp. 7088

Author(s):

Wenhao Huang ◽

Kai Xue ◽

Qiuhong Li

Keyword(s):

Boundary Conditions ◽

Rectangular Plate ◽

Vibration Analysis ◽

Ritz Method ◽

Three Dimensional ◽

Functionally Graded ◽

General Boundary ◽

Global Coordinate System ◽

General Boundary Conditions ◽

Characteristic Analysis

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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