Free vibration analysis of circular plates by differential transformation method

2009 ◽  
Vol 212 (2) ◽  
pp. 377-386 ◽  
Author(s):  
Hasan Serter Yalcin ◽  
Aytac Arikoglu ◽  
Ibrahim Ozkol
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Circular Plates ◽  
Differential Transformation

Free Vibration Analysis of Rotating Tapered Bresse-Rayleigh Beams Using the Differential Transformation Method

2009 ◽  
Author(s):  
Dominic R. Jackson ◽  
S. Olutunde Oyadiji
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Free Vibration Analysis ◽  
Transformation Method ◽  
Differential Transformation Method ◽  
Algebraic Equations ◽  
Differential Transformation ◽  
Rayleigh Beam

The free vibration characteristics of a rotating tapered Rayleigh beam is analysed in this study. First, the strain-displacement relationship for the rotating beam is formulated and used to derive the kinetic and strain energies in explicit analytical form. Second, Hamilton’s variational principle is used to derive the governing differential equation of motion and the associated boundary conditions. Third, the Differential Transformation Method (DTM) is applied to reduce the governing differential equations of motion and the boundary conditions to a set of algebraic equations from which the frequency equation is derived. Next, a numerical algorithm implemented in the software package Mathematica is used to compute the natural frequencies of vibration for a few paired combinations of clamped, pinned and free end conditions of the beam. Also, the variation of the natural frequencies of vibration with respect to variations in the rotational speed, hub radius, taper ratio and the slenderness ratio is studied. The results obtained from the Bresse-Rayleigh theory are compared with results obtained from the Bernoulli-Euler and Timoshenko theories to demonstrate the accuracy and relevance of their application.

Free-Vibration Analysis of Compressed Clamped Circular Plates

1995 ◽  
Vol 121 (12) ◽  
pp. 1372-1376 ◽  
Author(s):  
You-He Zhou ◽  
Xiao-Jing Zheng ◽  
Issam E. Harik
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Circular Plates

scholarly journals Green’s function approach to frequency analysis of thin circular plates

2016 ◽  
Vol 64 (1) ◽  
pp. 181-188
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Influence Function ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Circular Plates ◽  
Natural Modes ◽  
Good Agreement ◽  
Analytical Frequency

Abstract The free vibration analysis of homogeneous and isotropic circular thin plates by using the Green’s functions is considered. The formulae for construction of the influence function for all nodal diameters are presented in a closed form. The limited independent solutions of differential Euler equations were expanded in the Neumann power series using the method of successive approximation. This approach allows to obtain the analytical frequency equations as power series rapidly convergent to exact eigenvalues for different number of nodal diameters. The first ten dimensionless frequencies for eight different natural modes of circular plates are calculated. A part of obtained results have not been presented yet in open literature for thin circular plates. The results of investigation are in good agreement with selected results obtained by other methods presented in literature.

Free vibration analysis of symmetrically laminated composite circular plates with curvilinear fibers

2017 ◽  
Vol 24 (1) ◽  
pp. 111-121 ◽  
Author(s):  
Ahmed Guenanou ◽  
Abderrahim Houmat
Keyword(s):  
Free Vibration ◽  
Fiber Orientation ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Published Data ◽  
Circular Plates ◽  
Simply Supported ◽  
Curvilinear Fibers

AbstractThe free vibration analysis of symmetrically laminated composite circular plates with curvilinear fibers is performed using the first-order shear deformation theory along with a curved hierarchical square finite element. The blending function method is used to describe accurately the geometry of the circular plate. The hierarchical shape functions are constructed from Legendre orthogonal polynomials. The element stiffness and mass matrices are integrated numerically by means of the Gauss-Legendre quadrature. The equations of motion are derived using Lagrange’s method. Results for the fundamental frequency are obtained for clamped and soft simply supported laminated composite circular plates with E-glass, graphite, and boron curvilinear fibers in epoxy matrices. The element is validated by means of the convergence test and comparison with published data for isotropic and laminated composite circular plates with rectilinear fibers. Contour plots of frequency as a function of fiber orientation angles for laminated composite circular plates with curvilinear fibers are presented. The fiber material and boundary conditions are shown to influence the distribution of frequency throughout the design space. Frequency curves as a function of fiber orientation angles for the first five modes of laminated composite circular plates with curvilinear fibers are also presented. They reveal that none of the first five modes of clamped and soft simply supported laminates is affected by crossing but modes 3 and 4 of clamped graphite/epoxy and boron/epoxy laminates are affected by veering.

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