Modal Analysis Of Circular Plates With A Free Edge And Three Simple Interior Supports

1993 ◽  
Vol 160 (2) ◽  
pp. 289-300 ◽  
Author(s):  
R.A. LeClair
Keyword(s):  
Modal Analysis ◽  
Free Edge ◽  
Circular Plates

scholarly journals Modal Analysis of Circular Symmetrical Plates by Means of Generalized Finite Difference Method

2019 ◽  
Vol 17 (3) ◽  
pp. 88-98
Author(s):  
A. E. Mansour
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Modal Analysis ◽  
Difference Method ◽  
Numerical Solutions ◽  
Analysis Procedure ◽  
Machine Design ◽  
Polar Coordinates ◽  
Circular Plates ◽  
Classical Formulation

In this paper, a simplified modal analysis procedure of circular plates procedures (on polar domains) through generalized (modernized) finite difference method (abbreviated next as – FDM) is developed.Generally, circular plates are widely used for a plenty of modern civilian and industrial utilities, machine design and many other purposes. They form a spectrum of elements starting with trains’ bogies along with engine pistons, dampers and up to slabs and roofs over circular-shaped buildings, train stationsand other transportation facilities. Nowadays, FDM predominates the numerical solutions of partial differential equations (abbreviated next as – PDE) not less than the method of finite elements (abbreviated next as – FEM). This is wide-famous mathematical-discretization method that is economic to compute and simple to code, less regarding to computation tools in hands and how powerful/less powerful they are, since it bases on replacing each derivative by a difference algebraic quotient in a classical formulation. In a sense, a finite difference formulation offers a more direct approach to the numerical solution of the PDE especially in polar coordinates domain problems considering curvilinear dimensions that even FEM does not.The generalized approach of FDM considers many parameters less regarded by the classical one.  Consequently, the use of classical approach negatively affects the accuracy of calculation (convergence to the exact solution values) and the tendency of results, the thing been healed by the generalized approach.

scholarly journals Vibration analysis of irregular-shaped plates on simple supports

2021 ◽  
Vol 477 (2252) ◽  
pp. 20210184
Author(s):  
Abhijit Ghosh ◽  
Anirvan DasGupta
Keyword(s):  
Boundary Conditions ◽  
Modal Analysis ◽  
Circular Plate ◽  
Solution Structure ◽  
Circular Plates ◽  
Perturbative Approach ◽  
Irregular Boundary ◽  
Generalized Fourier Series ◽  
Perturbative Solution ◽  
Smallness Parameter

In this work, we propose a general perturbative approach for modal analysis of irregular-shaped plates of uniform thickness with uniform boundary conditions. Given a plate of irregular boundary, first, a uniform circular plate of identical thickness and area, centred at the centroid, is determined. The irregular boundary is then treated as a perturbation with a suitable smallness parameter, and is expressed as a generalized Fourier series. The frequency parameter, shape function and boundary conditions are then perturbed in terms of the smallness parameter. The homogeneous zeroth-order equation corresponds to the circular plate, which is exactly solvable. We show that the inhomogeneous equations in the higher orders can also be solved exactly using a particular solution structure. We can then construct the exact perturbative solution up to any order. The proposed method is demonstrated through the modal analysis of simply supported super-circular plates. The results are validated using the numerical results obtained from ANSYS ® , which are an excellent match. Interestingly, the supposedly degenerate modes with an even number of nodal diameters of super-circular plates are found to split naturally.

scholarly journals ASYMMETRIC NON-LINEAR FORCED VIBRATIONS OF FREE-EDGE CIRCULAR PLATES. PART 1: THEORY

2002 ◽  
Vol 258 (4) ◽  
pp. 649-676 ◽  
Author(s):  
C. TOUZÉ ◽  
O. THOMAS ◽  
A. CHAIGNE
Keyword(s):  
Free Edge ◽  
Forced Vibrations ◽  
Circular Plates ◽  
Non Linear

scholarly journals Effect of Imperfections and Damping on the Type of Nonlinearity of Circular Plates and Shallow Spherical Shells

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Cyril Touzé ◽  
Cédric Camier ◽  
Gaël Favraud ◽  
Olivier Thomas
Keyword(s):  
Normal Modes ◽  
Free Edge ◽  
Nonlinear Normal Modes ◽  
Circular Plates ◽  
Spherical Shells ◽  
Geometric Imperfections ◽  
Softening Behaviour ◽  
Nonlinear Normal ◽  
Deflection Theory ◽  
Large Deflection Theory

The effect of geometric imperfections and viscous damping on the type of nonlinearity (i.e., the hardening or softening behaviour) of circular plates and shallow spherical shells with free edge is here investigated. The Von Kármán large-deflection theory is used to derive the continuous models. Then, nonlinear normal modes (NNMs) are used for predicting with accuracy the coefficient, the sign of which determines the hardening or softening behaviour of the structure. The effect of geometric imperfections, unavoidable in real systems, is studied by adding a static initial component in the deflection of a circular plate. Axisymmetric as well as asymmetric imperfections are investigated, and their effect on the type of nonlinearity of the modes of an imperfect plate is documented. Transitions from hardening to softening behaviour are predicted quantitatively for imperfections having the shapes of eigenmodes of a perfect plate. The role of 2:1 internal resonance in this process is underlined. When damping is included in the calculation, it is found that the softening behaviour is generally favoured, but its effect remains limited.

scholarly journals Comparative study for modal analysis of circular plates with various cutouts and end conditions

2019 ◽  
Vol 29 ◽  
pp. 87-93 ◽  
Author(s):  
Vedanth Bhatnagar ◽  
Pavan Kishore Mamaduri ◽  
Sreenivasulu B
Keyword(s):  
Comparative Study ◽  
Modal Analysis ◽  
Circular Plates ◽  
End Conditions
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