Hi,
So for a report I am writing, I am carrying out a modal analysis on a circular plate. The version of Ansys I am using is 19.2 Mechanical APDL. I am provided with a formula which allowed me to calculate the natural frequency of the plate and then I calculate the solution on ansys and compare the results. However for ANSYS I obtain 5 sets of frequency values, whereas the formula for my hand calculations I only obtain the first set. I have been informed progressive hand calculations can be carried out, which would allow me to obtain progressive values. Any advice on how I can approach this and obtain more natural frequency values?
The plate is circular and is fully fixed.
Thank you
Circular plate with fixed support, you have got results through ansys and theoretical values ( formulae). Claudio Pedrazzi sir already has provided all details. Only thing you have to do is plot the mode shape through ansys and compare with theoretical mode, which gives you a comparison and validation of your model.
Dear Shahid,
use Finite element method to evaluate the natural frequency of circular plate with fixed boundary condition, which will allow you to get the natural frequencies other than fundamental frequency.
Dear Shahid,
You can use the following MATLAB code for your problem:
https://www.mathworks.com/matlabcentral/fileexchange/6474-natural-frequencies-of-a-circular-plate
Be aware, that this code is for general type of boundary conditions, i.e. elastically supported plate.
In addition to what everybody has conveyed, in extracting mode shapes you can confirm that first mode will always be bending. Then, successive modes will have bending and twisting and combination of all(something like superposition). So, even the mode shape will give you the easiest way to diagnose the analytical calculated data comparison.
Mr. Arun Patil,
I wish to clarify few things about FEM formulations. It is not necessary that first mode will be a bending always. It all depends on how one considered the dof while formulating the K and M matrix.
Dear C V C sir,
I totally agree to your point of view. In most of the industrial cases, we find a scenario one end fixed and other end free, while extracting the mode shapes (In Free-Free run) even for current problem the same case.
The natural frequencies and mode shapes of circular plates can also be determined using Galerkin variational methods with the requisite modal degrees of freedom(dofs). If five or more natural frequencies are desired, then five or more modal dofs should be used in formulating and solving the system of Galerkin variational equations.
Dear Researcher
The dynamic analysis results for natural frequencies of vibration and natural vibration modes would also depend on the theoretical framework used in modelling the circular plate. Some theoretical models such as the classical Kirchhoff- Love theory disregard shear deformation effects while some others like Mindlin, Reissner, Refined shear deformation plate theories of Shimpi, and others take account of shear deformation effects.
Approximate/ numerical methods can still be used to determine the natural frequencies of shear deformable circular plates.
Numerical methods for the dynamic analysis of circular plates include Finite Element Method, Finite Difference Method, Galerkin Method, Kantorovich method, Boundary Element Method, Collocation methods, Ritz variational method etc. The degree of freedom assumed would enable the determination of many natural frequencies if the plate and the corresponding modal shape functions.
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