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Blackboard Ideas Color - 55418

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Summary of the study
Vibration analysis of rectangular plates
Using finite element method

FE Analysis of Plate Using ANSYS
What type of element is employed to model the structure?
Project Outline
Fe analysis of rectangular plate using ansys
Comparison of the results
Fe analysis of rectangular plate using matlab

questions?
How to find mass and stiffness matrices
find natural frequencies of the plate
&
FINITE ELEMENT METHOD
Natural frequency:

If a system, after an initial disturbance, is left to vibrate on its own, the frequency with which it oscillates without external forces is known as its natural frequency
Preparation of model:
Drawing of plate
Defining material property
Meshing the plate
Modal analysis using ANSYS
Applying boundary condition
Comparison of Results
Introduction
Vibration Parameters
FE Model in MATLAb
Obtaining Natural Frequencies and Mode Shapes
VIBRATION ANALYSIS OF PLATE USING FE METHOD
Why Vibration analysis of structures is important?
What Plate Theory?
What are the results extracted from matlab?
Natural Frequencies Obtained by ANSYS
Comparison of the Results
What is an accurate and robust technique in vibration analysis of rectangular plates?
Elementary Parts of Vibrating Systems:
Mass
Spring or elasticity
Damper

What is the most important vibration parameter of a structure?
Classical Plate Theory
The following kinematic assumptions that are made in the theory:
• Straight lines normal to the mid-surface remain straight after deformation
• Straight lines normal to the mid-surface remain normal to the mid-surface after deformation
• The thickness of the plate does not change during a deformation

Displacement Field Based on Classical Plate Theory:
Strains Based on Classical Plate Theory:
Potential and Kinetic Energy of the Plate Element
Equivalent Potential and Kinetic Energy
Assembilng Elemental Mass and Stiffness Matrices
Mode shapes
Natural frequencies
First mode: 17.96 Hz
Second mode: 42.91 Hz
Third mode: 110.02 Hz
Fourth mode: 134.43 Hz
Case Study:
A rectangular cantilevered steel plate with length and thickness of 1 m and 0.02 m, respectively
Mode shapes obtaiend by ANSYS
Number of Element = 20000
Number of Element = 100
There is an excellent agreement between the results obtained using MATLAB and ANSYS
The natural frequencies obtained using MATLAB
The natural frequencies obtained using ANSYS
First: 17.046 Hz
Second:
Third: 104.27 Hz
Fourth: 131.97 Hz
First: 17.96 Hz
Second: 42.91 Hz
Third: 110.02 Hz
Fourth: 134.43 Hz
FE Model in ANSYS
Comparison of the Results
41.387 Hz
Prepared by:
Hamed Eshaghi (40027040)

Reference:
S. S. Bhavikatti, Finite element analysis. new dehli: new age international, 2005.
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