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BDA 40303
FINITE ELEMENT METHOD
WEEK 7
LABORATORY SESSIONS
By
Dr. Izzuddin Zaman
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INTRODUCTION
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There is a common mistake for users who do not have sufficient knowledge in vibrations.
Users will think the displacement results and other results generated in every mode shape are absolute values.
They will interpret and read the result as seen in the contour.
The displacements, stresses, strains calculations of every mode are based on relative or normalized values.
The mode shapes represent relative amplitudes of vibration rather than absolute displacements.
Since there are no uniquely defined forces in eigen value analysis, the displacements are arbitrary but proportional to each other to properly define the mode shape.
Solid elements should replace the shell elements. The unit natural frequency in LISA is rad/s if you want to use Hz then you should divide it by 2.
EXERCISE 1: TWO-DIMENSIONAL
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A cantilever beam as illustrated in Figure. The length of the beam
is 1.2m and cross-section 0.2m x 0.05m. The material properties of
the beam are Young’s modulus E = 200GPa, Poisson ratio = 0.3,
density = 7860 kg/m3.
Determine natural frequencies of the cantilever beam.
EXERCISE 1: TIPS FOR SOLUTION
Analysis Type >2D >Modal Vibration > Plain and Truss
Model > Global Properties – To decide how many natural frequencies of interest.
Define the material properties – use plate membrane element with thickness 0.05m.
Create the basic geometrical model 1.2m x 0.2m and do the meshing 40×4 of Quad4 elements
Define constraints
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EXERCISE 1: TIPS FOR SOLUTION
Mode 1:The first natural frequency is 190.1792 rad/s or 30.628 Hz (the calculation prediction is 28.34 Hz).
Mode 2: The second mode is at frequency of 1183.943 rad/s or 188.43 Hz.
Mode 3: The third mode is at frequency of 3282.549 rad/s or 522.434 Hz.
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EXERCISE 2: THREE-DIMENSIONAL
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A cantilever beam as illustrated in Figure. The length of the beam
is 1.2m and cross-section 0.2m x 0.05m. The material properties of
the beam are Young’s modulus E = 200GPa, Poisson ratio = 0.3,
density = 7860 kg/m3.
Determine natural frequencies of the cantilever beam.
EXERCISE 2: TIPS FOR SOLUTION
Type of Analysis - 3D > Modal Vibration and Shell and Frame
Materials>Geometry- choose None
Materials> Mechanical tab - Choose Isotropic
Create nodes from defined geometry
Chose Hex8
Elements > Refine Customs; 40, 4, 5
Constraint
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EXERCISE 2: TIPS FOR SOLUTION
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EXERCISE 3:
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A building structure as seen in module 3 exercise 4 will be analyzed its natural frequencies. In this exercise every member is divided into two elements. The roof is represented by several concentrated mass as illustrated below. The concentrated mass is 100 kg each. Find the first four natural frequencies. All supported foundations are rigidly fixed (all translations and rotations are fixed). The mass density of the materials are all 8000 kg/m3.
EXERCISE 3:
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EXERCISE 3:
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Create Nodes
EXERCISE 3:
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Create Elements
EXERCISE 3:
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Material Properties
Fixed nodes 1, 6, 7, 12, 13 and 18 at all direction
Boundary Conditions
Mass 100 kg at allocated nodes
Loadings
