In this lecture, i have discussed about Free Vibration Analysis, Lumped mass approach and Degree of freedom
Free Vibration Analysis
If a structure is displaced by considerable amount and is then released suddenly, it starts vibration Without the action of any external forces except the first excitation. The study of response of a structure when it is vibrating without any external force is called free vibration analysis of structure.
This analysis gives information about natural time period, frequency, resonance and damping, etc.
Lumped mass
During an earthquake the earth only produces acceleration in the structure.
The force is produced when the mass of structure undergoes acceleration, which is called inertial Force.
F = ma (Newton’s 2nd Law)
In case of buildings, most of the mass is concentrated at the floor level.
Hence, for convenience in analysis, it is assumed that whole of the mass Is present at a particular height (at a point), known as lumped mass.
Degree of freedom
The number of displacement components that must be considered in order to represent the effects of all significant inertial forces of a structure are termed as the number of dynamics degree of freedom.
Most commonly only one degree of freedom, that is horizontal of the mass, is considered for each lumped mass.
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Негізгі бет Lecture 3 Free Vibration Analysis, Examples [ Structural Mechanics ]
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