Structural dynamics

Q.1. Differentiate Static analysis and Dynamic analysis with proper representing pictures.

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STATIC ANALYSIS	DYNAMIC ANALYSIS
1. Load is not variable with time and neglected due to slow applying of load.	1. Load is variable with time due to fast applying of load and vibration.
2. Motion of the structure can be disregarded.	2. Motion can not be disregarded (can't be considered as static).
3. There is no necessity to count Inertia and damping forces in case of static analysis, but the elastic force should be accounted.	3. Inertia and damping forces should be accounted for the calculation of dynamic analysis.
4. There is no inertia effect on static analysis.	4. Inertia effect is considered in dynamic analysis.

Inertia effects-

Q.2. Explain the following with relevant force-displacement graph.

1. Elastic behavior
2. Inelastic behavior
3. Plastic behavior
4. Non-linear Inelastic behavior

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1. Elastic Behavior:-

Elastic behavior is the property of the material upto which the material can retain it's shape. From the aforementioned graph it is clearly mentioned that upto a certain point from "O" the graph is linear and shown its elastic properties.

2. Inelastic Behavior:-

Inelastic behavior is the property of the material when the material can't retain it's previous shape after a certain deformation. In the aforementioned graph inelastic behavior has been shown in the upper shape of the curve upto point "a".

3. Plastic Behavior:-

Plastic behavior occurs when the material completely lost it's ductility. In the aforementioned graph plastic behavior occurs during unloading after point "a".

4. Non-linear Inelastic Behavior:-

Non-linear inelastic behavior occurs after the line from "O" tends to bend towards point"a".

Q.3. Explain Mass, Stiffness & Damping components in the equation of motion.

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• The Stiffness Component:- The frame is without damping or mass. The external force fs on the stiffness component is related to displacement u by fs= Ku, if the system is linearly elastic.
• The Damping Component:- The frame with its damping properties but no stiffness or mass. The external force on the damping component is related to velocity by fd=CV.
• The Mass Component:- The roof mass without the stiffness or damping of the frame. The external force fi on the mass component is related to the acceleration by fi=m(u^double dot).

Q.4. Provide relationship between Natural period (Tn) & Natural frequency (f) and provide their definitions.

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• Natural Period of vibration (Tn):- The time required for the undamped system to complete one cycle of free vibration (unit is seconds)
• It is related to the natural circular frequency of vibration, Wn, in units of radians per second.

Tn= (2`π`/Wn)

• Natural cyclic frequency (f):- The number of cycles (or one complete revolution) executed by system in one second (unit is hertz)

fn =(1/Tn)

Therefore, the relation between natural period of vibration of the system(Tn) and natural frequency(`fn`)

is fn=(1/Tn)

Q.5. Explain in detail about Response spectrum & its Graph.

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