Structural dynamics
1. Differentiate Static analysis and Dynamic analysis with proper representing pictures (30 marks)
ans:-
| Static Analysis | Dynamic Analysis |
| Load is Applied slowly | Load and vibrations are applied very rapidly |
| Load is not variable with time and is neglected | Load is variable with time |
| Motion of the structure can be disregarded | Motion of the structure cannot be disregarded |
| There is no inertia effect | Inertia effect is considered |
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2. Explain the following with relevant force-displacement graph (40 marks)
- Elastic behavior : - It is the ability of the material to regain its original state when the load acting on it is removed. The limiting load, above which the property loses its elasticity is called elastic limit. It occurs when a weaker force, lesser than the object's elastic limit are exerted. Hence, a material or an object undergoes elastic deformity before plastic deformity.
- Inelastic behavior- It is the behavior of non elastical materials, which may or may not regain its original shape when applied force is removed. They don't show a fixed trend of deformation vs applid force or they may not deform at all or the deformation observed is not completely recoverable.
- Plastic behavior: - When the elastic limit is completely exceeded ,the material will experience a permanent deformation even after the load is removed and it is said to have undergone plastic deformation.
- Non-linear Inelastic behavior- At large deformations the relationship between force and displacement becomes non linear and inelastic. A non liniear elastic is where the part return to a zero strain when the load is removed.
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3. Explain Mass, Stiffness & Damping components in the equation of motion (30 marks)
ans:
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 = mu
Stiffness Component:
It is the frame without damping or mass. The external force fs on the stiffness component is related to the displacement u by fs = ku, if the system is linearly elastic.
Damping Component:
It is the frame with its damping property but no stiffness or mass. The external force on the damping component is related to the velocity by fd = cv
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4. Provide relationship between Natural period (Tn) & Natural frequency (f) and provide their definitions (25 marks)
ans:
Natural period of Vibration(Tn)
It is the time required to undampen system to complete one cycle of free vibrations. It is measured in seconds. It is an inherent property of building controlled by its mass m and stiffness k
Tn = 2`pi`/wn
Natural frequency(f)
The number of cycle or one complete revolution executed by the system in one second is natural frequence. Hertz is its unit. It is the reciprocal of natural period of vibrations
f = 1/Tn
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5. Explain in detail about Response spectrum & its Graph (25 marks)
ans:
A plot of peak value of a respomse quantity ( u,v, a) as a function of the natural vibration period of the system is called the Response spectrum for that quantity. It is of three types.
1. Deformation Response Spectrum:
It is a plot of peak value of u agaist Tn for a fixed damping ratio
2.Relative Velocity Response Spectrum
It is the plot of peak value of u against Tn
3. Acceleration Response Spectrum
It is the plot of peak u^T
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