Structural dynamics

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

Static Analysis	Dynamic Analysis
Static analysis time invariant analysis of forces like Stress, strain and displacement etc.	Dynamic analysis is time dependent analysis
The results are a consequence of the applied constraints and loads, for example, bearings, gravity, forces, etc.	Inertia and damping forces taken into account
Static loads applied on structure slowy	Dynamic Loads applied on the structures Suddenly
Example- Dead Load , Live load	Example- Earthquake load , Wind Load
Static analysis done with minimum three degree of freedom	Dynamic analysis of structure done with single degree of freedom
Static analysis done where the structure deformations behave linear	Dynamic analysis done where structure behaves non-linear deformations

2. Explain the following with relevant force-displacement graph (40 marks)

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

1.Elastic Behaviour-Ability of deformed matrrial body to return to its original shape and size when force causing the deformation are removed Ex. Rubber band. spring. etc.

2.Inelastic Behaviour-Deformatoion material that does not disappear on removal of force that produced it Ex. wood, fabric, etc.

3.Plastic Behaviour-The material deforms irreversibly and does not return to its original shape and size even whe load is removed.

4.Non-linear elastic behaviour-Materials have elastic behaviour usually only upto a certain point after that deformation are plastic and relation in this is not linaer i.e. non linear elsatic behaviour.

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

Mass:

Newton's second law, which states that the force F acting on a body is equal to the mass m of the body multiplied by the acceleration a of its Centre of mass, F = ma, is the basic equation of motion in classical mechanics.

Mass is always constant for a body. One way to calculate mass: Mass = volume × density. Weight is the measure of the gravitational force acting on a mass.

Stiffness component:

The frame 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.

Damping component:

The frame with its damping property with no stiffness or mass. The external force on the damping component is related to velocity by

fd=cv

Where,

fD-Damping force

c-viscous damping coeff

u-velocity

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

Natural Period(Tn):-Time required for undamped system to complete one cycle of free vibration. Unit is in Seconds

Tn=2π/Wn

Natural Frequency(f):-Number of cycle (or one complete revolution) executed by system in one second. Unit is in hertz

f=1/Tn

Natural vibration properties Wn, Tn and f are depend only on mass and stiffness of structure.

5. Explain in detail about Response spectrum & its Graph

The typical earthquake ground motion response spectrum represents an envelope of the peak responses of many single-degree-of-freedom (SDOF) systems with different periods. The acceleration response spectrum of a ground motion is a relationship between the natural period of vibration of a sdof system and the maximum absolute acceleration that it experiences under the ground motion. Similarly, a displacement response spectrum typically represents the peak displacement, relative to the ground, of many sdof systems with different periods. Hence, the construction of a response spectrum involves the analysis of many different sdof systems. The value of each point on the spectrum is the peak response of a single degree of freedom system of a given period.