Structural dynamics

1) STATIC AND DYNAMIC ANALYSIS:

Dynamic analysis is the testing and evaluation of a structure during deformation ,Static analysis is the testing of a structure during resting.The main difference between Static analysis and Dynamic analysis is time.if the load is applied slowly ,that inertia effects would not play a role ,all you nee is static analysis.Dynamic analysis handles impacts and other fast happening situations,but also vibrations

2)ELASTIC BEHAVIOUR:

it is the condition in the force displacement graph where displacement increases proportional to the force and thid forms a 45 degree inclined line in the graph.

INELASTIC BEHAVIOUR:

It is the condition where after certain point with the increasing of force the displacement will be static and this forms a straight line parallel to displacement after a certain point of force

PLASTIC BEHAVIOUR:

It is the condition after the elastic limit , the deformations are permanent ie; the structure wouldnot return to its original shape and size after releasing of force . plastic behaviour is shown by a curve from yield force to the rupture point

NON LINEAR INELASTIC BEHAVIOUR:

It is the behaviour the curve will be parabolic and displacements varies from higher to lower with increase in force in different phases

3)Equation of motion :Mu + Cu + Ku = -mug(t)

where M is the Mass and C is the damping , K is the stiffness , u is the displacement of the structure ,t is the time period ,the negative sign indicates that the moment is in opposite direction g is the center of gravity

4)Natural period and Natural frequency:

fn =1/Tn

Tn = 2 pi/Wn

Wn =(k/m)^1/2

natural period is inversely proportional to the natural frequency

5) Repose spectrum

pseudo acceleration for an SDF system

A=W^2n D = (2PHI/Tn)^2D

where A - acceleration

Wn - natural frequency

peak deformation D - u0

Tn-natural period

WITH keeping the damping ratio constant easily natural vibration system can be derived

In Deformation region spectrum ,higher the period of vibration higher will be the deformation region

In pseudo acceleration reponse spectrum for higher period of vibration lower will be the pseudo acceleration reponse