Structural dynamics

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

Ans.-

AIM-: Differentiate Static analysis and Dynamic analysis

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

In dynamic analysis we assume the mass is concentrated at a point with single degree of freedom as see in below picture

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

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

1. Elastic Behaviour - Ability of deformed material body to return to its original shape and size when force causing the deformation are removed

Example: Rubber band. spring. etc.

2. Inelastic Behaviour - Deformatoion material that does not disappear on removal of force that produced it

Example : wood, fabric,etc.

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

4. Non-linear elastic behaviour-Materials have elastic behaviour usually only up to a certain point after that deformation are plastic and relation in this is not linear i.e. nonlinear elastic behaviour.

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

AIM-: Explain Mass, Stiffness & Damping components in the equation of motion

Single degree of freedom system can be viewed as combination of three pure independent system

The stiffness component-; the frame without damping or mass, the external forces fs on the stiffness component is related to displacement by u by fs= ku if the system is linearly elastic

The Damping component -: the frame with its damping property 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 acceleration by fi=mu

Mu+fd+fs = pt rightarrow mddot u+cdot u`+ku = pt

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

AIM-Provide relationship between Natural period (Tn) & Natural frequency (f) and provide their definitions

Natural period (tn)-The time required for the undamped system to complete one cycle of free vibration natural period of vibration of the system, which we denote as Tn in units of sec It is related to the natural circular frequency of vibration, ωn in units of radians per second

Tn=2π/ωn

A system executes 1/Tn cycles in 1 sec. This natural cyclic frequency of vibration is denoted by

fn=1/Tn

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

Aim- Explain in detail about Response spectrum & its Graph

Response spectrum analysis is a method to estimate the structural response to short, nondeterministic, transient dynamic events. Examples of such events are earthquakes and shocks. Since the exact time history of the load is not known, it is difficult to perform a time-dependent analysis.

A response spectrum is a function of frequency or period, showing the peak response of a simple harmonic oscillator that is subjected to a transient event. The response spectrum is a function of the natural frequency of the oscillator and of its damping. Thus, it is not a direct representation of the frequency content of the excitation (as in a Fourier transform), but rather of the effect that the signal has on a postulated system with a single degree of freedom (SDOF)

Example The El Centro Earthquake

One of the most studied earthquake recordings is that of the "El Centro" earthquake on May 18, 1940. Recorded signals (with some filtering) are shown below