Structural dynamics

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

• Static Analysis:
  • Definition: Static analysis involves examining the code without executing it to identify defects and vulnerabilities.
  • Process:
    • Performed after coding and before executing unit tests.
    • Detects possible defects early, before running the program.
    • Can be automated (machine-based) or manual (peer code review).
  • Advantages:
    • Finds issues before integration and further testing.
    • Detects unreachable code, variable misuse, and adherence to coding standards.
  • Limitations:
    • Time-consuming if done manually.
    • Automated tools may produce false positives/negatives.
• Dynamic Analysis:
  • Definition: Based on system execution, often using tools.
  • Process:
    • Analyzes code during runtime.
    • Considers actual program execution.
    • Useful for critical systems.
  • Advantages:
    • Realistic results compared to static analysis.
    • Captures system behavior under dynamic conditions.
  • Limitations:
    • Requires recorded ground motion data (accelerometers).
    • More complex than static analysis.

2. Explain the following with relevant force-displacement graph

• Elastic behavior

In elastic behaviour, the material returns to its original shape after the applied force is removed. The force - displacement graph for elastic behaviour is linear, shows proportinal relationaship between force and displacement

• Inelastic behavior

This behaviour involves permanent deformation even after the removal of the load applied .The force - displacement graph for Inelastic behaviour might exhibit non linear characteristic,indicating plastic deformation or a damage

• Plastic behavior

Plastic behaviour occurs when the material undergoes permanent deformation without fracture . The force - displacement graph for plastic behaviour shows a plateau region where the material deforms without an increase in force

• Non-linear Inelastic behavior

This behaviour includes a combination of non-linear and inelastic responses, often seen in materials like concrete and metal under sereve loading conditions. The force-displacement graph for non-linear inelastic brhaviour may show irregular patterns and fluctions

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

Mass (M) :

Reprensents the inertia of a system ,i.e., its resistance to acceleration.In the equation of motion (F=ma ) Mass(m),signifies the mass of the object being accelerated

Stiffness(K) :

Reprensents the rigidity of a system its resistance to deformation. In the equation of motion (F= Kx) , stiffness(K) indicates the force required to deform the system by certain displacement (X)

Damping(C):

Represents the dissipation of energy in the system Its resistance to motion . In the equation of motion (F= CV) , damping (C) denotes the damping coefficients, which determines how quickly oscillations in the system are damped out

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

Natural Period(Tn) :

It is the time taken for a structure to complete one full cycle of vibraton in freee vibration,i.e, without any external force . It is inversely proportional to the natural frequency and is given by Tn = 1/f , Where Tn is the natural period and f is the natural frequency.

5. Explain in detail about Response spectrum & its Graph

Response specturm :

It is graphical representation of the maximum response of a structure to a range of harmonic loading frequencies. it provides a convenient way to visualize how a structure will respond to different types of ground motion.

Graph :

The response specturm graph typically shows the maximum response (displacement,velocity or accleration) of the structure plotted against the frequency of the input motion . it helps engineers understand how the structure will behave under various seismic or dynamic forces,aiding in the design of structure to withstand such loads .