Earthquake Engineering - Vol 1 | 9. Impulse and Response to Unit Impulse by Abraham | Learn Smarter
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9. Impulse and Response to Unit Impulse

Understanding the response of structures to impulsive forces is crucial in Earthquake Engineering, particularly in predicting behaviors during earthquakes. This chapter examines impulse forces, the characteristics of the unit impulse function, and how linear time-invariant systems respond to these inputs. The impulse response function is a vital tool in dynamic analysis and structural vibration studies.

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Sections

  • 9

    Impulse And Response To Unit Impulse

    This section covers the concept of impulse forces, their mathematical representation, and how structures respond to unit impulses, emphasizing the importance of impulse response in understanding structural dynamics.

    Learning Practice

  • 9.1

    Impulse Force And Its Mathematical Representation

    This section covers the concept of impulse forces, their mathematical representation using the Dirac delta function, and the properties relevant to dynamic systems.

    Learning Practice

  • 9.2

    Equation Of Motion For Single Degree Of Freedom (Sdof) System

    This section introduces the equation of motion for a single degree of freedom (SDOF) system subjected to an external force, specifically an impulse.

    Learning Practice

  • 9.3

    Free Vibration Response Of Undamped Sdof System To Unit Impulse

    This section discusses the free vibration response of an undamped Single Degree of Freedom (SDOF) system when subjected to a unit impulse.

    Learning Practice

  • 9.4

    Response Of Damped Sdof System To Unit Impulse

    This section discusses how a damped single degree of freedom (SDOF) system responds to a unit impulse, highlighting the effects of damping on the system's dynamic behavior.

    Learning Practice

  • 9.5

    Unit Impulse Response Function (Green’s Function)

    This section introduces the impulse response function, also known as Green’s function, which describes a system's response to a unit impulse input within linear time-invariant systems.

    Learning Practice

  • 9.6

    Physical Interpretation In Earthquake Engineering

    This section explores how ground accelerations during earthquakes can be treated as impulse-like forces, emphasizing the importance of the impulse response function in predicting structural behavior.

    Learning Practice

  • 9.7

    Numerical Example

    This section presents a numerical example illustrating the calculation of the impulse response function for a damped single degree of freedom system.

    Learning Practice

  • 9.8

    Applications In System Identification And Seismic Analysis

    Impulse response functions are vital in system identification and seismic analysis to determine system parameters and evaluate structural performance during seismic events.

    Learning Practice

  • 9.9

    Convolution Integral And General Force Response

    The section discusses how the response of a linear time-invariant (LTI) system subjected to a general force can be computed using the convolution integral with the impulse response function.

    Learning Practice

  • 9.10

    Graphical Interpretation Of Impulse Response

    This section discusses the graphical interpretation of impulse response functions in dynamic systems, especially in the context of earthquake engineering.

    Learning Practice

  • 9.11

    Frequency Domain Representation Of Impulse Response

    This section discusses the frequency domain representation of impulse response through Fourier Transform, highlighting its relevance in earthquake engineering.

    Learning Practice

  • 9.12

    Importance In Seismic Design And Analysis

    This section highlights the critical role of impulse response analysis in structural earthquake engineering, focusing on its applications in time-history analysis, seismic hazard modeling, and system design.

    Learning Practice

  • 9.13

    Experimental Determination Of Impulse Response

    This section explains how the impulse response can be measured experimentally through various methods such as impact hammer tests, shaker systems, and laser vibrometry.

    Learning Practice

  • 9.14

    Extension To Multi-Degree-Of-Freedom (Mdof) Systems

    This section elaborates on the analysis of Multi-Degree-of-Freedom (MDOF) systems by extending the concepts of impulse response functions and equations of motion.

    Learning Practice

  • 9.15

    Computational Approaches

    This section discusses computational methods used to solve impulse response problems in structural dynamics.

    Learning Practice

References

Chapter_9_Impuls.pdf

Class Notes

Memorization

What we have learnt

  • Impulse forces are modeled ...
  • The response of linear syst...
  • Applications of impulse res...

Final Test

Revision Tests