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Topic:

STRUCTURAL DYNAMICS
AND EARTHQUKE ENGINEERING
UNIT I
THEORY OF VIBRATIONS
UNIT-I
1. 1

CONTENTS
No
TITLE
TECHNICAL TERMS
1.1
INTRODUCTION TO STRUCTURAL DYNAMICS
1.2
IMPORTANCE OF STRUCTURAL DYNAMICS
1.3
TYPES AND SOURCES OF DYNAMIC LOADS
1.4
DISTINGUISHING FEATURES OF A DYNAMIC
PROBLEMS
1.5
METHODOLOGY FOR DYNAMIC ANALYSIS
1.6
TYPES OF STRUCTURAL VIBRATION
QUESTION BANK
UNIT-I
1. 2

TECHNICAL TERMS
1.
Mass: Mass is obtained by dividing the weight on body by the acceleration of gravity.
Unit of mass is given in kilograms (kgs)
2.
Stiffness: It is defined as the force required producing unit deformation. It is an elastic
property that describes the level of resisting force that results when a body undergoes change
in length.
3.
Natural Period: It is defined as the time required to complete one cycle of free
vibration
4.
Natural frequency: When no external force acts on the system after giving it an
initial displacement, the body vibrates. These vibrations are called free vibration and their
frequency is natural frequency
5.
Simple Harmonic Motion: The motion of a body to and fro about fixed point is
called simple harmonic motion (SHM)
6.
Amplitude: The maximum displacement or deformation of a vibrating system from
its mean position is called as amplitude.
7.
Mode of Vibration: The structure possesses as many natural frequencies as it has the
degree of freedom. For each frequency the structure has its own way of vibration is known as
mode of vibration
8.
Fundamental mode of vibration: The fundamental mode of vibration of a structure
is the mode having the lowest natural frequency.
9.
Resonance: When the frequency of external force is equal to or matches with one of
the natural frequencies of the vibrating system, the amplitude of vibration becomes
excessively large. This phenomenon is called resonance.
10.
Free Vibration: Free vibration is a vibration in which energy is neither added to nor
removed from the vibrating system. It will just keep vibrating forever at the same amplitude.
Except from some superconducting electronic oscillators, or possibly the motion of an
electron in its orbit about an atomic nucleus, there are no free vibrations in nature. They are
all damped to some extent.
11.
Forced Vibration: Forced vibration is one in which energy is added to the vibrating
system, as for example in a clockwork mechanism where the energy stored in a spring
is
UNIT-I
transferred
a
bit
at
a
time
to
the
vibrating
element.
1. 3

I
BASICS OF STRUCTURAL DYNAMICS
1.1 Introduction to Structural Dynamics
Structural analysis is mainly concerned with finding out the behaviour of a structure when
subjected to some action. This action can be in the form of load due to the weight of things
such as people, furniture, wind, snow, etc. or some other kind of excitation such as an
earthquake, shaking of the ground due to a blast nearby, etc. In essence all these loads are
dynamic, including the self-weight of the structure because at some point in time these loads
were not there. The distinction is made between the dynamic and the static analysis on the
basis of whether the applied action has enough acceleration in comparison to the structure's
natural frequency. If a load is applied sufficiently slowly, the inertia forces (Newton's second
law of motion) can be ignored and the analysis can be simplified as static analysis. Structural
dynamics, therefore, is a type of structural analysis which covers the behaviour of structures
subjected to dynamic (actions having high acceleration) loading. Dynamic loads include
people, wind, waves, traffic, earthquakes, and blasts. Any structure can be subject to dynamic
loading. Dynamic analysis can be used to find dynamic displacements, time history, and
modal analysis.
A dynamic analysis is also related to the inertia forces developed by a structure when it is
excited by means of dynamic loads applied suddenly (e.g., wind blasts, explosion,
earthquake).
A static load is one which varies very slowly. A dynamic load is one which changes with time
fairly quickly in comparison to the structure's natural frequency. If it changes slowly, the
structure's response may be determined with static analysis, but if it varies quickly (relative to
the structure's ability to respond), the response must be determined with a dynamic analysis.
Dynamic analysis for simple structures can be carried out manually, but for complex
structures finite element analysis can be used to calculate the mode shapes and frequencies.
UNIT-I
1. 4

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