1.3 Comparison Between Static and Dynamic Analysis
5
Fig. 1.2 Application of
D’Alembert’s principle
It is the acceleration of the body which converts the problem into a dynamic one.
1.4 D’alembert’s Principle
The above example of the accelerating body can be considered as an equilibrium
problem. The state of equilibrium is referred to as dynamic equilibrium. The principle
that is adopted for its solution is known as D’Alembert’s principle.
Equation (1.1) is rewritten in the following form
P−R−ma = 0
( 1 . 2 )
Equation (1.2) can be conceived as an equation of equilibrium, i.e.
F x = 0
which means that in addition to the real forces acting on the body, a fictitious force-ma
acting opposite to the line and direction of motion is considered (Fig. 1.2).
For the solution of problems of dynamics, the inertia force, which is mass times
the acceleration opposite to the direction of motion, is to be incorporated in the
freebody diagram in addition to all impressed forces. This is known as D’Alembert’s
principle.
Structural dynamics and machine vibrations have their basic input to the
fundamental theory of vibration. To start with, let us look into some basic definitions.
1.5 Some Basic Definitions
When an elastic system is acted upon by an externally applied disturbance, it will
respond by oscillating to and fro.
5
Fig. 1.2 Application of
D’Alembert’s principle
It is the acceleration of the body which converts the problem into a dynamic one.
1.4 D’alembert’s Principle
The above example of the accelerating body can be considered as an equilibrium
problem. The state of equilibrium is referred to as dynamic equilibrium. The principle
that is adopted for its solution is known as D’Alembert’s principle.
Equation (1.1) is rewritten in the following form
P−R−ma = 0
( 1 . 2 )
Equation (1.2) can be conceived as an equation of equilibrium, i.e.
F x = 0
which means that in addition to the real forces acting on the body, a fictitious force-ma
acting opposite to the line and direction of motion is considered (Fig. 1.2).
For the solution of problems of dynamics, the inertia force, which is mass times
the acceleration opposite to the direction of motion, is to be incorporated in the
freebody diagram in addition to all impressed forces. This is known as D’Alembert’s
principle.
Structural dynamics and machine vibrations have their basic input to the
fundamental theory of vibration. To start with, let us look into some basic definitions.
1.5 Some Basic Definitions
When an elastic system is acted upon by an externally applied disturbance, it will
respond by oscillating to and fro.