what is the limitation of forced vibration
Answers
FORCE VIBRATION :-
Forced Vibrations:
Forced Vibrations:Forced vibrations are the vibrations produced in a body by applying an external periodic force having a frequency, normally different from the natural frequency of the body. ... The difference in frequencies of the external force and the natural frequency of the body. The amplitude of the applied force.
Answer:
5.4 Forced vibration of damped, single degree of freedom, linear spring mass systems.
Finally, we solve the most important vibration problems of all. In engineering practice, we are almost invariably interested in predicting the response of a structure or mechanical system to external forcing. For example, we may need to predict the response of a bridge or tall building to wind loading, earthquakes, or ground vibrations due to traffic. Another typical problem you are likely to encounter is to isolate a sensitive system from vibrations. For example, the suspension of your car is designed to isolate a sensitive system (you) from bumps in the road. Electron microscopes are another example of sensitive instruments that must be isolated from vibrations. Electron microscopes are designed to resolve features a few nanometers in size. If the specimen vibrates with amplitude of only a few nanometers, it will be impossible to see! Great care is taken to isolate this kind of instrument from vibrations. That is one reason they are almost always in the basement of a building: the basement vibrates much less than the floors above.
We will again use a spring-mass system as a model of a real engineering system. As before, the spring-mass system can be thought of as representing a single mode of vibration in a real system, whose natural frequency and damping coefficient coincide with that of our spring-mass system.
We will consider three types of forcing applied to the spring-mass system, as shown below:
External Forcing models the behavior of a system which has a time varying force acting on it. An example might be an offshore structure subjected to wave loading.
Base Excitation models the behavior of a vibration isolation system. The base of the spring is given a prescribed motion, causing the mass to vibrate. This system can be used to model a vehicle suspension system, or the earthquake response of a structure.
Rotor Excitation models the effect of a rotating machine mounted on a flexible floor. The crank with small mass rotates at constant angular velocity, causing the mass m to vibrate.
Of course, vibrating systems can be excited in other ways as well, but the equations of motion will always reduce to one of the three cases we consider here.
Notice that in each case, we will restrict our analysis to harmonic excitation. For example, the external force applied to the first system is given by
The force varies harmonically, with amplitude and frequency . Similarly, the base motion for the second system is
and the distance between the small mass and the large mass m for the third system has the same form.
We assume that at time t=0, the initial position and velocity of each system is
In each case, we wish to calculate the displacement of the mass x from its static equilibrium configuration, as a function of time t. It is of particular interest to determine the influence of forcing amplitude and frequency on the motion of the mass.
We follow the same approach to analyze each system: we set up, and solve the equation of motion.