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Free Vibration Engineering Report

1346 Words6 Pages

Name: Chin-Chin M. Buquis
Section: ME-5204
ME 564 – Vibration Engineering
Technical Report No. 2
Free Vibration of Single-Degree-of-Freedom System

Concepts from vibrations
NEWTON’S LAWS

First law:
If there are no forces acting upon a particle, then the particle will move in a straight line with constant velocity.

Second law:
A particle acted upon by a force moves so that the force vector is equal to the time rate of change of the linear momentum vector.

Third law:
When two particles exert forces upon one another, the forces lie along the line joining the particles and the corresponding force vectors are the negative of each other.

Free Vibration

A single degree of freedom system requires only one coordinate to describe its position at any instant of …show more content…

To define the displacement of the mass as a function of time, u(t), subject to the initial conditions of the system.

One approach to solving this partial differential equation is to assume a solution of the form:

Take the second derivative with respect to time of:

Substitute the given equation: which can be simplify as:

Solving for r makes two possible root of an imaginary number:

Where i = √(-1) following the solution given:

Defining the radical term in the exponent to be the circular natural frequency of vibration of the system:

Circular frequency is related to the natural frequency by:

Obataining the natural period by:

Evaluating the coefficent in the given equation, we neet to determine the two initial condition. This causes initial displacement and velocity mass:

Substituting these equation and its first derivative we attain this equation:

Damped Free Vibration
As shown in the figure single-degree-of-freedom (SDOF) system has both a spring and dashpot If we inspect a free-body diagram of the mass we see that an supplementary force is delivered by the dashpot. The force is proportional to the velocity of the

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