Damped Free Vibration Assignment

CENTRAL QUEENSLAND UNIVERSITY
AUSTRALIA
SCHOOL OF ENGINEERING AND TECHNOLOGY
HIGHER EDUCATION DIVISION
ENEM14015 LAB REPORT
LABWORK
DYNAMIC SYSTEM MODELLING

LAB 1: DAMPED FREE VIBRATION
BASIC OVERVIEW
Lab Instructions
(i) Students must don personal protective equipment while accessing the laboratories
(ii) Requirements are such as closed footwear and long or short sleeve shirts.
Damped Free Vibration
The free vibration response of a system is useful in determining the resonance frequency
of a system and other characteristics of the system such as the damping constant. A free vibration
response is readily obtained from a vibrating system where the spring, mass, and damper
characteristics may be possibly unknown. The free vibration is present in both linear and
rotational vibrating systems and both use the same concepts. The lab experiment uses rotational
theory. An undamped system will undergo free vibration once vibration is initiated. A typical
undamped free vibration response for a linear system (Bhattacharya, n.d.). The frequency of
vibration will be equal to the natural frequency of the system and can be determined from the
period of oscillation.
For a rotational system, the theoretical natural frequency can also be
determined by knowing the spring rate and the mass moment of inertia, as
shown below,

Rotational spring stiffness (kθ) is the measure of how much moment
the spring can supply to the system and is based on the linear spring
constant and the distance the spring is away from the pivot point. The mass
moment of inertia about the pivot point can be calculated for the system
from the typical equations in a dynamics textbook. For this lab a slender
beam equation and point mass equation will be the most useful. Damping is
present in all vibration systems to some extent. Damping causes a reduction
of the free vibration amplitude over time. The experimental damping ratio of
a system can be determined using logarithmic decrements of the
amplitudes.
Figure 1 Damped free vibrations

OBJECTIVES
(i) To observe damped free vibrations
(ii) To observe the effects of different damping levels.
(iii) To calculate damping ratio using the method of logarithmic
decrement to be used in
the following forced vibration laboratory.
(iv) To determine other system parameters such as the rotational spring
rate and the
theoretical natural frequency to allow a full analysis of the system
later in the forced
vibration laboratory.
The GUNT Tm150 Free Vibration Equipment is connected as shown in the illustration below,