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6.03 Calorimetry Paper

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For the damping measurement in simple structures such as a beam where the damping of the system is not too high (typically $\eta<0.01$) the free vibration condition in time domain is the most suitable method. In this method, there exist initial displacement in the structure. Releasing the structure from this initial displacement, the magnitude of vibrations of the displacement is recorded as a function of time. An example of measurement can be seen in Figure \ref{fig: measestfig2}.

\begin{figure}[!hb] \centering \includegraphics[width=0.7\columnwidth]{Abbildungen/oscdeflection} \caption{Oscillatory deflection as function of time with free vibration.}
\label{fig: measestfig2}
\end{figure}

The logarithmic decrement is considered an important parameter and can be defined as: …show more content…

The loss factor can therefore be expressed as:
\begin{equation}
\eta = \frac{\lambda }{\pi }=\frac{1}{\pi i}ln(\frac{x_{1}}{x_{i}})=\frac{20log(\frac{x_{1}}{x_{i}})}{27.3i}
=\frac{20log(\frac{x_{i}}{x_{1}})}{27.3\Delta

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