Vibration Damping of Adhesively Bonded Joints

Abstract

A study into the vibration characteristics of adhesively bonded single-lap joints has been carried out to investigate the effect of joint geometry and temperature variation on overall system damping. Concepts of vibration damping are introduced, and it is shown how to determine the damping of a system. The methodology of calculating the damping of even a simple bonded element in the form of a lap joint from material and geometric parameters is shown to be complex. The vibration damping of bonded joints has been extended into an experimental program using four different adhesives. These were AV119, a one-part epoxy; 9245, a structural bonding tape; 3532, a two-part polyurethane; and Hysol XEA 9359.3, a two-part structural adhesive. High-strength steel adherends were used to manufacture single-lap joints of varying overlap lengths. The specimens were vibrated flexurally and the damping values calculated using the free decay method. In this investigation, the damping of the adhesive layer dominates the damping of the specimens rather than the damping of the adherends. An optimum overlap ratio was found at approximately 0.25 in this study. The adhesives were tested under varying temperature conditions to illustrate the dominance of the glass transition temperature on the damping of the specimen.

It has been shown that the damping of a structure is unlikely to be improved by using adhesive bonding as a joining method.

Appendix

1.1 Damping Measurement by the Free Decay Method

This is a relatively simple method of measuring the damping of a freely vibrating system. The logarithmic decrement (log dec.), Δ, is measured from an amplitude-time graph and is based on measuring the rate of decay of the free vibrations. This method is only suitable for measuring low damping and free vibration.

During the experiment, readings are recorded by measuring the time taken for the amplitude of the waveform to decrease from A₁ to A₂ (Fig. 16).

Fig. 16

Variation of amplitude with time for a damped system

The relationship between log dec. and the damping ratio can be found by consideration of the equation for damped oscillation:

$$ \begin{array}{l} x={ A e}^{-\zeta w t} \sin \left({w}_d t+\theta \right) \\ {}{A}_1={ A e}^{-\zeta w t}\mathrm{and} {A}_2={ A e}^{-\zeta w\left( t+\tau d\right)}\end{array} $$

The log dec. is defined by

$$ \begin{array}{l}\Delta = \ln \frac{A_1}{A_2}\\ {}\Delta = \ln \frac{{A e}^{-\zeta w t}}{{A e}^{-\zeta w\left( t+{\tau}_d\right)}} \\ {}\Delta = \ln \left({e}^{-\zeta w t+\zeta w\left( t+\tau d\right)}\right)=\zeta w{\tau}_d\end{array} $$

Noting that ${\tau}_d=\frac{2\pi}{w_d}=\frac{2\pi}{w\sqrt{1-{\zeta}^2}}$

Therefore $\Delta =\frac{2\pi w\zeta}{w\sqrt{1-{\zeta}^2}}$

And so if the damping ratio is small, ζ → 0 and so

$$ \Delta =2\pi \zeta = \ln \left(\frac{A_1}{A_2}\right) $$

A more accurate result can be obtained by considering the decay over a number of peaks. The log dec. is then

$$ \Delta =\frac{1}{N} \ln \left(\frac{A_1}{A_{N+1}}\right) $$

where N is the number of peaks calculated using the formula ft = N, where f is the frequency of oscillation, and t is the time taken for the amplitude to decay from A₁ to A₂.