Investigating the sources of variability in the dynamic response of built-up structures through a linear analytical model

It is well established that the dynamic response of a number of nominally identical builtup structures are often different and the variability increases with increasing complexity of the structure. Furthermore, the effects of the different parameters, for example the variation in joint locations or the range of the Young's modulus, on the dynamic response of the system are not the same. In this paper, the effects of different material and geometric parameters on the variability of a vibration transfer function are compared using an analytical model of a simple linear built-up structure that consist of two plates connected by a single mount. Similar results can be obtained if multiple mounts are used. The scope of this paper is limited to a low and medium frequency range where usually deterministic models are used for vibrational analysis. The effect of the mount position and also the global variation in the properties of the plate, such as modulus of elasticity or thickness, is higher on the variability of vibration transfer function than the effect of the mount properties. It is shown that the vibration transfer function between the plates is independent of the mount property if a stiff enough mount with a small mass is implemented. For a soft mount, there is a direct relationship between the mount impedance and the variation in the vibration transfer function. Furthermore, there are a range of mount stiffnesses between these two extreme cases at which the vibration transfer function is more sensitive to changes in the stiffness of the mount than when compared to a soft mount. It is found that the effect of variation in the mount damping and the mount mass on the variability is negligible. Similarly, the effect of the plate damping on the variability is not significant.