Vibrations of circular cylindrical shells under random excitation and thermal gradients

The present paper is focused on the random vibrations of circular cylindrical shells subjected to thermal gradients across the shell thickness; the investigation is fully experimental. The topic is of practical interest in many engineering fields such as: Aerospace, Automotive, Civil, Nuclear. Indeed, in real environments the excitations are likely non deterministic, moreover, extreme thermal conditions can cause differences of temperature inside and outside the shell, e.g. thermal exchangers. Due to the importance of the subject the literature on shell vibration is extremely wide, it is not analyzed here for the sake of brevity; however, it is to note that the number of papers containing experimental results is not large. When a system is excited with random forcing one generally expects a random response of the system, the statistical properties of the random response are correlated with the forcing through the transfer function in the case of linear systems, or more complicated relationships in the case of nonlinear systems. However, in some particular conditions (e.g. internal resonances, parametric resonances,…) the presence of a nonlinearity in the systems can give rise to a surprising phenomenon, said synchronicity or entrainment (see [1, 2]), which consists in a response made of a combination of random and harmonic signals. In this work a shell subjected to a random base excitation is analyzed experimentally, the excitation is random (flat or limited frequency band). The work take advantage from previous setup and experimental techniques [3–5] developed by the present research team. The phenomenon of synchronicity is clearly observed for some particular thermal conditions: a strong transfer of energy from a broad band excitation signal to an almost harmonic response is experimentally observed, confirming the general findings of refs. [1, 2].