Random vibration of two-curvature nanoshells with piezoelectric layers resting on viscoelastic foundations

Abstract

Simulating the random response of structures is a practical matter that is crucial for design, as the majority of masses operate on them according to random principles. This is the first publication to examine the random vibrations of a two-curvature shell that is supported by a viscoelastic foundation. The core layer is composed of numerous small layers that are arranged in accordance with biomimetic principles, while the two surface layers are composed of piezoelectric materials. This work has established the equilibrium equation system of the shell by integrating classical shell theory with nonlocal theory. The proposed problem has been resolved through the application of analytical solutions. The research problem has been rendered more comprehensible as a result of the experience obtained in analytical form, which is also the most intriguing aspect of this study. Furthermore, this investigation considers the impact of the flexoelectric effect on piezoelectric layers, with a particular emphasis on the viscous resistance parameter of the viscoelastic substrate. Despite the fact that this complicates the calculation expressions, it adds to the intriguing scientific significance of this research in relation to the oscillation of a two-curvature shell. The two-curvature shell is subjected to a stationary random load, and the response spectrum (displacement) is closely correlated with the input spectrum (excitation force) through the function transmission, which accurately represents the shell's response. This investigation has numerous valuable scientific implications, as the results are closely resembling reality.