Free and random vibration analyses of hourglass lattice sandwich panel using an equivalent model based on variational asymptotic method

Abstract

The hourglass lattice sandwich panel (hourglass LSP) represents a novel type of lightweight and high-strength structure, showcasing new random vibration characteristics related to its distinct geometric configuration. In this paper, a two-dimensional equivalent plate model (2D-EPM) is constructed based on the equivalent stiffness obtained by the variational asymptotic homogenization of the unit cell. The accuracy of 2D-EPM in analyzing the random vibration characteristics (power spectral density (PSD) and root mean square (RMS) responses, as well as effective mass fraction) is validated by the three-dimensional direct numerical simulation and experiments, and its computational efficiency is greatly improved due to the reduced degree of freedoms. On this basis, the effects of structural parameters on the free and random vibration characteristics are systematically analyzed by using the novelty of unit-cell tailorability. The investigation revealed direct correlations between the displacement PSD and RMS with the aspect ratio and lattice rod radius, whereas the inclination angle and face-to-core thickness ratio exhibited inverse correlations. Furthermore, similarities in the low-frequency behaviors of hourglass, pyramid and auxetic LSPs were evident. Specifically, the displacement–RMS curve of the auxetic LSP was comparatively lower, and the hourglass LSP exhibited a similar response, with the second-lowest RMS curve implying correspondingly strong deformation resistance.