A hybrid analytical method for predicting vibrations in vacuum and water of the sandwich plate with z-direction reinforcements and cavities

This paper presents a multi-functional sandwich plate with z-direction reinforcements and cavities that has the potential to meet the pressure resistance and the acoustic stealth requirement of the underwater equipment in deep sea. In order to predict its free and forced vibrations in both vacuum and water, a hybrid analytical method is proposed by combining a multi-level homogenization model and a layerwise model. The core with z-direction reinforcements and cavities is homogenized and effective elastic constants are calculated by the Mori-Tanaka formula. Vibration equations of the sandwich plate are derived utilizing the layerwise model based on the first-order shear deformation theory. The water effect is taken into account by the Euler's equation. Vibration results are solved under simply supported boundaries. Validation studies and parameter analyses are then conducted. It is found that different from the existing theoretical approach based on the equivalent single-layer model that is only applicable for the sandwich with a hard core material, the present hybrid analytical method is well suitable for vibration predictions of the sandwich plate with z-direction reinforcements and cavities, no matter the hard or soft core. Besides, due to the homogenization of the three-phase core and the neglecting of local vibrations in the layerwise model, the present analytical method only predicts accurate free vibrations when the half wave numbers are less than numbers of cavities in x and y directions, and also just shows the high precision in force vibration calculations as the maximum analysis frequency is less than the natural frequency of the mode corresponding to numbers of cavities.