Materials and designs for the aerospace industry must be lightweight, yet reliable and safe for response the environmental demands.A great deal of interest is focused on the question of noise reduction, since lightweight structures have a poor sound insulation properties.

Most sandwich structures are typically made of two relatively thin and stiff face sheets separated by a lightweight material known as core. The core is generally made up of a softer material than the skins. The three layers are attached together using an adhesive. Nowadays, various topologies are used to build the core. Honeycomb topology is a very popular choice among them. A common honeycomb structure has hollow cells which all have the same shape and they are attached by thin walls. The cells' shape is often hexagonal. As a result of this, a sandwich panel can be lightweight and designed to carry high mechanical loads. However, it tends to be poor when it comes to attenuation acoustic.

The aim of the present work is to find aperiodic optimal geometry of the honeycomb core. The suggested design strategy reported here is a numerical optimization procedure involving tow scales: the meso-scale for the unit cell of the honeycomb panel and the macro-scale for the whole panel.To this purpose, an analytical homogenization technique is developed to determine the effective properties of the honeycomb structure along with a comparison with existing models and a sensitive analysis in terms of the geometric parameters of the unit cell have been conducted. Then, the modal density of honeycomb panel is predicted using the macro homogenized parameters.