Metamaterials are materials engineered to have properties that are not found in naturally occurring materials, properties that can be controlled by designing their macro units. Leveraging on the local resonance mechanism, they are characterized by a frequency region called stopband in which noise and vibration are strongly attenuated. Therefore, a compact and lightweight design with high insulating properties can be achieved. After an initial literature review to establish the state of the art, vibroacoustic simulations will be carried out to produce numerical models which could help provide a fine description of the behaviour of the metamaterials, mainly focusing on the dispersion curves evaluation for stopband characterisation.