Wave propagation of porous nanoshells

This study aims at investigating the wave propagation of porous nanoshells. The bi-Helmholtz nonlocal strain gradient theory is employed in conjunction with a higher-order shear deformation shell theory, in order to include the size-dependent effects. The nanoshells are made of a Porous Functionally Graded Material (P-FGM), whose material properties vary continuously along the thickness direction. A variational approach is here applied to handle the governing equations of the problem, which are solved analytically to compute the wave frequencies and phase velocities as function of the wave numbers. The sensitivity of the wave response is analyzed for a varying porosity volume fraction, material properties, nonlocal parameters, strain gradient length scales, temperature, humidity, and wave numbers. Based on the results, it is verified that the size-dependence of the response is almost the same to the one of plates, beams and tubes.