Wavenumber analysis on vibrations of inner and outer shells in functionally graded porous doubly combined shells

Objectives The study aims to investigate the effects of annular plates on vibrational wavenumber spectrum characteristics of inner and outer shells in functionally graded porous (FGP) doubly combined shells. Methods Based on the first-order shear deformation theory and the generalized variational principle, the motion equation is established. The interface potential based on the sub-domain generalized variational principle and the least square weighted technique is introduced to ensure continuity compatibility conditions between substructures and boundary conditions. By expanding displacements in the circumferential direction with Fourier series, the vibration wavenumber spectrum is analytically derived. First, the free vibration characteristics of the doubly combined shells are discussed, and the influences of the annular plates on the modal characteristics of the shells are analyzed. Subsequently, the vibration and dispersion characteristics of the inner and outer shells are examined based on wavenumber analysis. Results The results indicate that the modes of the FGP doubly combined shells can be classified into two categories: local modes and global modes. The constraints at the ends of annular plates induces elastic wave reflection at the interface, where the incident and reflected waves superimpose to form standing waves, corresponding to the high-wavenumber vibration modes of the inner and outer shells. The coupling between the inner and outer shells is mainly concentrated in the low-wavenumber region (circumferential order n≤2). As the frequency increases, local vibrations with short wavelengths (circumferential order n≥4) become increasing significant in both shells, leading to greater differences in their vibration behavior. The coupling effects of annular plates significantly alter the dispersion curves of the shells, and the effects of porosity design on the dispersion curves behave as frequency shift in the wavenumber domain. Conclusions The proposed theoretical modeling method is reliable, and the research can serve as a reference for the vibration and acoustic design of doubly combined shell.