Spatio-temporal non-linear dynamics and chaos in plates and shells

  • J. Awrejcewicz
  • V.A. Krysko, Jr
  • I.V. Papkova
  • E.Yu. Krylov
  • A.V. Krysko


We investigate chaotic vibrations of flexible spherical rectangular shells loaded harmonically via the boundary conditions. In the first part of the paper we consider one-layer shell made from an isotropic and homogeneous material. The second part addresses non-linear dynamics of multi-layer
shells, taking into account gaps between the layers (design non-linearity). Contact pressure between the layers was explicitly defined. Phase portraits, Fourier power spectra and wavelet spectra were constructed and investigated. In addition, an appropriate choice of the wavelets suitable to study the stated problem was made and validated. Analysis of the shell curvature and shell design non-linearity
on the dynamical phenomena was carried out using also the phase difference as a new characteristic for monitoring and quantifying non-linear vibrations.