Effect of physical nonlinearity on bending vibrations of elements of packages

Bending vibrations of elements of packages are analyzed numerically by using a beam-type model containing physical nonlinearity. The model for the analysis of skeletal curves of bending vibrations of package element is presented. The 1D model with physical nonlinearity is based on cubic nonlinearity of Duffing type. Phase trajectory of steady state motion of the eigenmode is obtained and analyzed. The model for the analysis of bending vibrations of statically loaded physically nonlinear element of package is presented. First the static problem is solved and than the eigenproblem of small vibrations about the statically deflected structure is analyzed by taking into account cubic nonlinearity of Duffing type. It is demonstrated that the eigenmodes and eigenvalues are influenced by the physical nonlinearity. The setup for experimental investigation of polymeric films for symmetrically distributed loading is presented. The method of projection moiré is applied for this purpose. In the process of investigations the images of the first four eigenmodes of the polymeric HDPE film were determined. The obtained results are used for designing elements of packages.