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For predicting vibratory responses of multi-layered panels over a wide frequency range (100-10000 Hz), a new laminate theory has been developed. It overcomes the limit of classical zigzag laminate theory reached when panels start to undertake transverse resonant behavior.
This theory mixes the three degrees of freedom (u0, v0, w0) of the thin orthotropic panel, statically equivalent to the layup assembly with the three “blocked” degrees of freedom (ui, vi, wi) of each layer, considered in relative motion to (u0,v0,w0).
A panel made of N layers is thus described by 3(N+1) displacement variables coupled by a dynamic operator obtained by assembling plate, cylinder or doubly-curved shell thin orthotropic dynamical operators of individual layers depending on geometry. The real coupled operator is first analytically solved for all possible (m, n) quantic numbers to get eigenvalues and eigenmodes from which is derived the modal density of flexural, shear and extensional modes. In a second time, all material properties are made complex and the operator is solved again to predict the frequency band-averaged mean damping loss factor of the assembly from the complex eigenvalues.
Examples of modeling aerospace sandwich or sandwich with thin viscoelastic core are discussed against related FEM models.
This theory adds a new class of SEA subsystems to SEA+ software, extending its modeling capability in addition to the introduction of an “extended orthotropic” material described by frequency dependent elastic constants.
