Non‐linear vibration analysis of multilayer sandwich plates by incremental finite elements: 1. Theoretical development

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Abstract
The first part of this paper presents an incremental variational principle and an incremental finite element in time‐space domain for the analysis of large amplitude, periodic vibration of multilayer sandwich plates. A reduced basis composed of eigenvectors corresponding to linear free vibration is introduced to reduce the order of the resulting linearized equations governing the non‐linear motion which are solved incrementally in association with Newton‐Raphson iterative method and an extrapolating technique. In the second part the solution techniques are described in detail and a number of examples on various non‐linear responses of rectangular multilayer sandwich plates, including superharmonic, subharmonic and internal resonance, are included in the study. Viscous modal damping is also considered when the structure is under forced excitation.

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