Simulating vibrations of a double-leaf plate with uncertainties in material properties and interaction between components
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Modelling the vibration of composite structures requires including the effects of uncertain material properties of individual components at mid-frequency. The purpose of this model is to predict the vibration of double-leaf plate with random parameters. One plate is excited by some force, then the vibration travels to the other plate via beams. The random parameters are the elastic modulus of the plates, and coupling conditions between components. The finite element method often used to incorporate the uncertainties in the stiffness matrix. However composite structures typically have tens of components, and formulating the stiffness matrix becomes overwhelming. Here the solution is found by minimizing the lagrangian representing the energy in the structure. The solution is expressed using the Fourier series. The coupling between components are modelled as additional energy contribution. This energy is quantified using varying resistance due to relative separation, slipping, and rotation between neighbouring components. The uncertainties then can be represented by sub-matrices in the lagrangian. As a result, the computation is simplified.