Distribution of vibrations of a double-leaf plate with random inhomogeneities
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This paper shows how to compute vibrations of a double-leaf plate with random inhomogeneities in its components, two plates and reinforcement beams. The modelling method is based on the variational principle for elastic plates and beams. In addition to the deformation of individual components, the model includes contributions from junctions between components, e.g., how rigidly a beam is attached to a plate, and slightly twisted beams. The junction rigidity is included as potential energy in addition to the strain and the kinetic energies of the components. The random inhomogeneities are simulated as continuous smooth random functions of locations in the structure. A random function is realized using a predetermined probability density function, and an autocorrelation function over the dimension of the component. The vibration is computed for each set of random functions, and statistical properties of the simulations are analysed. The random stiffness and the junctions affect the behaviour of the structure in a wide frequency range and a lower frequency range, respectively. The spectrum of surface vibration level shows changes in resonance frequencies depending on the random functions. Further relationship between the vibrations and the distributions of the random functions will be presented.