Vibration transmission in a double-leaf plate with random rigidities and junctions
Predicting vibrations of composite structures such as double-leaf plates is difficult because of the large number of components. In the low and high frequency ranges, the components may be homogenized, so that a structure becomes simple enough to be mathematically and computationally tractable. However the vibrations in the mid-frequency range cannot be predicted using such methods because the wavelengths are comparable to the size of the components and junctions between components. In this paper a double-leaf plate is modelled using the Kirchhoff plate and Euler beam theories. The elastic moduli and junctions are allowed to be inhomogeneous. These inhomogeneities are simulated as smooth random functions rather than discrete random numbers. The random functions are incorporated into the model using the variational formulation. Response of the plates are studied with various parameters.