A dynamic stiffness method is presented for the vibrations of plate structures that are reinforced by eccentric stiffeners. The model incorporates both out-of-plane and in-plane deformations of the plates and the stiffeners. Based on the relationship between the forces and displacements along the common edges of the plate or beam elements, the dynamic stiffness formulae for the plate and the beam elements are derived, respectively. The globally assembled dynamic stiffness matrix is then obtained using the finite element method so that the dynamics of built-up stiffened plates can be readily addressed by using the present method. Compared to the conventional finite element model, the dynamic stiffness model can provide very accurate solutions using only one element over each uniform plate and beam member, regardless of its geometry.
The dynamic stiffness method (DSM) in our recent paper, which can consider both in-plane and out-of-plane vibrations simultaneously, is formulated to investigate the power flow characteristics of built-up plate structures. Prior to power flow analysis, comprehensive validation works on our DSM are performed so as to better exhibit its numerical capabilities. Power input and power transmission within a two-plate structure are then analyzed by following the context of in-plane and out-of-plane vibrations. In addition, three vibration transmission paths within a multiple plate structure are characterized in terms of power flow densities, which can provide better physical insights in vibration transmission within complex plate structures. Compared to power flow analysis based on the well-known reception/mobility method, our approach is strongly recommended for the dynamics of built-up structures since it can assemble the overall stiffness matrix in a straightforward manner like that in the conventional finite element technique.
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