Free vibration of long-span continuous rectangular Kirchhoff plates with internal rigid line supports

Exact analysis for free vibration of long-span continuous rectangular plates is presented based on the classical Kirchhoff plate theory, using the state space approach associated with joint coupling matrices. Lévy-type solution is adopted to model the field variation in the direction perpendicular to the pair of simply supported edges. The series of internal rigid line supports are parallel to the remaining pair of edges, which can be of an arbitrary combination of simply supported, clamped and free edges. Transfer relationship is derived in the span direction by the state space approach. The joint coupling matrices are employed to avoid numerical instability that exists in the conventional state space approach for high-frequency calculation or long-span geometry. Numerical calculation is carried out to validate effectiveness and efficiency of the present method. Influence of location of internal line supports on natural frequencies of multi-span plates with large aspect ratios is investigated and discussed.