An analytic method for vibration analysis of non-uniformly coupled L-shaped plates with arbitrary boundary conditions

L-shaped plates are extensively utilized in practical engineering and plates are uniformly coupled in most previous studies. However, spot welding, riveting or bolting is also employed to link two plates and these connection types lead to non-uniform coupling conditions. In this regard, an analytic model is developed for vibration analysis of L-shaped plates with non-uniform coupling conditions. The system is decomposed into two independent rectangular plates, and both bending and in-plane vibrations are analyzed via the classic plate theory and superposition method. The artificial spring technique is adopted to deal with non-uniform continuity conditions and arbitrary uniform boundary conditions, and these conditions are assembled into the governing equation. Comparisons of natural frequencies of L-shaped plates with different boundary and coupling conditions are firstly made, and high accuracy and wide application of the developed model are demonstrated. Furthermore, influences of boundary conditions, coupling conditions, coupling angle and length of plates are investigated. Results reveal that out-of-plane and in-plane displacements are coupled in every plate of L-shaped plate systems. Uniform distribution of coupling nodes can efficiently increase natural frequencies and a few coupling nodes play the role of uniform rigid coupling conditions. Natural frequencies of L-shaped plates at a right angle are the maximum or very close to maximum one. Besides, present results can be used as benchmarks for future researchers.