Free vibration analysis of plates by using a four-node finite element formulated with assumed natural transverse shear strain

A study on the free vibration analysis of plates is described in this paper. In order to investigate vibrational characteristics of plates, a four-node plate element is developed by using the assumed natural strains on the basis of Reissner–Mindlin (RM) assumptions which allows us to consider the shear deformation and rotatory inertia effect. All terms related to the plate finite element formulation are consistently defined in the natural domain. Assumed natural strains are derived to alleviate the locking phenomena inherited in the RM plate elements. In particular, the explicit expression of assumed natural transverse shear strain is described in this paper. The natural constitutive equation is used in conjunction with the natural strain terms. Several numerical examples are carried out and their results are then compared with the existing reference solutions.