Effect of built-in edges on 3-D vibrational characteristics of thick circular plates

The vibrational characteristics of thick circular plates built into a rigid medium in the vicinity of the circumference are studied. The analysis procedure is based on the exact, small-strain, three-dimensional linear elasticity theory. In the analysis, the plate is considered as comprising an inner circular disc with free upper and lower surfaces connected to an outer annulus that is built into the rigid medium. The Chebyshev polynomials multiplied by suitable boundary characteristic functions are selected as the admissible functions of the displacement functions, and the three-dimensional displacement fields in each part can be expressed accordingly. Through the Ritz method, the eigenvalue equations can be established for the inner disc and the outer annulus, respectively. Utilizing the displacement continuity conditions at the interface between the two parts, the eigenvalue equation for the whole plate is derived. Convergence and comparison studies demonstrate the correctness and accuracy of the present method. The effect of structural parameters such as plate thickness, built-in length and the end condition on eigenfrequencies of circular plate is investigated in detail. It is shown that with the increase of plate thickness, the effect of the built-in annulus on eigenfrequencies significantly increases. Therefore, for a thick plate, the flexibility of the built-in part should be considered in the dynamic analysis.