A characterization method for the rigid physical interval constraint on the boundary of the rectangular thin plate

The rectangular thin plate is one of the common components in engineering structures. Diverse constraints and connections result in various dynamical characteristics of the plate, which in turn have significance on the major structure. For the rectangular thin plate with a specific length constraint rather than the entire edge being restricted, the traditional polynomial method has limitations in dynamical modeling. This paper proposes the power series polynomial to express such rigid physical interval boundary condition of the thin plate. Based on the Rayleigh-Ritz method, the power series polynomial is applied on the structural energy expression directly in the form of a constraining functional. The unknown coefficient of the polynomial can be obtained simultaneously with the weight coefficients of the plate displacement expression. Comparisons of natural frequencies and modal shapes obtained by the presented method and the traditional orthogonal polynomial for the classical boundary conditions demonstrate the correctness of the power series polynomial. For the plate with a certain length constraint on the boundary, the natural characteristics are obtained by the modal experiment. Results show that the relative errors of natural frequencies are slight enough and the proposed method is valid for the interval constraint on the boundary of the plate. The computational efficiency of the proposed method also has significant advantages. Therefore, the proposed method can provide a theoretical foundation for the component dynamical modelling with sophisticated boundary conditions.