Variable Order Finite Elements for Plate Vibration

Rectangular finite elements with a variable number of degrees-of-freedom per element are developed for thin elastic plates. The displacement field for the element is described by a fixed series of polynomial terms plus a variable number of trigonometric terms. The polynomial terms alone are sufficient to describe the displacement field, and the additional trigonometric terms allow for better description of the displacement field within the element. If only the polynomial terms are used, the element becomes a standard type of finite element; whereas, if only one element is used, the procedure becomes the classical Rayleigh-Ritz method. A limited number of comparisons indicate that using one high-order element yields better frequencies than using many low-order elements with the same total number of system degrees-of-freedom. The low order elements have computational advantages which may make them superior when considering overall computational efficiency.