Effect of sliding-supported points on the lateral vibration of a rectangular plate

Abstract

This paper investigates the effect of a kind of point-supported points with a sliding degree of freedom (DoF) on the lateral deformation vibration frequencies of a rectangular plate. The Rayleigh-Ritz method was used to solve the natural frequencies. The study was carried out by replacing different support points on a four-corner-clamped plate with sliding-supported points and analyzing the changes in the natural frequencies. Comparisons were made with the cases in which simply-supported points and free points were used as substitutes for the sliding-supported points. The results indicate that the incorporation of sliding-supported points results in natural frequencies that are higher than those associated with free points and lower than those of simply-supported points. Moreover, the natural frequencies are observed to vary in relation to the number of sliding-supported points employed. As an extension, we investigated the scenario where two sliding-supported points are positioned on two adjacent edges of a plate clamped at two diagonal points. It revealed the specific locations of the sliding-supported points that result in a maximum of the first natural frequency. We also carried out parameter analyses on the aspect ratio and the Poisson’s ratio of the plate. The investigation provides considerations for the dynamic design and modelling of structures with similar boundary conditions.