Effect of Edge Stiffness on Vibration Characteristics of Upper-Opening Square-Base Box-Type Structures

The effect of edge stiffness on the natural vibrations of an upper-opening box structure with a square base is investigated theoretically and experimentally.

The analytical model of the topside aperture box structure comprises four thin-walled flat plates constrained by torsional springs with the lower end clamped, the upper side free, and left and right simple supports. The eigenfunction of a set of four beams connected to each other by a torsional spring as the admissible function is used in the circumferential vibration mode of the side plates.

To validate the analysis, an experiment is conducted using a test box with a top-opening box structure. The spring stiffness is adjusted by increasing the number of laminated tape layers.

When torsional springs are not used, the motions of the four sides are not coupled with each other, the natural vibration modes of each side can be classified into three types, and the natural frequencies of each side are similar. When the torsional spring constant is increased, the natural frequencies of the three types of vibration modes converge to the natural frequencies of the support-support, support-clamped, and clamped–clamped plates, where the upper and lower boundary conditions are clamped-free, and the left and right boundary conditions are different. In the experiment, some of the vibration modes predicted in the theoretical analysis appeared, thereby validating the theoretical analysis.

This study shows that natural vibrations can be classified into three types based on the corner stiffness.