带有集中质量矩形板的振动分析

Vibration analysis of rectangular plates coupled with concentrated masses

工程实际中有许多附有集中质量薄板结构,如船舶甲板、悬挂油箱机翼及房屋建筑楼板等,针对这类结构动力学问题,建立了带有集中质量矩形薄板的力学模型,该模型可作用任何类型载荷.运用约束模态分析法分析了有集中质量矩形薄板特征值及振型,并给出了薄板振动响应计算公式.研究结果表明,集中质量在板上某些特定位置起到了刚度强化作用,提升了薄板振动自然频率,该结果可用于实际工程中薄板振动主动控制的研究.

There are many examples of thin plates supporting concentrated masses in practical engineering, such as a ship＇s deck, wings containing fuel tanks, and floors of civil buildings subjected to any kinds of forces. A dynamic model of this kind of structure is presented in this paper. Constraint modal analysis was used to obtain the eigenvalues and mode shapes. The formula used to calculate the vibration response of the thin plate is given. The results show that a concentrated mass located at specific points stiffens the thin plate and increases the natural frequencies of the plate. Results given in this paper can be used in the study of active control of thin plates.