The Influence of Edge Restraining Stiffness on the Transverse Vibrations of Rectangular Plate Structures

• Published in: Journal of marine science and application 2010-12, Vol.9 (4), p.393-402
• Main Authors: Jin, Guo-yong, Chen, Hao, Du, Jin-tao, Yang, Tie-jun, Li, Wan-you
• Format: Article
• Language: English
• Subjects: Electrical Machines and Networks; Engineering; Geotechnical Engineering & Applied Earth Sciences; Machinery and Machine Elements; Offshore Engineering; Power Electronics; Research Papers; 傅立叶级数法; 板结构; 横向振动; 约束刚度; 自然频率; 转动刚度; 边界条件
• ISSN: 1671-9433; 1993-5048
• DOI: 10.1007/s11804-010-1025-2

This paper presents an analytical study on the influence of edge restraining stiffness on the transverse vibrations of rectangular plate structure. An improved Fourier series method was employed to analyze the transverse vibration of plate structure with general elastically restrained boundary conditions. A linear combination of a double Fourier series and eight auxiliary terms was sought as the admissible function of the flexural displacement of the plate, each term being a combination of a polynomial function and a single cosine series expansion. The auxiliary terms were introduced to ensure and improve the smoothness of the original displacement function and its derivatives at the boundaries. Several numerical examples were given to demonstrate the validity and accuracy of the current solution. The influences of translational and rotational stiffness on the natural frequencies and mode shapes of plate were analyzed by numerical results. The results show that the translational stiffness has bigger influence on the natural frequencies than the rotational stiffness. It is generally well known that little change of the rotational stiffness has little influence on the mode shapes of plate. However, the current work shows that a very little change of rotational stiffness value may lead to a large change of the mode shapes of a square plate structure.