筋上有开口裂缝的加筋矩形板横向振动特性分析

Analysis of transverse vibration characteristics of stiffened rectangular plates with single cracked stiffener

利用能量法分析筋上含有开口裂缝的四边简支加筋矩形板的横向振动。将矩形板与加强筋沿交界面切开,再将加强筋沿裂缝分成多个子块,采用薄板弯曲和平面应力理论分别建立矩形板和各子块的横向振动能量方程,解决了传统分析方法需给定开裂处筋的弯曲刚度问题。采用第一类切比雪夫多项式构造矩形板和各子块的位移试函数,由Ritz法和板-筋界面变形连续条件得出含有开口裂缝的加筋矩形板的横向振动特征方程。计算结果与有限元分析结果吻合很好,详细分析了裂缝深度和裂缝位置对无量纲频率的影响。

The energy method is used to analyze the transverse vibration of simply-supported stiffened rectangular plates with a sin⁃gle crack stiffener.The rectangular plate and the stiffener are cut along the interface,and then the stiffener is divided into several sub blocks along the crack.The energy equations of the transverse vibration of the rectangular plate and each sub blocks are ob⁃tained by using the thin plate model and the plane stress theory.The displacement functions of rectangular plates and sub blocks are constructed by using the first kind of Chebyshev polynomials.The transverse vibration characteristic equation of a stiffened rectan⁃gular plate with a single cracked stiffener is obtained by the Ritz method and plate-stiffener displacement continuity condition.Fi⁃nally,the effects of crack depth and crack position on the dimensionless frequency are analyzed.