This study presents the free vibration analysis of a double tapered beam having linearly varying both thickness and width, by using finite element and component mode synthesis methods. To determine the natural frequency and mode shape of the double tapered cracked beam, the stiffness and mass matrices of the beam have been obtained. The crack in the beam is modeled as a massless spring, and the beam is divided into two subcomponents from the crack section. The stiffness of spring has been derived from the linear elastic fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expressions. It has been observed that natural frequencies and mode shapes vary depending on the location of the crack, the depth of the crack and the aspect ratios of the beam. The results of the present study and those in the literature are compared and a great deal of consistency has been found.

这项研究通过使用有限元和分量模式合成方法，给出了厚度和宽度都线性变化的双锥形梁的自由振动分析。为了确定双锥形裂纹梁的固有频率和振型，已经获得了梁的刚度和质量矩阵。梁中的裂缝被建模为无质量弹簧，梁从裂缝部分被分为两个子组件。弹簧的刚度是从线性弹性断裂力学理论得出的，它是使用应力强度因子和应变能释放率表达式计算的柔度矩阵的逆。已经观察到，固有频率和振型形状根据裂纹的位置，裂纹的深度和光束的纵横比而变化。比较了本研究的结果和文献中的结果，发现了很多一致性。