A new finite element analysis of free axial vibration of cracked bars

作者：Ranjbaran A^*; Shokrzadeh A R; Khosravi S

来源：International Journal for Numerical Methods in Biomedical Engineering, 2011, 27(10): 1611-1621.

DOI：10.1002/cnm.1400

• finite element
• dynamic characteristics
• cracked bar
• equivalent mass
• heaviside step function
• Dirac's distribution

In this paper a new and innovative method for computation of longitudinal dynamic characteristics of multi-cracked bars is proposed. Cracks are modeled by equivalent axial springs with specified flexibility. Making use of the Heaviside step function and Dirac's delta distribution, a single governing equation for the whole bar is developed. The governing equation is an ordinary differential equation. With the help of Laplace Transform, a general analytical solution in terms of several unknown coefficients is determined. Boundary conditions are then used to determine the analytical solution for specific problems. Making use of the proposed governing equation a new finite element formulation is derived. In this formulation the effect of cracks is considered by adding an equivalent mass matrix to the element mass matrix. Through numerical study, the accuracy, efficiency and robustness of the work is verified.

• 出版日期2011-10