Natural frequency and time response variation for forced vibrations of cracked Timoshenko beams

Abstract

The aviation industry of the current era is dominated by the profound utilization of strengthened structures for a prolonged service life. High speed aircrafts are vulnerable to higher bending and torsional loads due to rapidly fluctuating aerodynamic loads. The need of the hour is to be aware of the loadings and their implications on the life of the beams. The current research paper focuses on a cracked Timoshenko beam. These beams can be easily co-related with numerous structures inside the wing and fuselage of the aircraft. As a first case, the crack depth and the crack locations were varied to observe the variations in natural frequencies of the vibrating Timoshenko beam. Following this, a harmonic force (F0∗cos(wt)) was applied and the forced beam response was observed at a constant time. Subsequently, time varying response was extracted for the same beam at different location. A variety of loads, including rectangular pulse, impulse, blast, step and ramp loads were applied and their complete forced responses were observed at specific locations on the beam over time. It was pertinent to mention here that the responses extracted at the crack locations were more severe than those farther from the crack location. The current research could be used to observe the time varying response of these loads and, subsequently, determining the fatigue life of cracked beams. This analysis can prove very fruitful in the field of SHM (Structural health monitoring) and the durability of materials used in the aviation industry can be easily accessed.