Longitudinal vibration of temperature dependent bar with variable cross-section

Abstract

Vibration behavior of a bar with variable cross-section, which its material properties vary with temperature, is investigated in this study. In the analysis, not only theoretical solution but also numerical solution is performed for validation. The numerical analysis is overcome by SolidWorks program based on finite element method. Four types of effects on the bar are investigated. These are effects of temperature variation, geometric ratio, slenderness ratio and mode numbers variation. The temperature is increased from 22 degrees C to 250 degrees C. The geometric ratio is varied from 0 to -1/L at intervals of 0.25/L. The slenderness ratio is varied from 1/10 to 1/20 by increasing the length of bar from 200 mm to 400 mm. As for the mode numbers, the first three mode shapes are examined in the analysis. The boundary condition of the bar is taken as clamped-free. According to the results, the natural frequency decreases with increasing the temperature. The natural frequency also decreases with decreasing the slenderness ratio. But, it increases with decreasing the geometric ratio and also increases with increasing the mode number. When the theoretical and numerical results are examined, it is seen that the results are in harmony.