| Abstrakt: |
Non-prismatic beams, which serve crucial roles in mechanical engineering applications, are subjected to both static and dynamic loads. Hence, their thorough analysis— particularly under free vibration—is of significant importance. This research undertakes an in-depth investigation into the free vibration characteristics of non-prismatic Euler-Bernoulli beams that exhibit linear variations in both width and height. These beams were studied under two distinct boundary conditions: simple support and clamped-clamped scenarios. The study's approach was twofold: analytical and numerical. The analytical method entailed computing the equivalent area and the equivalent second moment of area, thereby enabling an exploration of how variations in the second moment of inertia and cross-sectional area affect the natural frequencies and mode shapes of non-prismatic beams. Conversely, the numerical method employed the finite element method through ANSYS APDL software (version 17.2). The study's findings revealed that as the height and width of the beam decrease, natural frequencies decline and the maximum amplitude of the mode shapes escalates. It should be noted that the rate of decrease is more pronounced with changes in height than with alterations in width. Furthermore, the diminishing rate of natural frequencies and the decreasing maximum amplitude of the mode shape became more pronounced with the increase in mode number when the beam's height and width decreased. The results derived from the analytical procedure were validated against those from finite element analysis and other literature sources, demonstrating the reliability of the current method. The proposed analytical methodology, in its simplicity of use and accuracy, demonstrates considerable promise in comparison to numerical results. [ABSTRACT FROM AUTHOR] |
