Paper Title
Free Vibration Analysis of Tapered Cantilever Beam

Abstract
Tapered cantilever beams are widely utilized in engineering structures, where understanding their dynamic behavior is critical for structural integrity and performance optimization. This study investigates the free vibration characteristics of such beams with varying taper ratios, using structural steel and aluminum as materials. Numerical simulations conducted in ANSYS and analytical methods were employed to determine natural frequencies and mode shapes, while parametric studies explored the effects of taper ratios (0.2, 0.5, 0.8) on vibrational responses. Results reveal that taper ratios significantly influence modal frequencies and deformation patterns, with notable differences in dynamic responses between modes. Analytical and numerical results align closely, with observed deviations highlighting the impact of modeling techniques. This research provides valuable insights into the optimization of tapered beam designs, mitigating resonance risks and enhancing structural reliability. Future work includes expanded parametric studies and nonlinear material considerations to refine predictions further. Keywords - Tapered Cantilever Beams, Free Vibration Analysis, Natural Frequencies, Taper Ratio, Numerical Simulation, Structural Integrity, Dynamic Behavior.