Modal Transition and Crack Effects of Pre-Shaped Curved Beams

Curved beams are pivotal in modern engineering applications, such as mechanical switches and adaptive structures, due to their dynamic response. This study investigates the free vibration characteristics of pre-shaped curved beams, emphasizing their vibration frequencies and mode transitions, which are critical for reliability in dynamic environments. A finite element analysis (FEA) approach, grounded in Euler–Bernoulli beam theory and Lagrange formulation, is employed to derive the characteristic equation of motion. The research addresses the practical challenge of edge cracks by incorporating a local flexibility matrix to quantify their impact on structural integrity. Key parameters, including beam geometry, crack location, and depth, are systematically analyzed to reveal their influence on vibration behavior. Experimental validation using a Laser Doppler Vibrometer (Polytec PSV-500) and ANSYS simulations corroborate the numerical results. The findings highlight a critical height-to-thickness ratio ([Formula: see text], triggering modal transition, with cracks inducing far-reaching effects on vibration modes, particularly in high-curvature beams. By explicitly linking geometric parameters, structural damage, and the resulting vibrational performance, this work provides concrete design guidelines and analysis tools directly applicable to industries utilizing curved structures.