Investigating the Influence of a Laterally Placed Void on Natural Frequency Shifts Using Timoshenko Beam Theory

Abstract Additive Manufacturing (AM), particularly metal 3D printing, has revolutionized the production of complex and highly customized components across various industries. Metal AM facilitates the creation of intricate geometries; however, it introduces risks of internal defects such as voids, which can significantly impact the structural integrity of the final product. This study investigates the vibrational behavior of a 3D-printed metal beam with a lateral void defect, comparing the analytical predictions of Euler-Bernoulli and Timoshenko beam theories. The presence of a lateral void disrupts beam stiffness, affecting vibrational characteristics. The orientation and location of the void significantly influence bending stiffness, shear deformation, and natural frequencies, critical for understanding the dynamic response under operational conditions. Timoshenko theory, which accounts for shear deformation and rotary inertia, is used to model these effects more accurately than Euler-Bernoulli theory. An algorithmic approach models the void’s effects on deflection and natural frequency, with results validated through the Finite Element Method (FEM) in Ansys. The analysis highlights the superior accuracy of Timoshenko theory in predicting frequency shifts caused by void defects. A key aspect of the study is the use of the Relative Frequency Shift (RFS) method, which examines variations in natural frequencies to locate and evaluate the void’s impact. This research provides a comprehensive methodology for detecting internal voids using Timoshenko theory, ensuring structural integrity and enhancing quality assurance of 3D-printed metal components. The findings offer valuable insights for industries relying on metal AM, emphasizing the importance of early defect detection for reliable and efficient components.