Inhomogeneities and damage in additively manufactured components, such as 3D-printed beams, can significantly impact their structural performance and dynamic behavior. This study presents a novel analytical framework for detecting, locating, and quantifying such inhomogeneities using shifts in natural frequencies as diagnostic indicators. Central to the approach is an original mathematical method that considers the weak axis bending moments, enabling accurate prediction of frequency drops due to spatially varying material properties and internal damages. The analytical model is used to simulate inhomogeneity scenarios by parametrically varying material density and local stiffness degradations, generating a dataset of frequency responses. These simulated frequency drop values serve as training data for machine learning models that are tasked with identifying the presence, location, and severity of damage. To validate the approach, finite element analysis (FEA) is conducted in ANSYS, and results are compared with experimental measurements from PLA 3D printed beams with controlled variations in infill parameters. The experimental setup includes vibration testing under clamped-free boundary conditions, with frequency response functions used to extract the modal properties. The correlation between predicted and observed frequency shifts confirms the reliability of the proposed method. This integrated analytical-ML framework not only reduces the dependency on extensive experimental datasets but also offers a scalable solution for non-destructive evaluation of printed components. It represents a significant step toward embedding structural health monitoring capabilities in AM conduits by employing structural mechanics, modal FEM simulation, and artificial intelligence.