Vibration analysis of a multi-span nonhomogeneous beam involves studying the dynamic behavior of the beam under different loading and boundary conditions. Nonhomogeneous beams have varying material properties along their length, which adds complexity to the analysis compared to homogeneous beams. Mathematical modelling describes the geometry of the beam, including length, cross-sectional properties, and variations in material properties and expresses the material properties as functions of the spatial coordinates, considering variations in stiffness, density, and other relevant parameters. The equation of motion for the nonhomogeneous beam based on the chosen beam theory is derived. The equation should include terms related to bending, shear, and axial deformation. The eigenvalue problem to obtain the natural frequencies and mode shapes of the nonhomogeneous beam is solved. To perform modal analysis, numerical methods or software tools are considered.