Vibration Analysis of Multi-Span Nonhomogeneous Beam

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.