Mechanical Free Vibration Response of Cantilever Beams with Functionally Graded Materials

Mechanical vibration is vital for structural design and analysis in many fields. For manned lunar rover foldable chassis, such as Apollo 17, front and rear chassis can be regarded as cantilever beams. However, since the lunar rover chassis needs to be loaded, the beam’s equivalent material properties are factually not homogeneous. In this paper, cantilever beams with functionally graded material (FGM) properties (in terms of elastic modulus and density) subjected to free vibration conditions are investigated. Comparisons among straight beams, circular curved beams, cracked beams, and uncracked beams are included. Materials are considered to be distributed within the beam with increased density and elastic modulus along the axis. The functions are designed so that the materials are denser at the clamped end. Natural frequencies for the first mode shape are studied due to the variable gradient index. For cracked beams, variable locations and depths for the cracks are added to see how these variables affect the results. ANSYS Mechanical APDL is performed to present the finite element model and extract natural frequencies and animations for each mode shape. Results inform that natural frequencies of the first mode shape decrease when the gradient index increases. Crack effects on the free vibration response of beams are very limited. Nevertheless, when the crack is closer to the clamped end, the impact is more distinct. Similarly, when the crack becomes extremely deep and almost breaks through the beam, the impact will be noticeable.