Free vibration analysis of layered functionally graded beams with experimental validation

Highlights: ► An improved third order shear deformation theory. ► Energy approach. ► Vibration analysis of layered functionally graded beam with experimental validation. ► The effect of added mass. ► Sample fabrication, volume fraction analysis, vibration testing. -- Abstract: An improved third order shear deformation theory is employed to formulate a governing equation for predicting free vibration of layered functionally graded beams. The Ritz method is adopted to solve the governing equation for various types of boundary conditions and the frequency results are validated by some available and experimental results. A multi-step sequential infiltration technique is used to fabricate the layered functionally graded beams for vibration testing. For the first time, a simple mathematical model, based on a power law distribution, is introduced to approximate material volume fraction of the layered beams. The details of layered beam fabrication according to the infiltration technique, microstructure and volume fraction analysis as well as vibration experimental set up are included and described in this investigation. Aspects which affect natural frequencies, such as material compositions, thickness ratio, and boundary conditions, are then taken into consideration. The impact on frequency of added mass is presented and discussed.