Frequency analysis and shock response studies in bidirectional functionally graded microbeam with thermal effects

Functionally graded (FG) micro-structures showing high strength to weight ratios, good energy efficiency, absorption ability and high thermal conductance have wide applications in micro-sensors, actuators and resonators. In the design of FG microscale components, various factors including material grading distribution, porosity and thermal loads have considerable influence on the overall dynamics. Present work deals with surrogate multi-objective optimization methodology to predict the material indices and geometric parameters of FG microbeam using firefly optimization technique in conjunction with neural network function estimation model. The bidirectional polynomial distribution is considered as the material grading law for the metal and ceramic phases with uniform porosity. The kinematic relations are formulated using first order shear deformation model and the modified couple stress theory(MCST) is used to account the micro-scale effects. Using the energy expressions and Hamilton's principle, the equations of motion are derived and the free vibration analysis and mechanical shock responses using transient analysis are obtained using finite element modeling. Initially, the natural frequencies and shock responses of the micro-beam under different boundary conditions are obtained. The effects of power law index, beam aspect ratio, foundation stiffness parameters and porosity factor on the fundamental frequency and shock response amplitudes are studied in detail. Furthermore, the relationship between the effective input variables and the three output dynamic properties including fundamental frequency, shock response amplitude and normalized structural mass is obtained from neural network model by training with a set of dominant data. Finally, the optimal values of material and geometric parameters are arrived using a surrogate model with firefly optimization scheme adopting the trained neural network in function evaluation. It is found that the proposed scheme is computationally effective and time saving approach.