Heat flux topology optimization treatment of vibrational damped cellular composite flexible structures

During the damped vibration process, mechanical energy can be converted partially to other forms of energy such as thermal energy. Thermal energy is normally low and is therefore difficult to measure. Measuring and capturing the thermal energy in a damped vibration is greatly interested in thermo-electric sensor applications. This paper aims to optimally design a flexible composite structure through an optimization procedure that can effectively harvest more thermal energy from a damped vibration process. The overall increased temperature is considered as the objective function and the optimization formulation is written for a cellular flexible composite structure in which one or many layers are cellular layer(s) with multi-volume fractions and constraints, and considering the damping effects of viscous or hysteretic. Different loading conditions such as modal load, harmonic load, and transient load are considered. By solving a governing equation of motion, the novel formulations for temperature increment due to damping effects in vibrational structure for each loading condition are derived. These formulations lead to novel physical response functions, which are integrated over the cellular damping design domain (layer). Several numerical examples are considered to validate the effectiveness and reliability of the derived formulations by maximizing the extraction of overall thermal energy from damped vibration structures.