Nondimensional characterization and asymptotic model development for multifunctional structures with application to load-bearing antennas

This paper (i) presents a mathematical approach to formulate leading-order models for complex multifunctional systems with coupled thermomechanical and electromagnetic field interactions, and (ii) demonstrates its applicability to the modeling and analysis of a load-bearing antenna, a multifunctional sensing and transmitting device integrated with a load-bearing structure. Starting from first-principle equations, i. e. the thermomechanical balance laws coupled with Maxwell's equations, nondimensionalization and perturbation techniques are employed to formulate a leading-order model for the coupled system. Depending on the design of the structure and nature of the excitation, the nondimensional numbers arising in the coupled multifunctional system are quantified, and through a relative ordering of these quantities, the dominant physical effects are extracted. The resulting dominant effects determine the regime of operation of the structure, and in turn dictate the appropriate computational model. This approach is demonstrated through an application to a load-bearing antenna for a prototypical design. The resulting leading-order model is subsequently solved, and the electrical and structural response of the load-bearing antenna is analyzed and compared for different combinations of material properties. The framework introduced in this paper is envisioned to have applications in developing leading-order models for a wide range of complex multifunctional systems and can be utilized for their efficient design.