Structural Dynamics in Biology: A Bridge Given by Implicit Vibratory Crossed Models

This article proposes a synthesis and contribution at three levels: generation of dynamic equations of shell structures interacting with fluids, reduction of implicit resolution, and cross-applications to aerospace tanks and living systems. The synthesis of the equations is proposed around the four principles of thermodynamics at the level of discrete, structural and digitized systems. The implicit approach envisages an innovative analysis in terms of condensation and digitization, with in particular a perspective towards singular and integral methods. Some illustrations are proposed, in the field of performed research models and also in the fields of educational applications in biodynamics. The proposed bridge links, on one hand, the analytical Lagrange-Feynman’s approach, and on the other hand experimental results obtained in laboratory and numerical experiments obtained with multiphysics software. Finally, the realized models concern conservative and dissipative models for the active and passive control of complex systems, in a unified approach.