Abstract
In this work a lumped mass mechanical model of a thorax subject to a blast pressure wave is taken into consideration. A thorax spring-dashpot model developed by Lobdell is implemented in numerical modeling of dynamics of the multibody system. The five degrees of freedom mechanical model of a chest adjacent to the elastic backrest is subject to an impulse loading generated by the blast pressure wave released by an explosion. The so-called coupling of the pressure wave to the thorax is reconsidered. With respect to the evident existence of inherent time delays of displacements, the system of coupled bodies is described by a time delay differential equations that are derived from the large-scale systems approach. Numerical solutions present interesting dynamical behavior of the bio-inspired system resulting from inherent time delays and a time of arrival of the blast pressure wave. There is pointed out that the inherent state time delays change dynamical response of the multibody system. Proper time of deployment of the foam-based armor plate reduces relative compression of the thorax, which is to be protected by a bullet-proof waistcoat.
Highlights
Intrinsic delays in states of physical quantities characterize many dynamical systems in physics, material engineering, ballistics, biology and chemistry [1,2,3,4,5]
Mathematics of systems with time delays pose basic mathematical challenges. They can be described mathematically by delay differential equations, which belong to the class of functional differential equations [6]
More effective methods based on an analytic approach to obtain the complete solution of systems represented by the delay differential equations based on the concept of Lambert W function was developed in [8]
Summary
Intrinsic delays in states of physical quantities characterize many dynamical systems in physics, material engineering, ballistics, biology and chemistry [1,2,3,4,5]. The time delay terms of differential equations produce an infinite number of roots of the characteristic equation, making the corresponding dynamical behavior difficult to analyze. One solves such problems indirectly by applying some approximations, but a limitation in accuracy that leads to the instability of systems can occur [7]. Awrejcewicz and linear elasticity material properties are assigned to each part of the model, whereas the human cartilages and bones may have different material properties Such conditions are taken into consideration by Lobdell’s model which has been reconsidered in this work to perform numerical solutions of a large-scale time-delay system. In view of reliability and practical implementation, time delays have to be incorporated into the numerical modeling of the large-scale physical systems due to the real transport of mass, propagation of vibrations and computation times
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
