Dynamics, Volume 1, Issue 1 (September 2021) – 8 articles

Multi-enzymatic reactions can successfully replace complex chemical syntheses, using milder reaction conditions, and generating less waste. The present model-based analysis compares the performances of several optimally operated Batch Reactors (BR) with those of an optimally operated serial Sequence of BRs (SeqBR). In multi-enzymatic systems, SeqBR could be more advantageous and flexible, allowing the optimization of costly enzymes amounts used in each BR in the series. Exemplification was made for the bi-enzymatic reduction of D-fructose to mannitol by using MDH (mannitol dehydrogenase) and the NADH cofactor, with the in situ continuous regeneration of NADH at the expense of formate degradation in the presence of FDH (formate dehydrogenase). For such coupled enzymatic systems, the model-based engineering evaluations are difficult tasks, because they must account for the common species’ initial levels, their interaction, and their dynamics. The determination of optimal operating modes of sole BR or of a SeqBR turns into a multi-objective optimization problem with multiple constraints to be solved for every particular system. The study presents multiple elements of novelty: (i) the proof of higher performances of an optimal SeqBR (including N-BRs) compared to a sole optimal BR operated for N-number of runs and (ii) the effect of using a multi-objective optimization criteria on SeqBR adjustable dynamics. Full article

Offshore structures are subjected to dynamic environmental loads (wave and wind loads). A stress-life fatigue strength curve is proposed for tubular joints which are in the splash zone area of offshore jacket structures. The Det Norske Veritas (DNV) offshore structures standards given design T-curve in the air is modified with the environment-dependent parameters to obtain this fatigue strength curve. Validity of the curve is done by comparing fatigue lives given by the proposed curve with experimental fatigue lives of tubular joints tested in seawater under different loading conditions. The fatigue assessment of a case study tubular joint is performed using the proposed curve. Nominal stress ranges of the members, which are connected to the joint, are obtained by dynamic analysis of the jacket structure. Stress concentration factors are utilized with the nominal stresses to obtain the hot spot stress ranges. Fatigue lives are calculated and compared with the conventional approach. Hence the applicability and significance of the proposed fatigue strength curve are discussed. Full article

Analytical solutions to a variety of simplified versions of the restricted three-body problem in celestial mechanics possess long running history that encompasses several centuries. Most of the successes were limited either to the planar configuration of the three bodies, to the motion around the Lagrange points, or to the Kozai–Lidov effect. We review some analytical advances obtained by separating rapid and slow subsystems as presented in recently published papers concerning the non-planar motion of the three bodies unrelated to the Lagrange points and to the Kozai–Lidov effect. Most (but not all) of the discussed advances correspond to the bound motion in the considered celestial systems. Full article

In this study, a dynamic Mindlin–Reissner-type plate is developed based on a simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations of motion and the corresponding boundary conditions are derived using the general virtual work variational principle. The presented model contains, apart from the two classical Lame constants, one additional microstructure material parameter g for the static case and one micro-inertia parameter h for the dynamic case. The formal reduction of this model to a Kirchhoff-type plate model is also presented. Upon diminishing the microstructure parameters g and h, the classical Mindlin–Reissner and Kirchhoff plate theories are derived. Three points distinguish the present work from other similar published in the literature. First, the plane stress assumption, fundamental for the development of plate theories, is expressed by the vanishing of the z-component of the generalized true traction vector and not merely by the zz-component of the Cauchy stress tensor. Second, micro-inertia terms are included in the expression of the kinetic energy of the model. Finally, the detailed structure of classical and non-classical boundary conditions is presented for both Mindlin–Reissner and Kirchhoff micro-plates. An example of a simply supported rectangular plate is used to illustrate the proposed model and to compare it with results from the literature. The numerical results reveal the significance of the strain gradient effect on the bending and free vibration response of the micro-plate, when the plate thickness is at the micron-scale; in comparison to the classical theories for Mindlin–Reissner and Kirchhoff plates, the deflections, the rotations, and the shear-thickness frequencies are smaller, while the fundamental flexural frequency is higher. It is also observed that the micro-inertia effect should not be ignored in estimating the fundamental frequencies of micro-plates, primarily for thick plates, when plate thickness is at the micron scale (strain gradient effect). Full article

Offshore structures are exposed to risks of vessel collisions and impacts from dropped objects. Tubular members are extensively used in offshore construction, and thus, there is scope to investigate their crashworthiness behaviour. Aluminium, glass fibre reinforced polymer (GFRP) and hybrid aluminium/GFRP circular tube specimens were fabricated and then tested under quasi-static and dynamic axial loading conditions. Two hybrid configurations were examined: external and internal layers from respectively aluminium and GFRP, and vice versa. The material impregnated with epoxy resin woven glass fabric was allowed to cure attached to the aluminium layer to ensure interlayer bonding. The quasi-static and dynamic tests were conducted using respectively a universal testing machine at a prescribed crosshead speed of 10 mm/min, and a 78 kg drop hammer released from 2.5 m. The non-hybrid configurations (aluminium and GFRP specimens) outperformed their hybrid counterparts in terms of crashworthiness characteristics. Full article

As it is known, the Womersley function models velocity as a function of radius and time. It has been widely used to simulate the pulsatile blood flow through circular ducts. In this context, the present study is focused on the introduction of a simple function as an approximation of the Womersley function in order to evaluate its accuracy. This approximation consists of a simple quadratic function, suitable to be implemented in most commercial and non-commercial computational fluid dynamics codes, without the aid of external mathematical libraries. The Womersley function and the new function have been implemented here as boundary conditions in OpenFOAM ESI software (v.1906). The discrepancy between the obtained results proved to be within 0.7%, which fully validates the calculation approach implemented here. This approach is valid when a simplified analysis of the system is pointed out, in which flow reversals are not contemplated. Full article

According to the existing paradigm, helium atoms and helium-like ions (hereafter, heliumic systems) in a relatively weak external static electric field do not exhibit the linear Stark effect—in distinction to hydrogen atoms and hydrogen-like ions. In the present paper we consider the classical dynamics of a muonic-electronic heliumic system in Rydberg states–starting from the concept from our previous paper. We show that there are two states of the system where the averaged electric dipole moment is non-zero. Consequently, in these states the heliumic system should exhibit the linear Stark effect even in a vanishingly small electric field, which is a counter-intuitive result. We also demonstrate the possibility of controlling the overall precession of the electronic orbit by an external electric field. In particular, we show the existence of a critical value of the external electric field that would “kill” the precession and make the electronic orbit stationary. This is another counter-intuitive result. We calculate analytically the value of the critical field and show that it is typically smaller or even much smaller than 1 V/cm. Full article