Total Mechanical Energy Research Articles

Observed Evolution of a California Undercurrent Eddy

AbstractA California Undercurrent eddy (Cuddy) was repeatedly surveyed using multiple Seagliders for over three months. Found and tracked off of the Washington–Vancouver Island coasts, this Cuddy traveled over 400 km, remaining between the 1000- and 2000-m isobaths, as it was swept along in poleward flow of the California Current System. Three Seagliders made repeat bisecting transects of the Cuddy core capturing its detailed three-dimensional structure in time. Its evolution was analyzed through comparison of 11 independent Cuddy “snapshots.” A two dimensional Gaussian model fit to the geopotential anomaly field for each snapshot allowed computation of dynamic fields inaccessible in Seaglider profiles alone. Results indicate that the Cuddy decayed as its core waters became less isolated over time: Cuddy total mechanical energy (kinetic + potential), salt content, and the magnitude of the core potential vorticity anomaly decreased. Core spice and dissolved oxygen variance increased tenfold, and thermohaline fine structure, suggestive of lateral intrusions, was observed progressively closer to the eddy core. The estimated gradient-wind balanced velocity field similarly weakened as the Rossby number decreased to 0.32 from an initial value of 0.48. The observed changes in eddy properties occurred as the Cuddy was exposed to changes in the background stratification and Coriolis parameter as it translated alongshore. Idealized modeling of eddy adjustment indicates that both erosion and changing background conditions are required to explain the observed eddy changes. Adjustment in response to both effects simultaneously leads to changes in eddy properties qualitatively consistent with those observed.

Fuel Combustion at Blast-Furnace Tuyeres

Abstract—In textbooks on the metallurgy of iron, the chapter regarding the processes in the blast-furnace hearth must be supplemented with information regarding the calculation of the total energy of the composite blast, which determine the size of the combustion zone ahead of the tuyeres; and the total mechanical energy of the hearth gas, which characterizes the penetration depth of the hearth gas with respect to the furnace axis and the temperature at the center of the hearth. Constant monitoring of these total-energy values is required in the blast furnace. Those readings must be compared with the values for the best operating periods.

Influence of the Quality of Iron Ore and Coke on Blast-Furnace Performance

Excellent blast-furnace performance is observed when using screened sinter that is free of fines, with the alternation of tuyeres of normal and enlarged diameter. If the total mechanical energy of the combined blast at the tuyere mouth and the total mechanical energy of the blast-furnace gas increase in these conditions, the combustion zone becomes longer and the blast-furnace gas penetrates further toward the furnace axis. In that case, the benefits of the high-quality raw materials may be maximized.

Left ventricular mechanoenergetics in excised, cross-circulated rat hearts under hypo-, normo-, and hyperthermic conditions

We investigated the effects of altering cardiac temperature on left ventricular (LV) myocardial mechanical work and energetics using the excised, cross-circulated rat heart model. We analyzed the LV end-systolic pressure–volume relationship (ESPVR) and linear relationship between myocardial oxygen consumption per beat (VO2) and systolic pressure–volume area (PVA; total mechanical energy per beat) in isovolumically contracting rat hearts during hypo- (32 °C), normo- (37 °C), and hyperthermia (42 °C) under a 300-beats per minute pacing. LV ESPVR shifted downward with increasing cardiac temperature. The VO2–PVA relationship was superimposable in these different thermal conditions; however, each data point of VO2–PVA shifted left-downward during increasing cardiac temperature on the superimposable VO2–PVA relationship line. VO2 for Ca2+ handling in excitation–contraction coupling decreased, which was associated with increasing cardiac temperature, during which sarcoplasmic reticulum Ca2+-ATPase (SERCA) activity was suppressed, due to phospholamban phosphorylation inhibition, and instead, O2 consumption for basal metabolism was increased. The O2 cost of LV contractility for Ca2+ also increased with increasing cardiac temperature. Logistic time constants evaluating LV relaxation time were significantly shortened with increasing cardiac temperature related to the acceleration of the detachment in cross-bridge (CB) cycling, indicating increased myosin ATPase activity. The results suggested that increasing cardiac temperature induced a negative inotropic action related to SERCA activity suppression in Ca2+ handling and increased myosin ATPase activity in CB cycling. We concluded that thermal intervention could modulate cardiac inotropism by changing CB cycling, Ca2+ handling, and basal metabolism in rat hearts.

On the Asymptotic Stability for Nonlinear Oscillators with Time-Dependent Damping

The equation $$\begin{aligned} x''+h(t,x,x')x'+f(x)=0 \qquad (x\in \mathbb {R},\ xf(x)\ge 0,\ t\in [0,\infty )) \end{aligned}$$ is considered, where the damping coefficient h allows an estimate $$\begin{aligned} a(t)|x'|^\alpha w(x,x')\le h(t,x,x')\le b(t) W(x,x'). \end{aligned}$$ Sufficient conditions on the lower and upper control functions a, b are given guaranteeing that along every motion the total mechanical energy tends to zero as $$t\rightarrow \infty $$ . The key condition in the main theorem is of the form $$\begin{aligned} \int _0^\infty a(t)\psi (t;a,b)\,{\mathrm{d}}t=\infty , \end{aligned}$$ which is required for every member $$\psi $$ of a properly defined family of test functions. In the second part of the paper corollaries are deduced from this general result formulated by explicit analytic conditions on a, b containing certain integral means. Some of the corollaries improve earlier theorems even for the linear case.

Band structure and absorption properties of (Ga, In)/(P, As, N) symmetric and asymmetric quantum wells and super-lattice structures: Towards lattice-matched III-V/Si tandem

Quaternary dilute nitride compound semiconductors like GaAsyP1−x−yNx and Ga1−zInzP1−xNx are lattice matched with silicon when y = 4.7 * x − 0.1 and z = 2.2 * x − 0.044 and also have direct bandgaps (with N > 0.6%), thus allowing for monolithic integration of III-V optoelectronics with silicon technology as well as III-V/Si tandem junction solar cells. By applying an eight-band k.p strained (tensile or compressive) Hamiltonian and a Band Anti-crossing model (to account for small amounts of nitrogen impurities) to the conduction band, the electronic band structure and the dispersion relation of these alloys can be determined near the center of Brillouin Zone. In this work, by minimizing the total mechanical energy of the stack of alternating layers of GaP1−xNx and GaAs1−xNx, we have evaluated the ratio of thickness of the respective layers for a strain-balanced superlattice GaAs1−xNx/GaP1−xNx structure on silicon. We calculated the confinement energies and the corresponding states of the respective carriers inside a quantum well (with and without resonantly coupled) or in the miniband of a superlattice structure as a function of the nitrogen composition using a transfer matrix approach under the envelope function approximation. Incorporating only a small amount of nitrogen (<5%), the bandgap of these lattice matched structures fulfils the optimum bandgap requirement of (1.65–1.8) eV for III-V/Si tandem solar cells and optoelectronic devices. The optical-absorption coefficient, in both symmetric and asymmetric quantum wells, is then evaluated with respect to nitrogen composition and temperature by using the Fermi-golden rule for both TE and TM polarization of incident light, including the effect of excitons and thermal broadening.

Влияние качества агломерата и кокса на технико-экономические показатели доменной плавки

Purpose: Compare the results of blast furnace smelting efficiency, when chang-ing the qualitative characteristics of the sinter and coke, and the calculated param-eters of the blowing regime of melting. Methodology: Analysis of technical and economic performance of blast furnaces during periods of work on the agglomerate with different metallurgical characteris-tics and different diameter of the tuyeres. Findings: The experience of blast furnaces with a volume of 2,700 and 2,000 m3 confirmed a known fact of the dependence of furnace efficiency and coke consump-tion not only through the quality of charge materials, but also through the distribu-tion of the gas flow along the furnace section. Originality: The technological analysis of the results of the operation of blast furnaces with the volume of 2700 and 2000 m3 with a change of the quality of the sinter and pellets in combination with the change of the blowing regime parame-ters was performed. On the basis of the performed analysis, it was confirmed the expediency of increasing the gas permeability of the charge by improving the quali-ty of the raw materials while increasing the total mechanical energy of the com-bined gas-blast and hearth-gas, which are responsible for the length of the com-bustion zone and the depth of penetration of the gas flow to the center of the blast furnace. Practical value: Alternation of tuyeres of different diameters along with the im-provement of the quality characteristics of charge materials, additionally contrib-utes to the enhancement of the positive effect due to the expansion of the combus-tion zones in the furnace hearth. And if in this case the total mechanical energy of the mountain gas rises and the depth of penetration of the furnace gas to the fur-nace axis increases, the effect of using high-quality raw materials can be maxim-ized. Keywords: agglomerate, coke, blowing, tuyeres, gas permeability, quality, total energy.

Duality symmetries behind solutions of the classical simple pendulum

Describing the motion of the classical simple pendulum is one of the aims in every undergraduate classical mechanics course. Its analytical solutions are given in terms of elliptic functions, which are doubly periodic functions in the complex plane. The independent variable of the solutions is time and it can be considered either as a real variable or as a purely imaginary one, which introduces a rich symmetry structure in the space of solutions. When solutions are written in terms of the Jacobi elliptic functions this symmetry is codified in the functional form of its modulus, and is described mathematically by the six dimensional coset group Γ=Γ(2) where Γ is the modular group and Γ(2) is its congruence subgroup of second level. A discussion of the physical consequences that this symmetry has on the motions of the simple pendulum is presented in this contribution and it is argued they have similar properties to the ones termed as duality symmetries in other areas of physics, such as field theory and string theory. Thus by studying deeper a very familiar mechanical system, it is possible to get an insight to more abstract physical and mathematical concepts. In particular a single solution of pure imaginary time for all allowed values of the total mechanical energy is given and obtained as the S-dual of a single solution of real time, where S stands for the S generator of the modular group.

Stability of boundary layer flow based on energy gradient theory

The flow of the laminar boundary layer on a flat plate is studied with the simulation of Navier–Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient theory. The simulation results show that there is an overshoot on the velocity profile at the external edge of the boundary layer. At this overshoot, the energy gradient function is very large which results in instability according to the energy gradient theory. It is found that the transverse gradient of the total mechanical energy is responsible for the instability at the external edge of the boundary layer, which induces the entrainment of external flow into the boundary layer. Within the boundary layer, there is a maximum of the energy gradient function near the wall, which leads to intensive flow instability near the wall and contributes to the generation of turbulence.

An enstrophy-based linear and nonlinear receptivity theory

In the present research, a new theory of instability based on enstrophy is presented for incompressible flows. Explaining instability through enstrophy is counter-intuitive, as it has been usually associated with dissipation for the Navier-Stokes equation (NSE). This developed theory is valid for both linear and nonlinear stages of disturbance growth. A previously developed nonlinear theory of incompressible flow instability based on total mechanical energy described in the work of Sengupta et al. [“Vortex-induced instability of an incompressible wall-bounded shear layer,” J. Fluid Mech. 493, 277–286 (2003)] is used to compare with the present enstrophy based theory. The developed equations for disturbance enstrophy and disturbance mechanical energy are derived from NSE without any simplifying assumptions, as compared to other classical linear/nonlinear theories. The theory is tested for bypass transition caused by free stream convecting vortex over a zero pressure gradient boundary layer. We explain the creation of smaller scales in the flow by a cascade of enstrophy, which creates rotationality, in general inhomogeneous flows. Linear and nonlinear versions of the theory help explain the vortex-induced instability problem under consideration.

Balance Control and Energetics of Powered Exoskeleton-Assisted Sit-to-Stand Movement in Individuals With Paraplegic Spinal Cord Injury

ObjectiveTo quantify the effects of initial hip angle and angular hip velocity settings of a lower-limb wearable robotic exoskeleton (WRE) on the balance control and mechanical energy requirements in patients with paraplegic spinal cord injuries (SCIs) during WRE-assisted sit-to-stand (STS). DesignObservational, cross-sectional study. SettingA university hospital gait laboratory with an 8-camera motion analysis system, 3 forceplates, a pair of instrumented crutches, and a WRE. ParticipantsPatients (N=12) with paraplegic SCI. InterventionsNot applicable. Main Outcome MeasuresThe inclination angle (IA) of the body’s center of mass (COM) relative to the center of pressure (COP), and the rate of change of IA (RCIA) for balance control, and the mechanical energy and forward COM momentum before and after seat-off for energetics during WRE-assisted STS were compared between conditions with 2 initial hip angles (105° and 115°) and 3 initial hip angular velocities (800, 1000, 1200 rpm). ResultsNo interactions between the main factors (ie, initial hip angle vs angular velocity) were found for any of the calculated variables. Greater initial hip angle helped the patients with SCI move the body forward with increased COM momentum but reduced RCIA (P<.05). With increasing initial angular hip velocity, the IA and RCIA after seat-off (P<.05) increased linearly while total mechanical energy reduced linearly (P<.05). ConclusionsThe current results suggest that a greater initial hip angle with smaller initial angular velocity may provide a favorable compromise between momentum transfer and balance of the body for people with SCI during WRE-assisted STS. The current data will be helpful for improving the design and clinical use of the WRE.

Micromachined integrated self-adaptive nonlinear stops for mechanical shock protection of MEMS

This paper presents a novel concept of self-adaptive nonlinear stops (SANS) for the generic in-plane shock protection of microelectromechanical systems (MEMS) suspensions. This new shock protection strategy decouples the reliability design from the device design and is compatible with wafer-level MEMS batch fabrication without the requirement of additional processes or materials. SANS increase shock reliability by limiting the travel of the suspension in a compliant manner with efficient energy dissipation. Using numerical simulation, we analyzed the energy dissipation and the impact force between suspensions and shock stops under a half-sine shock impulse (3000 g (1 g ≈ 9.8 m s−2), 0.15 ms). The simulation results indicate that SANS can reduce approximately 89.4% of the impact force compared with hard stops, and additionally, dissipate more than 22.7% of the total mechanical energy in a round trip of the proof mass. To prove the improvement in shock protection, we designed and fabricated model test specimens of both SANS and conventional hard stops. The experimental results demonstrate that test specimens of SANS achieved twice the robustness compared with those of hard stops.

Mechanical latching stops for reliability improvement of MEMS in shock environments

This paper presents a novel design of mechanical latching shock stops (latching stops) for in-plane shock protection of microelectromechanical systems (MEMS). With three shock protection modes, latching stops are capable of limiting the displacement of silicon suspensions in a compliant manner with efficient energy dissipation. The energy dissipation and the impact force between suspensions and shock stops were analyzed by numerical simulation. The analysis results indicate that latching stops, under a half-sine shock impulse [3000 g (1 g ≈ 9.8 m/s2), 0.15 ms], reduce more than two-third of the impact force compared with hard stops, and additionally, dissipate 33.23% of the total mechanical energy during the latching process. Test specimens of both latching stops and conventional hard stops were developed for comparison. The experimental results demonstrate that test specimens of latching stops achieve more than double the robustness compared with those of hard stops. This new shock protection approach decouples the reliability design from the device design. Moreover, latching stops are compatible with wafer-level MEMS batch fabrication without the requirement of additional processes or materials.

Nonlinear phenomena in vibro-impact dynamics: central collisions and energy jumps between two rolling bodies

Central collisions and energy jumps between two rolling bodies as singular nonlinear phenomena are investigated in vibro-impact system dynamics. For that purpose, an extension of theory of collision of two rigid bodies, in rolling dynamics, is presented. Under the authors’ use of the Petroviċ’s elements of mathematical phenomenology, especially mathematical analogy between kinetic parameters of central collision of two bodies in translator motions and central collision of two rolling different axial symmetrically bodies, new original expressions of two post-collision outgoing angular velocities for each of rolling bodies after collision are defined. Presented results are the generalization of author’s previous published results. Using this new and original result for collisions, the vibro-impact dynamics of two rolling heavy thin disks with different radiuses on the rotating circle trace in vertical plane in the period of series of collisions is investigated. Using the series of the elliptic integrals, new nonlinear equations for obtaining the angles, which defined the disks positions of successive collisions, are defined. Phase trajectories of the disks in vibro-impact dynamics are analytically and graphically presented. Two cases of vibro-impact dynamics when phase portraits contain trigger of coupled singularities and homoclinic phase trajectory in the form of number “eight,” as well as in the case without that trigger of coupled singularities, are discussed. Phase trajectory branches of dynamics of both of the rolling disks in the period from initial positions to first collision between them are presented. By using the pre-collisions impact (arrival) angular velocities and post-collision (outgoing) angular velocities of the rolling bodies, the rates of the total mechanical energy change for each disk in comparison under kinetic state that corresponds to pre- and post-collision are expressed, and also of both of the rolling bodies as system pre-collision and post-collision kinetic states. From the energy analysis, some conclusions are formulated. Full theory and new methodology for the investigation of the vibro-impact system dynamics with rolling bodies is found.

Laser Irradiation‐Induced SiC@Graphene Sub‐Microspheres: A Bioinspired Core–Shell Structure for Enhanced Tribology Properties

AbstractFriction generally happening among all moving material interfaces wastes nearly one‐third of total mechanical energy in the world each year, although different kinds of lubricants are adopted. Particle additives, like diamond, inorganic fullerene, and graphene, can enter tribological contacts to reduce friction and protect surfaces from wear. However, the growth of such additives with spherical morphology and high dispersibility in oil without molecular ligands is a major problem. Inspired by the impressive dispersion stability of Noctiluca scientillans in ocean, one novel core–shell composite constructed with superhard SiC sub‐microsphere as core and exclusive floating flat‐blade graphene sheet as shell (SiC@G) is designed. These core–shell SiC@G sub‐micropheres are synthesized for the first time by in situ pulsed laser irradiating commercial SiC powders in liquid at ambient conditions. Both laser‐stimulated surface tension energy release and photothermal decomposition involved in the laser irradiation process assure the reshaping of SiC particles and the formation of graphene sheets derived from SiC surface. Due to the synergistic effect of SiC spheres changing effectively sliding friction into rolling friction and flexible self‐lubricating graphene forming a tribofilm easily, such composites as additives remain well dispersed in lubricating oil and exhibit enhanced antiwear and friction‐reduction performance.

The effects of real and artificial Leg Length Discrepancy on mechanical work and energy cost during the gait

BackgroundThe impacts of Leg Length Discrepancy (LLD) on the kinematic and dynamic parameters of walking have been widely discussed. But little is known on total mechanical work and energy cost. These two variables are more representative of the functional impairment undergone by the LLD patients. AimTo assess the changes of the mechanical work and energy cost of walking in subjects with real LLD and to compare their results with healthy subjects in whom the LLD has been simulated. MethodThe mechanical work and energy cost data of 60 healthy subjects (speed: 4km/h) with artificial LLD induced by soles (2 and 4cm), 20 patients (speed: 3.75±0.5km/h) with real LLD and 20 matched subjects (speed: 3.75±0.5km/h) were collected. Statistical comparisons between the groups were performed using a t-paired test and ANOVA. ResultsPatients with a real LLD showed a significant decrease in mechanical work and energy cost when compared to norms. Patients with real LLD provide a better recovery when compared to subjects with artificial LLD of 2cm, and a decrease of energy cost and higher muscular efficiency (mechanical work/energy cost) when compared to subjects with artificial LLD of 4cm. ConclusionsOur results showed that patients with a real LLD develop compensatory strategies during gait, probably to minimize the displacement of the body center of mass and consequently reduce the amount of energy expenditure useful for their displacement. Moreover, they adopt a better gait strategy compared to the subjects in whom LLD was simulated.

A comparative study on the mechanical energy of the normal, ACL, osteoarthritis, and Parkinson subjects.

The influence of various musculoskeletal disorders has been evaluated using different kinetic and kinematic parameters. But the efficiency of walking can be evaluated by measuring the effort of the subject, or by other words the energy that is required to walk. The aim of this study was to identify mechanical energy differences between the normal and pathological groups. Four groups of 15 healthy subjects, 13 Parkinson subjects, 4 osteoarthritis subjects, and 4 ACL reconstructed subjects have participated in this study. The motions of foot, shank and thigh were recorded using a three dimensional motion analysis system. The kinetic, potential and total mechanical energy of each segment was calculated using 3D markers positions and anthropometric measurements. Maximum value and sample entropy of energies was compared between the normal and abnormal subjects. Maximum value of potential energy of OA subjects was lower than the normal subjects. Furthermore, sample entropy of mechanical energy for Parkinson subjects was low in comparison to the normal subjects while sample entropy of mechanical energy for the ACL subjects was higher than that of the normal subjects. Findings of this study suggested that the subjects with different abilities show different mechanical energy during walking.

Turbulent Mechanical Energy Budget in Stably Stratified Baroclinic Flows over Sloping Terrain

Analysis of second-moment budget equations in a slope-oriented coordinate frame exhibits the pathways of exchange between the potential energy of mean flow and the total turbulent mechanical energy. It is shown that this process is controlled by the inclination of the potential temperature gradient. Hence, this parameter should be considered in studies of turbulence in slope flows as well as the slope inclination. The concept of turbulent potential energy is generalized to include baroclinicity, and is used to explain the role of along-slope turbulent heat flux in energy conversions. A generalization of static stability criteria for baroclinic conditions is also proposed. In addition, the presence of feedback between the turbulent heat flux and the temperature variance in stably-stratified flows is identified, which implies the existence of oscillatory modes characterized by the Brunt–Väisäla frequency.

A reflected wave superposition method for vibration and energy of a travelling string

This paper considers the analytical free time domain response and energy in an axially translating and laterally vibrating string. The domain of the string is either a constant or variable length, dependent upon the general initial conditions. The translating tensioned strings possess either fixed-fixed or fixed-free boundaries. An alternative analytical solution using a reflected wave superposition method is presented for a finite translating string. Firstly, the cycles of vibration for both constant and variable length strings are provided, which for the latter are dependent upon the variable string length. Each cycle is divided into three time intervals according to the magnitude and the direction of the translating string velocity. Applying d’Alembert's method combined with the reflection properties, expressions for the reflected waves at the two boundaries are obtained. Subsequently, superposition of all of the incident and reflected waves provides results for the free vibration of the string over the three time intervals. The variation in the total mechanical energy of the string system is also shown. The accuracy and efficiency of the proposed method are confirmed numerically by comparison to simulations produced using a Newmark-Beta method solution and an existing state space function representation of the string dynamics.

Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms

In this work we extend a total Lagrangian formulation developed for dynamical nonlinear analysis of elastic plane frames to include structural energy dissipation and sliding connections (as prismatic and cylindrical joints). The joints move in a path that may present an arbitrary roughness profile along its trajectory. Their exact kinematical restraints are introduced in the total mechanical energy of the system by the method of Lagrange multipliers. The structural energy dissipation is considered by a modified Kelvin-Voigt rheological model, for which a pure numerical procedure for the strain rate approximation (finite difference) is proposed. The dynamical equilibrium equation is obtained by a variational principle and the nonlinear solution procedure is done by the Newton-Raphson method. Several examples are presented to demonstrate the efficiency of the proposed formulations.