Journal articles on the topic 'Force and energy'
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1
Ramakrishnan, P. "Electronegativity: A Force or Energy." International Journal of Trend in Scientific Research and Development Volume-3, Issue-4 (June 30, 2019): 665–85. http://dx.doi.org/10.31142/ijtsrd23864.
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Spandan, Vamsi, Daniel Putt, Rodolfo Ostilla-Mónico, and Alpha A. Lee. "Fluctuation-induced force in homogeneous isotropic turbulence." Science Advances 6, no. 14 (April 2020): eaba0461. http://dx.doi.org/10.1126/sciadv.aba0461.
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Understanding force generation in nonequilibrium systems is a notable challenge in statistical physics. We uncover a fluctuation-induced force between two plates immersed in homogeneous isotropic turbulence using direct numerical simulations. The force is a nonmonotonic function of plate separation. The mechanism of force generation reveals an intriguing analogy with fluctuation-induced forces: In a fluid, energy and vorticity are localized in regions of defined length scales. When varying the distance between the plates, we exclude energy structures modifying the overall pressure on the plates. At intermediate plate distances, the intense vorticity structures (worms) are forced to interact in close vicinity between the plates. This interaction affects the pressure in the slit and the force between the plates. The combination of these two effects causes a nonmonotonic attractive force with a complex Reynolds number dependence. Our study sheds light on how length scale–dependent distributions of energy and high-intensity vortex structures determine Casimir forces.
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Rainey, R. C. T. "Key features of wave energy." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1959 (January 28, 2012): 425–38. http://dx.doi.org/10.1098/rsta.2011.0251.
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For a weak point source or dipole, or a small body operating as either, we show that the power from a wave energy converter (WEC) is the product of the particle velocity in the waves, and the wave force (suitably defined). There is a thus a strong analogy with a wind or tidal turbine, where the power is the product of the fluid velocity through the turbine, and the force on it. As a first approximation, the cost of a structure is controlled by the force it has to carry, which governs its strength, and the distance it has to be carried, which governs its size. Thus, WECs are at a disadvantage compared with wind and tidal turbines because the fluid velocities are lower, and hence the forces are higher. On the other hand, the distances involved are lower. As with turbines, the implication is also that a WEC must make the most of its force-carrying ability—ideally, to carry its maximum force all the time, the ‘100% sweating WEC’. It must be able to limit the wave force on it in larger waves, ultimately becoming near-transparent to them in the survival condition—just like a turbine in extreme conditions, which can stop and feather its blades. A turbine of any force rating can achieve its maximum force in low wind speeds, if its diameter is sufficiently large. This is not possible with a simple monopole or dipole WEC, however, because of the ‘ nλ /2 π ’ capture width limits. To achieve reasonable ‘sweating’ in typical wave climates, the force is limited to about 1 MN for a monopole device, or 2 MN for a dipole. The conclusion is that the future of wave energy is in devices that are not simple monopoles or dipoles, but multi-body devices or other shapes equivalent to arrays.
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GUPTA, V. K. "BROWNIAN DYNAMICS SIMULATION OF CATCH TO SLIP TRANSITION OVER A MODEL ENERGY LANDSCAPE." Journal of Biological Systems 24, no. 02n03 (June 2016): 275–93. http://dx.doi.org/10.1142/s0218339016500145.
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We perform Brownian dynamics simulation (BDS) of catch to slip transition over a model energy landscape. Through our BDS we demonstrate that for forces below the critical force the bond rupture occurs mostly through the catch pathway while for forces above the critical force the bond rupture occurs mostly through the slip pathway. We also demonstrate that the shoulder in the bond rupture force distribution switches to peak as the loading rate increases progressively and the bond lifetime is maximized at the model dependent critical force. The force dependent bond lifetime obtained via transforming the bond rupture force distribution at a given loading rate is in excellent agreement with that obtained from our BDS at constant forces. An alternative to the current mechanism of catch to slip transition is presented and validated through BDS.
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Wells, Daniel R., and Lawrence Carl Hawkins. "Containment forces in low energy states of plasmoids." Journal of Plasma Physics 38, no. 2 (October 1987): 263–74. http://dx.doi.org/10.1017/s0022377800012563.
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The application of Hamilton's principle to the problem of the determination of the structure of low free energy state plasmoids is discussed. It is shown that Clebsch representations of the vector fields and representations involving side conditions on the functional result in the same sets of Euler–Lagrange equations. The relationship of these representations to the problem of containment forces in vortex structures (plasmoids) is considered. It is demonstrated that the lowest free energy state of an incompressible plasma is always Lorentz force and Magnus force free. For a compressible plasma obeying the adiabatic gas laws, the Magnus force is finite. Introduction of conservation of angular momentum as an additional side condition also results in finite containment forces.
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Numrich, Robert W. "Computational Force, Mass, and Energy." International Journal of Modern Physics C 08, no. 03 (June 1997): 437–57. http://dx.doi.org/10.1142/s0129183197000370.
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This paper describes a correspondence between computational quantities commonly used to report computer performance measurements and mechanical quantities from classical Newtonian mechanics. It defines a set of three fundamental computational quantities that are sufficient to establish a system of computational measurement. From these quantities, it defines derived computational quantities that have analogous physical counterparts. These computational quantities obey three laws of motion in computational space. The solutions to the equations of motion, with appropriate boundary conditions, determine the computational mass of the computer. Computational forces, with magnitudes specific to each instruction and to each computer, overcome the inertia represented by this mass. The paper suggests normalizing the computational mass scale by picking the mass of a register on the CRAY-1 as the standard unit of mass.
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Balakin, Alexander B., Diego Pav n, Dominik J. Schwarz, and Winfried Zimdahl. "Curvature force and dark energy." New Journal of Physics 5 (July 4, 2003): 85. http://dx.doi.org/10.1088/1367-2630/5/1/385.
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Pincus, HJ, GM Filz, and TL Brandon. "Compactor Force and Energy Measurements." Geotechnical Testing Journal 16, no. 4 (1993): 442. http://dx.doi.org/10.1520/gtj10284j.
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Varriano, John A. "Energy diagrams with drag force." Physics Teacher 34, no. 9 (December 1996): 546–48. http://dx.doi.org/10.1119/1.2344563.
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Hayward, J. A. "BORAL ENERGY-A LEADING FORCE." APPEA Journal 36, no. 2 (1996): 146. http://dx.doi.org/10.1071/aj95075.
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BRACCIALI, A., and G. CASCINI. "ROLLING CONTACT FORCE ENERGY RECONSTRUCTION." Journal of Sound and Vibration 236, no. 2 (September 2000): 185–92. http://dx.doi.org/10.1006/jsvi.1999.2533.
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Gao, Yun Kai, and Da Wei Gao. "The Analysis of Automotive Door Seal Energy Consumption." Applied Mechanics and Materials 80-81 (July 2011): 714–18. http://dx.doi.org/10.4028/www.scientific.net/amm.80-81.714.
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The seal deformation of automotive door is caused by the door compression forces, including non-linear elastic force and non-linear damping force. The working principles of them are analyzed and a new simplified analysis model is built. Based on the Bernoulli equation and the law of conservation of mass, the mathematical models are established to calculate energy consumption of the seal system. According to the analysis results, the energy consumption of non-linear elastic force and non-linear damping force are respectively 84% and 16% of the total energy consumption of the seal system. At last, the calculation data is compared with the test data and the error is less than 5%, so the calculation method proposed in this paper is observed to be accurate.
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Nisirat, Mahdi A. "A New External Force for Snake Algorithm Based on Energy Diffusion." International Journal of Machine Learning and Computing 9, no. 3 (June 2019): 316–21. http://dx.doi.org/10.18178/ijmlc.2019.9.3.804.
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SAKAI, Satoru, and Rintaro FURUMOTO. "D207 Energy based side force formula and attenuation for agricultural vehicles." Proceedings of the Symposium on the Motion and Vibration Control 2011.12 (2011): 425–30. http://dx.doi.org/10.1299/jsmemovic.2011.12.425.
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El-Mongy, Sayed A. "Sayed`s Theory of Dark Energy and Dark Matter Forces Nature." JOURNAL OF ADVANCES IN PHYSICS 22 (April 12, 2024): 100–110. http://dx.doi.org/10.24297/jap.v22i.9605.
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Allah (God) is the Creator of the wonderful accelerated expansion of universe. The nature of Dark energy (DE) and matter (DM) is enigmatic mystery of the modern astrophysics. This article is a theory establishes the nature and laws of DE and DM forces. They are among the forces controlling the universe harmony and homogeneity. The derived equations were based on the published Sayed quantum gravity force formula. The Sayed`s Dark energy force (SDEF) formulas indicate that they are function in quantum gravity force (FQG), energy density(ρ), cosmological (Ʌ), Hubble (H), and Planck (h) constants. The formulas were verified and validated. For Planck and cosmos scales, the Dark energy force, energy density, and Ʌ were calculated and found to be 2.538x1084 N, 10-26 Kg/m3, and 10-52 m-2 respectively. These values are in high concordance with the declared values. The results obtained show that the DE force represents more than ¾ of the universe forces as the observations. The disputed Hubble constant was also calculated and found to be in the range; ~2.2 x10-18 s-1. It can also be stated and emphasized that the light speed violation (E≠mc2) is a must to solve the DE nature and many other universe mysteries.
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Yuan, Yan Jie, Xiu Bing Jing, Huai Zhong Li, and Jun Wang. "An Experimental Investigation of Cutting Forces in Micro End-Milling Process." Key Engineering Materials 693 (May 2016): 710–17. http://dx.doi.org/10.4028/www.scientific.net/kem.693.710.
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This paper presents an experimental study of cutting forces during micro end-milling of brass. The influences of cutting speed and feed per tooth on cutting forces have been researched. The results show that the resultant force Fr and feed force Fx significantly increase with increasing the feed per tooth. The resultant force Fr, feed force Fxand normal force Fy increase with increasing cutting speed. The specific shear energy is also investigated. It is observed that the specific shear energy increases greatly with decreasing the feed per tooth when the feed per tooth is less than minimum chip thickness.
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Bennet-Clark, H. C., and A. G. Daws. "Transduction of mechanical energy into sound energy in the cicada cyclochila australasiae." Journal of Experimental Biology 202, no. 13 (July 1, 1999): 1803–17. http://dx.doi.org/10.1242/jeb.202.13.1803.
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The anatomy of the paired tymbal muscles of Cyclochila australasiae was described. Force-distance relationships of the sound-producing in-out cycle of tymbal movement were measured. The largest forces were measured when the push occurred at the apodeme pit on the tymbal plate at angles similar to the angles of internal pull of the tymbal muscle. Initially, inward movement was opposed by the elasticity of the tymbal, which stored energy. At a mean force of 0. 38 N after a mean inward strain of 368 microm, the tymbal ribs buckled, the mean energy release being 45.1 microJ. The energy release occurred over 2–10 ms in three or four sound-producing steps as successive tymbal ribs buckled inwards. After the ribs had buckled, the force decreased to a mean value of 0.17 N. The force returned to zero during the outward movement, during which the tymbal ribs buckled outwards. The mean energy dissipated in the outward movement was 32.8 microJ. During contraction, the tymbal muscle produced mean values for the peak active force of 0.31 N over 295 microm, which gave mean values for the area of the work loops of 47.0 microJ. The calling song of C. australasiae had a mean pulse rate of 234 Hz (117 Hz for each side of the insect). The peak power to mean power ratio for the songs was 8.51:1 (+9.30 dB). Measurements of the sound field around tethered insects and of the peak power to mean power ratio of the songs gave values for the mean power of the song of 3.15-7 mW; these correspond to an energy per song pulse of 13.5-30 microJ. Previously reported mean values are 3. 15 mW for protest song and 5.1 mW for calling song. The efficiency of transduction of mechanical energy into sound energy is between 18 and 46 %.
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Carrión, Elena Ángela, Pedro Ignacio Saez, Juan Carlos Pomares, and Antonio Gonzalez. "Average Force of Deployment and Maximum Arrest Force of Energy Absorbers Lanyards." International Journal of Environmental Research and Public Health 17, no. 20 (October 20, 2020): 7647. http://dx.doi.org/10.3390/ijerph17207647.
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Energy-absorbing lanyards (EAL) are part of fall arrest systems (FAS), their main mission is to dissipate the energy generated during the fall, ensuring that the arresting force does not cause injury to the user. For the design of FAS as set out in the American standard Z359.6 and the Canadian Z259.16 it is essential to know the deployment force or average arrest force (Fa). Fa is necessary to estimate the elongation that the absorber will suffer during the fall and therefore essential data to calculate the clearance distance. There is a lack of useful experimental data for the design of this personal protective equipment (PPE). This work provides empirical data required for the design of FAS with EAL in accordance with EN 355. This paper covers different types of EAL that are marketed internationally; different empirical data, average and maximum forces, required for improving safety design are researched. Six manufacturers, 10 models, and 2 samples of each model were selected, with total of 20 tests being performed. Dynamic performance tests were carried out, the free fall of a person was simulated using a 100 kg steel ballast from the maximum height allowed by the equipment, obtaining the maximum arrest force (Fm), average deployment force (Fa), and, by calculating the balance of forces, the maximum and average acceleration suffered by the ballast during its arrest. In light of the results, relevant conclusions for user safety are obtained. It is feasible to raise the safety requirements established by the different standards. The Fm can be established below 6 kN in the EAL, and the Fa can be estimated at 87.5% of the Fm. The categorization of the force–time curve in fall arrest with EAL has been obtained. Two EAL purchased on the market exceed the Fm permitted, therefore it is recommended to increase the quality controls of EAL.
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Shiratani, Masaharu, Masahiro Soejima, Hyun Woong Seo, Naho Itagaki, and Kazunori Koga. "Fluctuation of Position and Energy of a Fine Particle in Plasma Nanofabrication." Materials Science Forum 879 (November 2016): 1772–77. http://dx.doi.org/10.4028/www.scientific.net/msf.879.1772.
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We are developing plasma nanofabrication, namely, nanoand micro scale guided assembly using plasmas. We manipulate nanoand micro objects using electrostatic, electromagnetic, ion drag, neutral drag, and optical forces. The accuracy of positioning the objects depends on fluctuation of position and energy of a fine particle (= each object) in plasmas. Here we evaluate such fluctuations and discuss the mechanism behind them. In the first experiment, we grabbed a fine particle in plasma using an optical tweezers. The fine particle moves in a potential well made by the optical tweezers. This is a kind of Brownian motion and the position fluctuation can be caused by neutral molecule collisions, ion collisions, and fluctuation of electrostatic force. Among theses possible causes, fluctuation of electrostatic force may be main one. In the second experiment, we deduced interaction potential between two fine particles during their Coulomb collision. We found that there exist repulsive and attractive forces between them. The repulsive force is a screened Coulomb one, whereas the attractive force is likely a force due to a shadow effect, a non-collective attractive force. Moreover, we noted that there is a fluctuation of the potential, probably due to fluctuation of electrostatic force. These position and potential energy fluctuations may limit the accuracy of guided assembly using plasmas.
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Xu, Xipeng, Yuan Li, and Stephen Malkin. "Forces and Energy in Circular Sawing and Grinding of Granite." Journal of Manufacturing Science and Engineering 123, no. 1 (March 1, 2000): 13–22. http://dx.doi.org/10.1115/1.1344900.
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An investigation is reported of the forces and energy in circular sawing and grinding of gray granite. Measurements were made of the forces and power over a wide range of sawing and grinding conditions. Calculated tangential force components were found to be much different than the measured horizontal force components for sawing, but the two forces were almost identical for grinding. The location of the resultant force was proportionally further away from the bottom of the cutting zone with longer contact lengths. For sawing, the normal force per grain was nearly proportional to the calculated undeformed chip thickness. The G-ratios at different sawing rates reached a maximum value at the same intermediate undeformed chip thickness, which was attributed to a transition in the diamond wear mechanism from attrition to fracture at a critical normal force per grain. SEM observations indicated material removal mainly by brittle fracture, with some evidence of ductile plowing especially for grinding and to a lesser extent for sawing. The corresponding fracture energy was estimated to constitute a negligible portion of the total energy expenditure. About 30 percent of the sawing energy might be due to the interaction of the swarf with the applied fluid and bond matrix. Most of the energy for sawing and grinding is attributed to ductile plowing. Analogous to recent studies on grinding of ceramics and glass, the power per unit width was found to increase linearly with the generation of plowed surface area per unit width.
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Rodgers, Geoffrey W., J. Geoffrey Chase, and John B. Mander. "Repeatability and High-Speed Validation of Supplemental Lead-Extrusion Energy Dissipation Devices." Advances in Civil Engineering 2019 (January 13, 2019): 1–13. http://dx.doi.org/10.1155/2019/7935026.
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Recent research on supplemental damping enabling low to no damage structures has led to new devices, such as lead-extrusion-based high force-to-volume (HF2V) devices. They provide significant energy dissipation and force capacity in a small volume, enabling a range of novel low to no damage connections and systems. However, despite several research study tests and a limited range of velocity testing, they have never been tested across a realistic velocity range or for robustness to manufacture and design across several devices. These issues are hurdles that limit professional design uptake and add uncertainty and risk to their use in design. To address them, a serious damage-free dissipation device characterise its force capacity and variability due to manufacture (repeatable quasistatic force) and velocity input (peak force to connections). These outcomes are critical to size all the connections and foundations for the resultant demands and ensure robust, effective design. This manuscript presents the quasistatic testing of 96 devices designed for the same quasistatic force capacity, as well as high-speed prototype testing at velocities up to 200 mm/sec. Quasistatic tests show device forces vary with standard deviation,σ< 6.2% of design and average force. Peak input velocities of ∼200 mm/s produced peak resistive forces of ∼350 kN and increasingly weak velocity dependence as device input velocity increased, which is an advantage as it limits large demand forces to connecting elements and surrounding structure if larger than expected response velocities occur. Overall, the devices show stable hysteretic performance, with slight force reduction during high-speed testing due to heat build-up and softening of the lead working material. This testing quantified important HF2V device dynamics and robustness for designers and is an important step towards design uptake.
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Campos, Luiz M. B. C., and Manuel J. S. Silva. "On the Countering of Free Vibrations by Forcing: Part I—Non-Resonant and Resonant Forcing with Phase Shifts." Applied Mechanics 3, no. 4 (December 3, 2022): 1352–84. http://dx.doi.org/10.3390/applmech3040078.
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The question addressed is whether the free oscillations of a continuous system can be suppressed, or at least the total energy reduced, by applying external forces, using as example the linear undamped transverse oscillations of a uniform elastic string. The non-resonant forcing at an applied frequency, distinct from all natural frequencies, does not interact with the normal modes, whose energy is unchanged, and adds the energy of the forced oscillation, thus increasing the total energy, that is the opposite of the result being sought. The resonant forcing at an applied frequency, equal to one of the natural frequencies, leads to an amplitude growing linearly with time, and hence the energy is growing quadratically with time, implying an increase in total energy after a sufficiently long time. A reduction in total energy is possible over a short time, say over the first period of oscillation, by optimizing the forcing. In the case of a concentrated force, by optimizing its magnitude and location, the total energy with forcing in one period is reduced by a modest maximum of 2% relative to the free oscillation alone. The conclusion is similar for several concentrated forces. In the case of a continuously distributed force, by optimizing the spatial distribution, it is possible to reduce the energy of the total oscillation to one-fourth of that of the free oscillation over the first period of vibration. This shows that continuously distributed forces are more effective at vibration suppression than point forces.
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Gottschall, Jinger S., and Rodger Kram. "Energy cost and muscular activity required for leg swing during walking." Journal of Applied Physiology 99, no. 1 (July 2005): 23–30. http://dx.doi.org/10.1152/japplphysiol.01190.2004.
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To investigate the metabolic cost and muscular actions required for the initiation and propagation of leg swing, we applied a novel combination of external forces to subjects walking on a treadmill. We applied a forward pulling force at each foot to assist leg swing, a constant forward pulling force at the waist to provide center of mass propulsion, and a combination of these foot and waist forces to evaluate leg swing. When the metabolic cost and muscle actions were at a minimum, the condition was considered optimal. We reasoned that the difference in energy consumption between the optimal combined waist and foot force trial and the optimal waist force-only trial would reflect the metabolic cost of initiating and propagating leg swing during normal walking. We also reasoned that a lower muscle activity with these assisting forces would indicate which muscles are normally responsible for initiating and propagating leg swing. With a propulsive force at the waist of 10% body weight (BW), the net metabolic cost of walking decreased to 58% of normal walking. With the optimal combination, a propulsive force at the waist of 10% BW plus a pulling force at the feet of 3% BW the net metabolic cost of walking further decreased to 48% of normal walking. With the same combination, the muscle activity of the iliopsoas and rectus femoris muscles during the swing phase was 27 and 60% lower, respectively, but the activity of the medial gastrocnemius and soleus before swing did not change. Thus our data indicate that ∼10% of the net metabolic cost of walking is required to initiate and propagate leg swing. Additionally, the hip flexor muscles contribute to the initiation and propagation leg swing.
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Yilmaz, Cagri, and Eyup Sabri Topal. "Virial and Energy Dissipation in Measurement of Dynamic Acoustic Forces Using Bimodal-frequency Excitation of Micro-cantilever Array." Academic Perspective Procedia 4, no. 1 (October 16, 2021): 332–40. http://dx.doi.org/10.33793/acperpro.04.01.50.
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Virial and energy dissipation, related to oscillation observable responses, possess complementary information regarding acoustic force measurements. In this paper, we introduce a mathematical framework describing the analytic relationship between oscillation observables and energy quantities at the second eigenmode in the measurement of dynamic acoustic forces. We utilize a bimodal-frequency excitation scheme for actuation of the micro-cantilever array to obtain high-sensitivity frequency bands. Herein, we analyze the virials of acoustic force interaction and the energy dissipation levels on the domain of acoustic force frequency. For our case, we obtain the high-frequency bands of around 200-270 kHz and 440-570 kHz for the force strengths in the range of 4.0-36.0 pN. In addition, results of virials and dissipated power with respect to acoustic force strengths are introduced for low- and high-sensitivity frequency regions. Therefore, the energy quantities can be robustly utilized to determine high-sensitivity frequency windows in the measurement of dynamic acoustic forces.
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Cheng, Xian Guo, and Wei Jun Liu. "A New Method for Deformation of B-Spline Surfaces." Advanced Materials Research 139-141 (October 2010): 1260–63. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.1260.
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This paper presents an efficient method for deforming B-spline surfaces, based on the surface energy minimization. Firstly, using an analogy between the B-spline surface patch and the thin-plate element of the finite element method, and applying external forces on the surface with some given geometric constraints, the forces can locate on part of the surface or the surface. Then, the energy of the B-spline surface can change with the change of the forces. Finally, a new B-spline surface is generated by solving an optimization problem of change of the energy. The forces can be a single force, a distributed force and set of isolated force. The method can accomplish easily local deformation and total deformation of the B-spline surface.
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Kabutey, A., D. Herák, O. Dajbych, M. Divišová, W. E. Boatri, and R. Sigalingging. "Deformation energy of Jatropha curcas L. seeds under compression loading." Research in Agricultural Engineering 60, No. 2 (June 30, 2014): 68–74. http://dx.doi.org/10.17221/15/2012-rae.
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The present research is a follow-up of the previous studies on mechanical behaviour of Jatropha curcas L. seeds under compression loading. The research describes in detail the deformation energy which was determined from the area under the force-deformation curve. The compression device ZDM 50-2313/56/18 with a chart recorder and pressing vessel of diameter 76 mm were used to record the force-deformation functions of varying moisture content between 8.46% and 36.50% w.b. of Jatropha curcas L. seeds. Under the force-deformation curve, three main descriptions namely the increasing function (smooth curve), wave-effect characteristics (serration effect) and whole area under the force-deformation curve were analysed. For each of the force-deformation curve descriptions, it was found that moisture content influenced the values of compressive force, deformation, deformation energy and seed hardness. Interestingly, the research findings conclude that moisture content is a primary factor contributing to the wave-effect characteristics on the force-deformation curve.
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Matsumura, Takashi, Motohiro Shimada, Kazunari Teramoto, and Eiji Usui. "Predictive Cutting Force Model and Cutting Force Chart for Milling with Cutter Axis Inclination." International Journal of Automation Technology 7, no. 1 (January 5, 2013): 30–38. http://dx.doi.org/10.20965/ijat.2013.p0030.
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A force model for milling with cutter axis inclination is presented. The model predicts the cutting force and chip flow direction. Three-dimensional chip flow is interpreted as a piling up of the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities in the inclined coordinate system with a ball end mill. The chip flow direction is determined to minimize the cutting energy consumed into the shear energy on the shear plane and the friction energy on the rake face. Then, the cutting force is predicted in the chip flow determined model. The presented cutting model is verified by comparing the predicted cutting forces to the measured forces in the actual cutting tests. As an advantage of the presented force model, the change in the chip flow direction during one rotation of the cutter is also predicted in the simulation for the cutter axis inclination and the cutting parameters. In the simulation, the effect of cutter axis inclination on the cutting process is discussed in terms of the tool wear and surface finish. The cutting force charts, in which the maximum values of the positive and the negative cutting forces are simulated for the inclination angles, are presented to review the cutter axis inclination. The applicable cutter axis inclination can be determined by taking into account the thresholds of the cutting force components.
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Setúbal, Fábio Antônio do Nascimento, Sérgio de Souza Custódio Filho, Newton Sure Soeiro, Alexandre Luiz Amarante Mesquita, and Marcus Vinicius Alves Nunes. "Force Identification from Vibration Data by Response Surface and Random Forest Regression Algorithms." Energies 15, no. 10 (May 20, 2022): 3786. http://dx.doi.org/10.3390/en15103786.
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Several dynamic projects and fault diagnosis of mechanical structures require the knowledge of the acting external forces. However, the measurement of such forces is often difficult or even impossible; in such cases, an inverse problem must be solved. This paper proposes a force identification method that uses the response surface methodology (RSM) based on central composite design (CCD) in conjunction with a random forest regression algorithm. The procedure initially required the finite element modal model of the forced structure. Harmonic analyses were then performed with varied parameters of forces, and RSM generated a dataset containing the values of amplitude, frequency, location of forces, and vibration acceleration at several points of the structure. The dataset was used for training and testing a random forest regression model for the prediction of any location, amplitude, and frequency of the force to be identified with information on only the vibration acquisition at certain points of the structure. Numerical results showed excellent accuracy in identifying the force applied to the structure.
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Zhang, Yuchen, Zhenquan Zhang, Jun Wang, Jian Qin, Shuting Huang, Gang Xue, and Yanjun Liu. "Research on Excitation Estimation for Ocean Wave Energy Generators Based on Extended Kalman Filtering." Energies 17, no. 3 (February 1, 2024): 704. http://dx.doi.org/10.3390/en17030704.
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Wave energy generation methods have significant energy costs. The implementation of sophisticated control techniques in wave energy generators can lower the cost of power generation by optimizing the energy recovered from wave energy converters (WECs). To determine control inputs, most control systems rely on knowledge of the wave excitation force, including information on past, present, and future excitation forces. For the excitation of WEC devices, wave excitation force can only be inferred and predicted because it is an unmeasurable quantity. One of the more widely used observers in wave excitation estimates at the moment is the Kalman filter, but its use is primarily restricted to linear Kalman filtering. The mooring system is an integral component of floating wave energy producers. The mooring force of the device is actually nonlinear; however, the majority of current studies on excitation estimates for wave energy producers based on Kalman filter methods employ an ideal motion model based on the linearization of the mooring force. This paper, in an attempt to make things more realistic, creates a WEC system with highly nonlinear mooring forces, suggests a way to build a wave excitation force estimator for a nonlinear WEC system using the extended Kalman filtering method, and assesses the impact of various factors, such as measurement noise, random phase, and the number of equal-energy methods dividing the frequency, on the accuracy of the wave excitation force estimate.
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Franji?, Siniša. "In Shortly about Energy and Energy Sources." Advances in Politics and Economics 4, no. 4 (October 25, 2021): p1. http://dx.doi.org/10.22158/ape.v4n4p1.
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Energy is an effective force, a life activity, a determination. Energy in physics is the ability of a body or system to do some work; a quantity that characterizes the motion, rest, or position of a body, liquid, particle, or system of particles, and a quantity to describe field particles transmitted by natural forces and particle interactions. Energy appears in nature, technology and industry in various forms that are transformed into each other according to the principle of energy conservation: it cannot be spend or created, but only change its form. An energy source is any substance which serves as a raw material in the process of obtaining energy.
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Mori, Kunio, Satoshi Kaneda, Kentaro Kanae, Hidetoshi Hirahara, Yoshiyuki Oishi, and Akira Iwabuchi. "Influence on Friction Force of Adhesion Force between Vulcanizates and Sliders." Rubber Chemistry and Technology 67, no. 5 (November 1, 1994): 797–805. http://dx.doi.org/10.5254/1.3538711.
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Abstract The effects of vulcanizate and slider surface free energy—as well as the adhesion force (P) between them—on friction the force (F) and the coefficient of friction (μ) has been investigated. SBR and NBR vulcanizates were prepared using three molds differing in surface free energy. The mold with a high surface free energy gave a vulcanizate surface possessing polar groups. The mold with low surface energy gave a vulcanizate surface with many nonpolar groups. The coefficient of friction increased with the surface free energy of SBR and NBR vulcanizates. With SBR vulcanizate (surface free energy, 31.3 mJ·m−2) and teflon slider (surface free energy, 28.1 mJ·m−2) combination having the least surface free energy, the coefficient of friction was constant at greater than a 0.2N load. With vulcanizates and an aluminum slider with high surface free energy, friction force could be detected even at zero load because of the adhesion force at the interface. Friction force increased linearly with adhesion force between vulcanizates and sliders when the physical properties of the vulcanizates and net work chain density were constant. The present results clearly demonstrate the contribution of adhesion force to the friction of vulcanizates.
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Frommer, Nicole, and Po Wen Cheng. "Sensitivity analysis of parameters impacting the performance of an energy ship using airborne wind energy." Journal of Physics: Conference Series 2767, no. 7 (June 1, 2024): 072018. http://dx.doi.org/10.1088/1742-6596/2767/7/072018.
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Abstract This study assesses the impact of different model parameters on the power performance of energy ship systems using point-mass models, focusing on two operational modes. The first mode involves a kite operating in a pumping mode with adjustable tether lengths, aided by additional propellers for ship propulsion. It utilizes a quasi-steady kite model coupled with ship motion’s drag force and velocity triangles. The second mode features a kite pulling the ship, while underwater hydraulic turbines harness energy from ship velocity. Derived from a sail-based model, calculations deploy the force balance equation in line with ship motion, considering the drag forces of the ship and hydraulic turbines, alongside the propulsive force resulting from the kite’s interaction with the ship. The investigated parameters influencing the power performance include kite surface, ship length, wind speed, the angle between the ship’s motion direction and wind direction, and, for the pumping mode, ship speed. The power production of the propulsion mode is generally lower, with differences of at least 72%, depending on the combination of considered parameters.
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Moe, G., and Z. J. Wu. "The Lift Force on a Cylinder Vibrating in a Current." Journal of Offshore Mechanics and Arctic Engineering 112, no. 4 (November 1, 1990): 297–303. http://dx.doi.org/10.1115/1.2919870.
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This paper reports an extensive program of forced and free vibration tests on a single circular cylinder moving mainly perpendicularly to a uniform current. For both free and forced vibration tests, two cases were investigated: one in which the cylinder was restrained in the in-line direction and the other in which it was supported on suitable springs. The cross-flow vibrational response and hydrodynamic forces on the cylinder were measured. Large variations of motion frequency in the “lock-in” range were found from the free vibration tests. This leads to two different definitions of reduced velocity, namely, a so-called nominal reduced velocity based on one reference frequency and the true reduced velocity based on the actual vibration frequency. When different results are compared, the true reduced velocity should be used. The forced vibration tests showed, as may be expected, that the transverse force in the “lock-in” range on the average will add energy to the cylinder at moderate motion amplitudes and subtract energy at large amplitudes. Some conditions resulting in a steady-state vibration of a flexibly mounted cylinder were analyzed. The actual force traces also show very large and apparently random deviations from the average force amplitude. The results from the forced and the free vibration tests are consistent with each other if the true reduced velocity and reduced amplitude are the same.
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Ahmed, Rizwan, Christian Maria Firrone, and Stefano Zucca. "Design and Calibration of a Tri-Directional Contact Force Measurement System." Applied Sciences 11, no. 2 (January 19, 2021): 877. http://dx.doi.org/10.3390/app11020877.
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In low pressure turbine stages, adjacent blades are coupled to each other at their tip by covers, called shrouds. Three-dimensional periodic contact forces at shrouds strongly affect the blade vibration level as energy is dissipated by friction. To validate contact models developed for the prediction of nonlinear forced response of shrouded blades, direct contact force measurement during dynamic tests is mandatory. In case of shrouded blades, the existing unidirectional and bi-directional contact force measurement methods need to be improved and extended to a tri-directional measurement of shroud contact forces for a comprehensive and more reliable validation of the shroud contact models. This demands an accurate and robust measurement solution that is compatible with the nature and orientation of the contact forces at blade shrouds. This study presents a cost effective and adaptable tri-directional force measurement system to measure static and dynamic contact forces simultaneously in three directions at blade shrouds during forced response tests. The system is based on three orthogonal force transducers connected to a reference block that will eventually be put in contact with the blade shroud in the test rig. A calibration process is outlined to define a decoupling matrix and its subsequent validation is demonstrated in order to evaluate the effectiveness of the measurement system to measure the actual contact forces acting on the contact.
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Mirahmadi, Marjan-S., Amir H. Fatollahi, and Mohammad Khorrami. "The similarity of attractive and repulsive forces on a lattice." Modern Physics Letters A 30, no. 23 (July 20, 2015): 1550112. http://dx.doi.org/10.1142/s0217732315501126.
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On a lattice, as the momentum space is compact, the kinetic energy is bounded not only from below but also from above. It is shown that this somehow removes the distinction between repulsive and attractive forces. In particular, it is seen that a region with attractive force would appear forbidden for states with energies higher than a certain value, while repulsive forces could develop bound-states. An explicit transformation is introduced which transforms the spectrum of a system corresponding to a repulsive force, to that of a similar system corresponding to an attractive force. Explicit numerical examples are presented for discrete energies of bound-states of a particle experiencing repulsive force by a piecewise constant potential. Finally, the parameters of a specific one-dimensional (1D) translationally invariant system on continuum are tuned so that the energy of the system resembles the kinetic energy of a system on a 1D lattice. In particular, the parameters are tuned so that while the width of the first energy band and its position are kept finite, the gap between the first energy band and the next energy band goes to infinity, so that effectively only the first energy band is relevant.
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BRECHET, SYLVAIN D., ALEXANDRE ROULET, and JEAN-PHILIPPE ANSERMET. "MAGNETOELECTRIC PONDEROMOTIVE FORCE." Modern Physics Letters B 27, no. 21 (August 11, 2013): 1350150. http://dx.doi.org/10.1142/s0217984913501509.
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The dynamics of a system consisting of a matter continuum with a weak linear magnetoelectric coupling interacting with electromagnetic fields is examined on a local scale in a nonrelativistic limit. A consistent expression for the internal energy of the system is derived. The internal energy density and the continuity equation for the momentum lead to the derivation of ponderomotive forces. A nonuniform magnetoelectric coupling generates a "magnetoelectric" ponderomotive force that could be distinguished from the purely electric or magnetic ponderomotive forces by applying alternating electric and magnetic fields at distinct frequencies.
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Yi, Yan. "Force and energy in gravitational field." Physics Essays 34, no. 1 (March 22, 2021): 28–34. http://dx.doi.org/10.4006/0836-1398-34.1.28.
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This is the second paper of the induction theory of gravitational field. In the first paper, a new space-time view, which considers the influence of gravity, was constructed. In the new view of time and space, classical mechanics no longer holds. In this paper, the theory of mechanics and energy is established in the new space-time relation. In this paper, the basic mechanical law in the new space-time relationship is derived from the inertial force of the observed object relative to the reference object. Second, according to this basic law, the new formulas of gravitation and electromagnetic force in the space-time relationship are derived. Third, the influence of the moving of the observation object on the force is discussed. Finally, the new law of mass energy conversion is discussed.
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Lane, Nick. "Life force: why energy shapes evolution." Biochemist 37, no. 5 (October 1, 2015): 6–11. http://dx.doi.org/10.1042/bio03705006.
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Life on earth began some 4 billion years ago, but then got stuck at the level of bacteria for more than 2 billion years. The complex ‘eukaryotic’ cell arose abruptly in a singular event around 1.5–2 billion years ago. All eukaryotes share a long list of complex traits, from the nucleus to sex and senescence, which are all but unknown in bacteria. Why are humans so similar to mushrooms at the level of cells, even though we live so differently? Why did evolution follow such a peculiar trajectory? The answers might lie in the equally strange mechanism by which all cells generate ATP: chemiosmotic coupling.
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Bays, Jennifer L., and Kris A. DeMali. "It takes energy to resist force." Cell Cycle 16, no. 19 (September 1, 2017): 1733–34. http://dx.doi.org/10.1080/15384101.2017.1360654.
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Ji, Yan. "The Attract Force Equation of Energy." American Journal of Modern Physics 3, no. 6 (2014): 224. http://dx.doi.org/10.11648/j.ajmp.20140306.13.
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Slaughter, Julie, Jim Kosterman, Barry Arbetter, and Eric Summers. "A galfenol force-based energy harvester." Journal of the Acoustical Society of America 126, no. 4 (2009): 2276. http://dx.doi.org/10.1121/1.3249328.
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Suntola, Tuomo. "Fundamental Concepts − from Force to Energy." International Journal of Astrophysics and Space Science 2, no. 6 (2014): 46. http://dx.doi.org/10.11648/j.ijass.s.2014020601.16.
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Shevchenko, Volodymyr, and Heorhii Shevchenko. "Energy-force interactions in vibroimpact systems." IOP Conference Series: Earth and Environmental Science 1156, no. 1 (April 1, 2023): 012026. http://dx.doi.org/10.1088/1755-1315/1156/1/012026.
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Abstract The energy-force interactions in vibroimpact systems are studied according to the developed universal mathematical model, which simulates multi-mass vibroimpact systems, the masses of which are connected to each other and to a fixed base by nonretaining one-sided and retaining two-sided elastic bonds, with the excitation of these systems by inertial debalanced vibrators driven by a limited power The results of the research indicate a higher efficiency of vibrations of vibroimpact systems in comparison with a non-vibroimpact system of similar parameters. The highest energy efficiency of oscillations of vibroimpact systems and, accordingly, their maximum efficiency takes place at the excitation parameters that precede the disruption of vibroimpact oscillations. At the same time, maximum accelerations and reactions in their elastic bonds are excited in the systems. Based on this, it is necessary to accept the maximum permissible acceleration of the elements of their constructions as criteria for choosing rational process parameters in viboimpact systems, which ensures the reliability and durability of their operation.
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Teoh, Choe-Yung. "Design of Two-Stage Force Amplification Frame for Piezoelectric Energy Harvester." Journal of Mechanical Engineering 20, no. 3 (September 15, 2023): 49–62. http://dx.doi.org/10.24191/jmeche.v20i3.23900.
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This paper describes the design of a two-stage force amplification frame for the piezoelectric energy harvester to capture mechanical energy from walking human footsteps. The frame design optimises the stress distribution to improve the force amplification ratio on the existing footstep energy harvesters. The magnification of the input force exerted on a piezoelectric stack increases the system's power output. A combination of single and compound two-stage frame design with additional linkage support was proposed, which maximise the conversion of tension to compression forces. The proposed frame also significantly reduces the maximum displacement of the frame to ensure walking comfort. The frame is tested with the input force of 85 N to 120 N based on the adult footstep during walking and running. The simulated results show that the proposed frame has a force amplification ratio of 25.3, an 11.85% improvement from the existing frames. The frame also limits the maximum displacement to 1.02 mm, 22.14% compared to the existing frames.
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Gaidamak, Oleg. "STUDY OF AN ENERGY-SAVING DIE FOR RADIAL REDUCTION." ENGINEERING, ENERGY, TRANSPORT AIC, no. 4(119) (December 23, 2022): 90–95. http://dx.doi.org/10.37128/2520-6168-2022-4-11.
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Reducing the power of forging and pressing equipment is an important task of modern metal forming technologies. The article is devoted to the development and research of dies capable of significantly (tens or more times) reducing the power of the used forging and pressing equipment due to the use of energy-saving dies that can significantly increase the deforming force. A stamp capable of significantly increasing the deforming force is called energy-saving . The article shows that using different types of levers, it becomes possible to significantly increase the useful force of stamping tools acting on a deformable workpiece. Thus, it becomes possible to use relatively low-power pressing equipment to achieve significant forces of the working tool. Based on the given mathematical dependences of the geometric and power characteristics of the energy-saving stamp, a computer program was developed in MS Excel and modeling was carried out, with the help of which it was studied how the deforming force R changes depending on the change in the angle of inclination of the punches and the corresponding graph was plotted at a predetermined constant pushing force F = 1 N. After analyzing the resulting graph, it can be argued that a tenfold increase in the deforming force R compared to the pushing force F, which is created by the pressing equipment, is observed at an angle of = 5.35 degrees, fifty times at an angle of 1.1 degrees. At angles approaching 0 degrees, the increase in the deforming force can reach significant values and is limited only by the strength of the energy-saving stamp itself. Calculation formulas are given that allow calculating the main dimensions of the punches and the working stroke of the forging and pressing equipment for a given working stroke of the punches and a given increase in the deforming force. Possible areas of application of the energy- saving stamp are shown.
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Esposito, Daniele, Sergio Savino, Chiara Cosenza, Emilio Andreozzi, Gaetano Dario Gargiulo, Caitlin Polley, Giuseppe Cesarelli, Giovanni D’Addio, and Paolo Bifulco. "Evaluation of Grip Force and Energy Efficiency of the “Federica” Hand." Machines 9, no. 2 (January 27, 2021): 25. http://dx.doi.org/10.3390/machines9020025.
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The actual grip force provided by a hand prosthesis is an important parameter to evaluate its efficiency. To this end, a split cylindrical handlebar embedding a single-axis load cell was designed, 3D printed and assembled. Various measurements were made to evaluate the performances of the “Federica” hand, a simple low-cost hand prosthesis. The handlebar was placed at different angular positions with respect to the hand palm, and the experimental data were processed to estimate the overall grip force. In addition, piezoresistive force sensors were applied on selected phalanxes of the prosthesis, in order to map the distribution of the grasping forces between them. The electrical current supplied to the single servomotor that actuates all the five fingers, was monitored to estimate the force exerted on the main actuator tendon, while tendon displacement was evaluated by a rotary potentiometer fixed to the servomotor shaft. The force transfer ratio of the whole system was about 12.85 %, and the mean dissipated energy for a complete cycle of closing-opening was 106.80 Nmm, resulting lower than that of many commercial prostheses. The mean grip force of the “Federica” hand was 8.80 N, that is enough to support the user in many actions of daily life, also considering the adaptive wrapping capability of the prosthesis. On average, the middle phalanges exerted the greatest grip force (2.65 N) on the handlebar, while the distal phalanges a force of 1.66 N.
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Tiwari, Puja, Prof M.N Bandyopadhyay, Satakshi Chatterjee, and Prof S. N. Bandyopadhyay. "Expansion of the universe and its correlation with dark energy." International Journal of Advanced Astronomy 8, no. 1 (May 15, 2020): 10. http://dx.doi.org/10.14419/ijaa.v8i1.30599.
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The Universe is expanding and science has got the relevant amount of evidence to prove that. The red shift of the distant galaxies prove that the Universe is expanding and at a good rate. The trouble is not with the expansion rather the force that is helping in this expansion. The Four Forces that is understood by physics are Gravitational Force, Electromagnetic Force, The Weak Force and The Strong Force. The four forces mentioned above unfortunately does not help in understanding the expansion of the Universe even after 13.8 billion years from the Big Bang. Initially it was thought that the Universe had an exponential expansion just after the Big Bang and this expansion will slow down before Gravity starts contracting the Universe. Well this theory got a setback after the Red Shift of the Galaxies showed that the Universe is still expanding.The expansion is happening still which means that the Gravitational Force is not being able to drift the galaxies towards one another. So what could be the unknown force that is repelling the galaxies from one another? Scientists have been working on this issue and many new concepts have been developed. Many scientists have argued that there is some force that is repelling the Universe but understanding this force has been difficult till now. Major scientists now agree that there is a force that is repelling the Universe and this force is not the four fundamental forces that are known to us. They have termed this force as the Dark Energy.What is this Dark Energy is a haunting question in today’s world. Only around 5% of the observable Universe is known till date. The rest around 95% is still a mystery to us. Of that 95% around 68% is Dark Energy. So the importance of understanding this force is the need of the hour. This force can tell a lot about the formation of the Universe from the start or it can even enlighten us if the Universe is eternal.The issue is as of now, this Dark Energy is hypothetical in nature as it has not been seen or felt by the instruments available to science today. The idea of Dark Energy goes to explain the expansion of the Universe, if Dark Energy is taken as some sort of Anti- Gravitational Force.Einstein’s theory of relativity talks of how space and time is intermingled with gravity. According to this theory space time gets modified due to the amount of matter that falls into the space. So if a planet sits on a space in the Universe it will cause a deviation in the space time field in such a way that it will accommodate the matter of the planet. So Einstein placed time as the fourth dimension and showed its importance in space. This theory stands true in majority of the cases in the Universe. The only hurdle being that inside the Black Hole this theory falters.Einstein and Schrodinger did interact with one another after he had understood that the Universe was expanding through the theory presented by Hubble. Earlier Einstein had stated that the Universe was Static. To counter the exigency that space time changes with matter he had proposed a constant by the name Cosmological Constant. Later he took the constant away stating that it was his blunder not to understand that the Universe was Expanding. Schrodinger had proposed to put the Cosmological Constant in the right side of the equation. This meant the constant may change with time and be considered more of a variable force. Though, Einstein later did not agree to the idea. Still it can be considered that both of them were talking about an extra force but could not come to any conclusion on this.Einstein in his special relativity theory had talked of conversion of energy to matter with his famous equation, E=mc^2. This meant that energy can be formed by matter and matter can be converted into energy. Though energy created from matter can be seen in Atom Bomb but matter created from energy is not seen. This paper will try to show how matter can be created from energy where Dark Energy acts as a Catalyst.This paper also tries to analyze the concept of Dark Energy as a non interacting supermassive energy (NISE). The paper will try to see the relationship between expanding Universe and Dark energy. The paper will try to develop a new spectrum that can make Dark Energy or NISE as stated in the paper visible or understandable. The paper will also like to see the relationship between Dark Energy and Photon. The paper will try to show how energy is converted from matter with the help of Dark Energy.
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Naizabekov, Abdrakhman B., Sergey N. Lezhnev, and Evgeniy Panin. "Experimental Study of Energy Force Parameters of Combined Process "Rolling - ECA-Pressing"." Materials Science Forum 946 (February 2019): 850–55. http://dx.doi.org/10.4028/www.scientific.net/msf.946.850.
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The article is devoted to the study of energy-force parameters of combined process "rolling-equal-channel angular pressing". The objectives of the work were to determine the forces of rolling and pressing in the deformation by this combined method. The strength calculation of the matrix and the experiment on deformation of AISI 6063 aluminum samples were carried out. During the experiment, the force values were recorded using a tensometric station. The results of the strength analysis showed that this matrix design is suitable for creating an experimental stand of combined process "rolling – equal-channel angular pressing", since the calculated safety margin is sufficient to implement the pressing under extreme conditions. Analysis of the results of force measurement showed that rolling forces at all stages of deformation exceed the corresponding pressing forces, which is a necessary condition for the implementation of this combined process. The obtained results can be used in the design of experimental stands that implement investigated combined process. At the same time, the used tensometric technique for studying strength characteristics is suitable for the case of calibrated rolls.
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Czupy, I., and E. Horváth-Szováti. "Vertical force requirement for stump lifting." Journal of Forest Science 59, No. 7 (August 28, 2013): 267–71. http://dx.doi.org/10.17221/4/2013-jfs.
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In harvest areas the soil preparation is occasionally necessary before reforestation including the removal, collection and transportation of stumps from the soil. Issues related to climate change and the shortage of fossil energy sources call for an increased rate of renewable energy sources. Using the stumps removed from the soil as fuel is a significant resource for biomass. For lifting a stump together with its roots a grab mounted on a shovel is generally used. To rationalise this operation, analyses of stump lifting time have been carried out. We tested a machine mounting one grab for stump lifting on three tree types (Scots pine, robinia and poplar) and found functions correlating stump extraction force and stump diameter, which can be used in order to choose the right machine and determine the cost of the operation.
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Khodor, Jad, Kaan Özenç, Aurel Qinami, Guoyu Lin, and Michael Kaliske. "Fatigue fracture characterization by cyclic material forces in viscoelastic solids at small strain." International Journal of Fracture 233, no. 2 (January 3, 2022): 129–49. http://dx.doi.org/10.1007/s10704-021-00607-x.
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AbstractThe study at hand introduces a new approach to characterize fatigue crack growth in small strain linear viscoelastic solids by configurational mechanics. In this study, Prony series with n-Maxwell elements are used to describe the viscoelastic behavior. As a starting point in this work, the local balance of energy momentum is derived using the free energy density. Moreover, at cyclic loading, the cyclic free energy substitutes the free energy. Using the cyclic free energy, the balance of cyclic energy momentum is obtained. The newly derived balance law at cyclic loading is appropriate for each cycle. In the finite element framework, nodal material forces and cyclic nodal material forces are obtained using the weak and discretized forms of the balance of energy momentum and cyclic energy momentum, respectively. The crack driving force and the cyclic crack driving force are determined by the nodal material forces and the cyclic nodal material forces, respectively. Finally, numerical examples are shown to illustrate path-independence of the domain integrals using material forces and cyclic material forces. The existence of the balance of energy momentum and cyclic energy momentum are also illustrated by numerical examples.