Energy Theorem Research Articles

Elliptical orbit constraint of a small ring under the influence of gravity and sliding friction

We investigate the constraint problem of a small ring on non-smooth elliptical orbits. The influence mechanism of the orbital shapes on the motion velocity and constraint force of the small ring are analyzed. Taking circular orbit as an example, the influence of gravity and sliding friction on the orbital motion is given, and the results are verified by kinetic energy theorem. Finally, the characteristics of the orbital motion of the small ring at different initial velocities are analyzed.

In-plane elasticity of a novel vertical strut combined re-entrant honeycomb structure with negative Poisson’s ratio

In this study, a new vertical strut combined re-entrant auxetic structure was designed and its mechanical behaviors have been studied. An analytical model was established based on energy theorems considering bending, shearing and stretching. Numerical simulations and experiments were both carried out to confirm the validity of the analytical model based on beam theory. Results exhibited a good agreement between the refined analytical model, the numerical simulation and experimental study. Four deformation mechanisms were analyzed and the effect of deformation on the effective Poisson’s ratio (EPR) and elastic module were investigated. A parametric study was further performed to quantitatively illustrate the influences of the geometrical parameters on the effective elasticity properties of the designed structure. The results showed that the lightweight structures can significantly enhance the auxetic behavior and achieve a high degree of anisotropy with wide vertical strut lengths and internal angles compared with conventional re-entrant honeycomb configurations.

Modeling of a Symmetric Five-Bar Displacement Amplification Compliant Mechanism for Energy Harvesting.

This paper presents an analytical model to determine a closed form mathematical representation for the output displacement of a displacement amplification compliant mechanism used for energy harvesting. A symmetric five-bar compliant mechanism with right-circular and corner-filleted flexure hinges was mathematically modeled and its displacement was determined using the Castigliano energy theorem. The stresses within the flexure joints, the weakest points in the mechanism body, were calculated. The mathematical model expresses both the displacement amplification and the stresses as functions of the design parameters and the load caused by the harvester. The developed model can be used to optimize the mechanism dimensions for maximum harvested power, while minimizing its structural stresses. The mechanism was also modeled numerically using finite element methods; both the analytical and numerical models were verified experimentally. The mathematical model of the mechanism was integrated with a model representing a piezoelectric energy harvester to calculate the open-circuit voltage. As a proof of concept, experiments were performed using an unimorph piezoelectric cantilever at low-frequency (less than 1 Hz) harmonic excitation inputs. The measured open-circuit voltage was found to be in agreement with that calculated using the proposed model, when integrated with the model representing the piezoelectric beam. The power generated by the piezoelectric harvester, equipped with the proposed displacement amplification mechanism, was more than a hundred times that without amplification.

Arduino-based STEM education material: work-energy theorem

Twenty first century expertise often requires high-level and cross-disciplinary skills that ought to be a part of todays’ educational activities. Therefore, educational undertakings should be designed in such a way that students can gain the desired expertise and skills. The present work offers an Arduino-based STEM education material, specifically designed to teach the work–energy theorem. The designed physical system is experimentally resolved by directly measuring position-time trajectories which lead to instant velocities. Measured instant position values are employed to determine the amount of work and corresponding velocity values are used to determine the instant kinetic energies of the system. Experimental data, on average, lead to a ratio of 0.959 which is reasonable concerning the range of experimental error limits therefore smartly validating the work–energy theorem.

Closed-form solution and analysis of the plate twist test in sandwich and laminated composites

A new anticlastic bending solution for the deflection and rotations of laminated composite plates and sandwich panels applicable to plates under torsion or bending with opposite curvatures is developed using first-order shear deformation theory and the theorem of minimum potential energy. The novelty of the proposed solution relies on being algebraic, taking into account the overhang, employing variable shear correction factors and twisting moment (Mxy), and considering the influence of the twist (D66), bending (D11,D12,D22) and shear stiffnesses (A44,A55). A finite element model is also developed for comparison. Both approaches are validated with compliance measurements previously reported, observing good agreement (less than 10% difference with respect to experiments) for most orthotropic and isotropic plates. Because Mxy is the main driving-load of anticlastic bending, its distribution is analyzed on several plates. According to finite element modeling, Mxy attains a quarter of the applied load (P/4) within the mid-plane of a glass/epoxy 0/906s laminated composite, but it has a parabolic behavior for sandwich panels with compliant cores. Good match is obtained between compliance predictions by the first-order shear deformation theory and the finite element model for square laminate plates with aspect ratios between (8.4<width/thickness<101) and square sandwich panels with (3.9<width/thickness<59) and shear modulus ratios (from 1 to 1800) between core and face sheets.

Coupled Bending Inwards Motion and Control Strategy Analysis of a Cable-Driven Underactuated Finger

Motion strategy analysis at the pre-bending stage is a fundamental component of underactuated finger grasp research. This study presents the pre-bending motion strategy and corresponding analysis of cable driving forces a 3-DOF underactuated finger comprising cable truss units. The structure and four motion strategies at the pre-bending stage are illustrated. The equivalent joint-driven and quasi-static motion models are established in the case where one or two cable driving forces drive the finger. Quasi-static motion model is established, and four typical quasi-static coupled motion space and distributions of corresponding cable driving forces are analysed. In accordance with the kinetic energy theorem and Lagrange’s dynamical method, a sampled and general dynamic model is established. Through matrix transformation, a hypothetical “PPA” type dynamic model is obtained. On the basis of the “PPA” dynamic model, three grasping control strategies at pre-bending stage are carried out. Valid simulations and experiments are conducted to verify the accuracy of the coupled bend inwards motion and control strategy.

An Intertwining of Curvelet and Linear Canonical Transforms

In this article, we introduce a novel curvelet transform by combining the merits of the well-known curvelet and linear canonical transforms. The motivation towards the endeavour spurts from the fundamental question of whether it is possible to increase the flexibility of the curvelet transform to optimize the concentration of the curvelet spectrum. By invoking the fundamental relationship between the Fourier and linear canonical transforms, we formulate a novel family of curvelets, which is comparatively flexible and enjoys certain extra degrees of freedom. The preliminary analysis encompasses the study of fundamental properties including the formulation of reconstruction formula and Rayleigh’s energy theorem. Subsequently, we develop the Heisenberg-type uncertainty principle for the novel curvelet transform. Nevertheless, to extend the scope of the present study, we introduce the semidiscrete and discrete analogues of the novel curvelet transform. Finally, we present an example demonstrating the construction of novel curvelet waveforms in a lucid manner.

Thermal buckling of ballasted tangent track

Euler type analysis usually used for compression members in structural engineering does not work for railroad track. Euler type analytical formulas for horizontal and vertical buckling endorsed in a recent literature is reviewed to demonstrate its weakness. Using definition of moment and curvature as well as principle of equilibrium, the author suggests formula for horizontal buckling load of railroad track and demonstrates validation in context with currently accepted values, published results, and past field tests. The buckling load from suggested formula agrees with the recent buckling load formula based on total energy theorem. A formula is suggested to study the effect of misalignment on critical temperature differential or critical load. A vertical buckling load formula is derived from horizontal buckling load formula. A buckling process is narrated through step by step computation. Formulas are suggested to compute the effect of track misalignment on critical buckling load and threshold radius of a vertical curve.

Temperature-Rate-Dependent Thermoelasticity Theory With Memory-Dependent Derivative: Energy, Uniqueness Theorems, and Variational Principle

Abstract This article is focused on developing a new mathematical model on the temperature-rate-dependent thermoelasticity theory (Green–Lindsay), using the methodology of memory-dependent derivative (MDD). First, the energy theorem of this model associated with two relaxation times in the context of MDD is derived for homogeneous, isotropic thermoelastic medium. Second, a uniqueness theorem for this model is proved using the Laplace transform technique. A variational principle for this model is also established. Finally, the results for Green–Lindsay model without MDD and coupled theory are obtained from the considered model.

John Hadji Argyris (1913–2004) and the Computational Structural Analysis in the British Aircraft Engineering in the Mid-20th Century

This work deals with the context of formation of Professor Dr. John Hadji Argyris (1913-2004) in Germany during the 1930s and Switzerland during the 1940s. Using primary documentation, we elucidate publications with scientific theories of structural analysis made during his job as a member of a secret Commission in the Royal Aeronautical Society, in England. We explore the content of the serial publication of the Theorems of Energy and Structural Analysis of the Aircraft Engineering Journal, from 1954 and 1955, from Argyris’s lectures at Imperial College, London, where he was a professor and director of the Department of Aeronautical Structures. The goal of this research is to analyze the systematic method of calculation of Argyris, starting from the theory of Computational Simulation. From this point of view, the conceptual mathematical model would be a computational model based on the unification of the concepts of Elasticity Theory and Energy Theorems formulated in matrix mathematics for communication with the computer.

Stress-free-state based structural analysis and construction control theory for staged construction bridges

Structural analysis and construction control of staged construction process is a major subject for modern long-span bridges. This paper introduces the concept of stress-free-state variable of structural elements and deduces the mechanical equilibrium equations and geometric shape governing equations for staged construction structures utilizing the minimum potential energy theorem. As the core of stress-free-state theory, the two aforementioned equations demonstrate following principles, 1) when the stress-free-state variable of a structural element is set, the internal force and deformation of the element are unique at the completion state of the structure regardless of its construction process; 2) the stress-free length of a cable is independent of its external loads, change in stress-free length of the cable corresponds to a unique variation of the cable force when load is constant; and 3) the internal force of a structural element can be independent from its geometric shape within the completion state of a staged construction structure through an active manipulation of stress-free-state variables of the element. Stress-free-state theory establishes the stage-to-stage and stage-to-completion relationships for staged construction bridges, provides a direct and efficient method for theoretical calculations and a flexible and convenient approach for the control of staged construction, and makes parallel construction and auto-filtering of thermal and temporary loading effect possible.

Nernst heat theorem for an atom interacting with graphene: Dirac model with nonzero energy gap and chemical potential

We derive the low-temperature behavior of the Casimir-Polder free energy for a polarizable atom interacting with graphene sheet which possesses the nonzero energy gap $\Delta$ and chemical potential $\mu$. The response of graphene to the electromagnetic field is described by means of the polarization tensor in the framework of Dirac model on the basis of first principles of thermal quantum field theory in the Matsubara formulation. It is shown that the thermal correction to the Casimir-Polder energy consists of three contributions. The first of them is determined by the Matsubara summation using the polarization tensor defined at zero temperature, whereas the second and third contributions are caused by an explicit temperature dependence of the polarization tensor and originate from the zero-frequency Matsubara term and the sum of all Matsubara terms with nonzero frequencies, respectively. The asymptotic behavior for each of the three contributions at low temperature is found analytically for any value of the energy gap and chemical potential. According to our results, the Nernst heat theorem for the Casimir-Polder free energy and entropy is satisfied for both $\Delta > 2\mu$ and $\Delta < 2\mu$. We also reveal an entropic anomaly arising in the case $\Delta = 2\mu$. The obtained results are discussed in connection with the long-standing fundamental problem in Casimir physics regarding the proper description of the dielectric response of matter to the electromagnetic field.

BONE ORTHOTROPIC REMODELING AS A THERMODYNAMICALLY-DRIVEN EVOLUTION

In this paper, we present and discuss a model of bone remodeling set up in the framework of the theory of generalized continuum mechanics which was first introduced by DiCarlo et al. [Sur le remodelage des tissus osseux anisotropes, Comptes Rendus Mécanique 334(11):651–661, 2006]. Bone is described as an orthotropic body experiencing remodeling as a rotation of its microstructure. Thus, the complete kinematic description of a material point is provided by its position in space and a rotation tensor describing the orientation of its microstructure. Material motion is driven by energetic considerations, namely by the application of the Clausius–Duhem inequality to the microstructured material. Within this framework of orthotropic remodeling, some key features of the remodeling equilibrium configurations are deduced in the case of homogeneous strain or stress loading conditions. First, it is shown that remodeling equilibrium configurations correspond to energy extrema. Second, stability of the remodeling equilibrium configurations is assessed in terms of the local convexity of the strain and complementary energy functionals hence recovering some classical energy theorems. Eventually, it is shown that the remodeling equilibrium configurations are not only highly dependent on the loading conditions, but also on the material properties.

Analysis of average-closing-speed for medium-vacuum circuit breaker from theoretical calculation aspects

Average closing speed is an important indicator for evaluating the performance of CB, in order to calculate the average closing speed of the spring operating mechanism of the medium voltage vacuum circuit breaker, the paper establishes a simplified model of CB mechanism, combined with the kinetic energy theorem, and obtains the average closing speed by analyzing the equivalent mass and energy of the mechanism. In order to verify the correctness of the proposed method, the paper establishes a CB simulation model to obtain the simulated average closing speed. In the calculation of the energy of the open-off phase, the paper adopts a segmentation calculation method, which divides the closing process into the open-distance phase and the over-travel phase, and the calculated average closing speed is more accurate. This theoretical calculation method provides a theoretical basis for the research and development of the medium-voltage vacuum CB spring operating mechanism, and plays a positive role in related research and development work.

Construction of the bending model of micropolar elastic thin beams with a circular axis and its implementation using finite element method

This paper considers the problem of transition from the system of two-dimensional equations of the micropolar (moment) theory of elasticity in a thin curved area to the one-dimensional system of equations describing deformation of the micropolar elastic thin beam with a circular axis. During the transition process, Timoshenko's hypotheses generalized to the micropolar case are applied. As a result, the applied model (with independent fields of displacements and rotation) of a micropolar elastic thin beam with a circular axis has been constructed. It is shown that the model includes the law of conservation of energy, energy theorems and variation principles. All main functionals for the model of the micropolar elastic thin beam with a circular axis are obtained from the functional of the two-dimensional micropolar theory of elasticity, containing only the first derivatives of displacements and rotations. The finite element method (FEM) is taken to study the boundary problems of statics and dynamics of applied model of the micropolar elastic thin beam with a circular axis. The basic concepts and stages of the FEM are formulated: the discretization, the selection of basic nodal unknowns, the approximation of the solution, and the construction of the basic FEM equations. The finite-element solutions of some problems of statics and problems on natural vibrations of beams with a circular axis are considered according to the micropolar theory of elasticity. A comparative analysis with similar problems of beams with a circular axis according to the classical theory of elasticity is carried out. Based on the results, some effective properties of beams with a circular axis have been established when considering their deformations in the context of the micropolar theory of elasticity.

Work has nothing to do with energy expenditure

Abstract We show that, contrary to common sense, the author of mechanical work does not necessarily provide the required energy. By the most simple example one can ever conceive – a standing person starting to move, this point is made clear: the floor does not spend energy and it does work on the person (in relation to its own reference frame). We analyse two additional examples in order to ilustrate the subtle aspect of Newtonian theory: despite something is said about where the work is going to, namely the Work – Kinetic Energy Theorem, absolutely nothing is said about where the work comes from (we explain in our conclusions, making reference to Aristotelian philosophy, why it happens in that way). In all these examples, explicit calculations of work are done in both inertial and non-inertial frames.

Anatomy of large perpendicular magnetic anisotropy in free-standing Co/Ni (1 1 1) multilayer

We investigated the magnetic anisotropy energy (MAE) in the free-standing Co/Ni (111) multilayer as both Ni thickness dependence (tNi = 1-4MLs) and number of multilayer repetition times (N = 1–3) by means of a first-principles electronic structure calculation based on spin density functional theory. We included both contributions to the MAE from magnetocrystalline anisotropy energy (MCAE) originating from spin-orbit coupling and shape magnetic anisotropy energy (SMAE) originating from spin dipole-dipole interaction. The MCAE part was evaluated from both methods of total energy (TE) and grand-canonical force theorem (GCFT). The SMAE part was calculated by using a spin density approach (SDA). All MCAE values from the TE are well reproduced by those from the GCFT method. In N = 1, the total MAE (MCAE + SMAE) for tNi showed a perpendicular MAE (PMAE) with a maximum value of 1.67 mJ/m2 at tNi = 2MLs. The PMAE increases with increasing N. The series of tNi = 3MLs showed a linear behavior as N dependence with an increasing ratio of 0.68 mJ/m2, which is in good agreement with experimental measurement. By using the GCFT, we evaluated the atom-resolved and k-resolved MCAEs. The atom-resolved MCAE indicates that the Co/Ni interface is the main origin of PMAE. The PMAE is mainly located at Γ¯-K¯ line in the two dimensional Brillouin zone. This is attributed to large components of the d-orbitals extending along the multilayer plane on Co and Ni near the Fermi energy. We also calculated the SMAE using a discrete approach (DA) and found that there is a reduction of SMAE part in the SDA, compared to the DA. This reduction originates from a prolate quadrupole component of spin density distribution. The present comprehensive study may provide a better understanding of magnetic properties in Co/Ni multilayers as widely used in spintronic devices.

On energy, uniqueness theorems and variational principle for generalized thermoelasticity with memory-dependent derivative

The research article theoretically deals with the three-phase-lag (TPL) heat conduction model of generalized thermoelasticity, reformulated in terms of the memory-dependent derivative (MDD). The energy theorem and the variational principle of this proposed model are established for an isotropic, homogeneous, thermoelastic continuum. The uniqueness theorem is derived from the energy theorem, and a few special cases are also obtained from the present model. For numerical simulation of the present model, a one-dimensional thermoelastic problem in a semi-infinite medium subjected to a time-dependent thermal shock on its bounding plane is considered. The Laplace transform together with its numerical inversion is adopted to obtain the solutions in the physical domain. The influence of the kernel function and time delay on the variation of the non-dimensional thermophysical quantities are studied graphically and finally some remarkable points are mentioned as conclusions.

Positive energy theorem for asymptotically anti-de Sitter spacetimes with distributional curvature

We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.

Variational principles and generalized Hill’s bounds in micromechanics of linear peridynamic random structure composites

We consider a static problem for statistically homogeneous matrix linear peridynamic composite materials (CMs). The basic feature of the peridynamic model considered is a continuum description of a material behavior as the integrated non-local force interactions between infinitesimal particles. In contrast to these classical local and non-local theories, the peridynamic equation of motion introduced by Silling (J Mech Phys Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. Estimation of effective moduli of peridynamic CMs is performed by generalization of some methods used in locally elastic micromechanics. Namely, the admissible displacement and force fields are defined. The theorem of work and energy, Betti’s reciprocal theorem, and the theorem of virtual work are proved. Principles of minimum of both potential energy and complimentary energy are generalized. The strain energy bounds are estimated for both the displacement and force homogeneous volumetric boundary conditions. The classical representations of effective elastic moduli through the mechanical influence functions for elastic CM are generalized to the case of peridynamics, and the energetic definition of effective elastic moduli is proposed. Generalized Hill’s bounds on the effective elastic moduli of peridynamic random structure composites are obtained. In contrast to the classical Hill’s bounds, in the new bounds, comparable scales of the inclusion size and horizon are taken into account that lead to dependance of the bounds on both the size and shape of the inclusions. The numerical examples are considered for the 1D case.