Dimensional Equations Of Motion Research Articles

Representation of compact stars using the black string set-up

This work is devoted to provide a way of representing $4D$ spherically symmetric and static compact stellar configurations into a $5D$ space time, using the black string framework. We write the four and five dimensional line elements and the four and five dimensional energy momentum tensor such that the four and five dimensional quantities are related by a function $A(z)$, where $z$ represents to the extra dimension. Remarkably, one consequence of our chosen form for the line element, for the energy momentum tensor and for $A(z)$, is the fact that the $5D$ equations are reduced to the usual form of the four dimensional equations of motion. Also, the five dimensional conservation equation adopts the form of the four dimensional conservation equation. It is worth mentioning that, although our methodology is simple, this form of reduction could serve to represent other types of four dimensional objects into an extra dimension in future works. Furthermore, under our assumptions the sign of the pressure along the extra dimension is given by the trace of the four dimensional energy momentum tensor. Furthermore, our simple election for the function $A(z)$ modifies some features of the induced 4--dimensional compact stellar configuration, such as the mass--radius relation, the momentum of inertia, the central values of the thermodynamic variables, to name a few. Besides, the topology of this model is ${S}^{2}\times {S}^{1}$ and not the ${S}^{3}$ topology of the 5--dimensional structures.

Exact solutions to nonlinear symmetron theory: One- and two-mirror systems. II.

We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one or two mirror system in the case of a spontaneously broken phase in vacuum as well as in matter. This complements a similar analysis performed in a previous article [1], in which the symmetron is in the spontaneously broken phase in vacuum but in the symmetric phase in matter. Here again, the one dimensional equations of motion are integrated exactly for both systems and their solutions are expressed in terms of Jacobi elliptic functions. In the case of two parallel mirrors the equations of motion provide also in this case a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to qBOUNCE experiments, neutron interferometry and to the calculation of the symmetron field induced "Casimir force" in the Cannex experiment and allow to extend the investigation to hitherto unavailable regions in symmetron parameter space.

Free Vibration Analysis of Functionally Graded Piezoelectric Material Beam by a Modified Mesh Free Method

A mesh-free method based on moving least squares approximation (MLS) and weak form of governing equations including two dimensional equations of motion and Maxwell’s equation is used to analyze the free vibration of functionally graded piezoelectric material (FGPM) beams. Material properties in beam are determined using a power law distribution. Essential boundary conditions are imposed by the transformation method. The mesh-free method is verified by comparison with a finite element method (FEM) which performed for FGPM beams. Comparisons showed that this model has a good accuracy. After validation of the presented model, a parametric study was carried out to investigate the effect of mechanical and electrical boundary conditions, slenderness ratio and distribution of constituent materials on natural frequencies of FGPM beams. It is concluded that slenderness ratio has more significant effect on lower frequencies. On the other hand higher frequencies are affected by the volume fraction power index much more than lower frequencies.

Non-dimensional simple beam models for the elastic forces in ANCF: 3D equation and simulation

Absolute nodal coordinate formulation can be used to represent large displacement and large deformation in flexible body analysis based on the concept of continuum mechanics. However, the analysis takes a long time because of the increase in the degrees of freedom at a nodal point. In this study, the analysis time was reduced by using non-dimensional variables for the time, length, and force to convert a dimensional equation of motion into a non-dimensional one. Revolute and spherical joint were used to obtain numerical solutions by applying the non-dimensional equation of motion of free-falling pendulum. The non-dimensional equation of motion was verified by comparing the solutions with the numerical solution obtained using a dimensional equation of motion. The motion of a flexible hose was predicted by using the absolute nodal coordinate formulation, and it was shown the efficiency of non-dimensional equation of motion.

Exact solutions to nonlinear symmetron theory: One- and two-mirror systems

We derive the exact analytical solutions to the symmetron field theory equations in the presence of a one or two mirror system. The one dimensional equations of motion are integrated exactly for both systems and their solutions can be expressed in terms of Jacobi elliptic functions. Surprisingly, in the case of two parallel mirrors the equations of motion generically provide not a unique solution but a discrete set of solutions with increasing number of nodes and energies. The solutions obtained herein can be applied to qBOUNCE experiments, neutron interferometry and for the calculation of the symmetron field induced "Casimir force" in the CANNEX experiment.

Nondimensional analysis of a two-dimensional shear deformable beam in absolute nodal coordinate formulation

Absolute nodal-coordinate formulation is a technique that was developed in 1996 for expressing the large rotation and deformation of a flexible body. It utilizes global slopes without a finite rotation in order to define nodal coordinates. The method has a shortcoming in that the central processing unit time increases because of increases in the degrees of freedom. In particular, when considering the deformation of a cross section, the shortcoming due to the increase in the degrees of freedom becomes clear. Therefore, in the present research, the dimensional equation of motion concerning a two-dimensional shear deformable beam, developed by Omar and Shabana, is converted into a nondimensional equation of motion in order to reduce the central processing unit time. By utilizing an example of a cantilever beam, wherein an exact solution for the static deflection exists, the nondimensional equation of motion was verified. Moreover, by using an example of a free-falling flexible pendulum, the efficiency of the nondimensional equation of motion gained by increasing the number of elements was compared with that of the dimensional equation of motion.

Analytical assessment of a novel rotating fluidized bed solar reactor for steam gasification of char particles

A novel rotating fluidised bed solar reactor for the gasification of carbonaceous materials is presented. A simplified single particle model, in which the particle gasification is coupled with three dimensional equations of motion, is developed and used to study the particle residence time and gasification conversion within the proposed reactor, together with their sensitivity to changes in key operating parameters, namely reactor rotational speed, initial feedstock particle radius, radiation intensity, and particle release position. The proposed reactor is shown to offer potential for increased particle residence time and conversion relative to conventional fluidised beds through adjustments of the operating parameters other than the particle release position. The results presented assist in developing an understanding of the operation of the proposed reactor and optimising its performance.

Efficiency of non-dimensional analysis for absolute nodal coordinate formulation

Absolute nodal coordinate formulation was developed in the mid-1990s. The adoption of the continuum mechanics concept has allowed large displacements and large deformations to be expressed in flexible body analysis. However, the analysis time increases due to the increased number of degrees of freedom at nodal points. Therefore, we aimed to reduce the analysis time by converting a dimensional equation of motion (EOM) to a non-dimensional EOM by using non-dimensional variables of time, length, and force. A non-dimensional mass matrix, a non-dimensional longitudinal stiffness matrix, and a non-dimensional conservative force vector are derived and applied to the non-dimensional EOM. To verify the non-dimensional EOM, a cantilever beam with static deflection, for which an exact solution exists, is considered. As the number of elements is increased, the mean value by the non-dimensional EOM converges to the static deflection. Revolute and spherical joints are used to propose two- and three-dimensional numerical solutions based on the non-dimensional EOM of a free-falling pendulum. These solutions are compared with the numerical solutions from using a dimensional EOM in order to verify the non-dimensional EOM. The analysis results for simple pendulum motion using dimensional and non-dimensional EOMs are in good agreement.

Two Dimensional Functionally Graded Material Finite Thick Hollow Cylinder Axisymmetric Vibration Mode Shapes Analysis Based on Exact Elasticity Theory

Abstract A thick hollow cylinder with finite length made of two- dimensional functionally graded material (2D-FGM) is considered and its natural modes are determined, based on great importance of mode shapes information in order to understand vibration behaviour of structures. Three dimensional theory of elasticity implemented for problem formulation, since mode shapes of a thick cylinder are three dimensional even with axisymmetric conditions. The axisymmetric conditions are assumed for the 2D-FGM cylinder. The material properties of the cylinder are varied in the radial and axial directions, with power law functions. Effects of volume fraction distribution on the different types of symmetric mode shapes configuration and vibration behaviour of a simply supported cylinder are analyzed. Three dimensional equations of motion are used and the eigen value problem is developed, based on direct variation method.

Concept of curved magnetically guided liquid lithium target without a back plate for IFMIF

Curved magnetically guided lithium target (MGLT) without a back plate was newly proposed in light of simplified structure, easy maintenance and enhanced availability and performance for international fusion materials irradiation facility (IFMIF). It can replace conventional lithium target with a curved material back plate under the most severe condition on neutron irradiation. Magnetic field suited for the curved MGLT is produced in combination of a couple of radiation-proof resistive coils and reduced activation ferritic/martensitic steel (F82H) parts (yokes, ducts/nozzles and high flux test module (HFTM)). Shape of the magnetic field becomes curved automatically in the target region by setting HFTM closely to MGLT. Characteristics of the lithium flow on MGLT was analyzed in detail by two dimensional equations of motion with the magnetic field calculated by the Poisson Superfish code. The necessary magnetic flux density at the target region was found to be about 0.5T to fulfill the IFMIF target conditions, i.e., lithium flow speed of 15m/s, curvature radius of 1–1.6m and flow thickness of 0.025m. A narrow gap (a few mm) between MGLT and HFTM could be controlled by adjusting the coil current. Future subjects for further development of this concept were identified.

Progress in the analysis of non-axisymmetric wave propagation in a homogeneous solid circular cylinder of a piezoelectric transversely isotropic material

Non-axisymmetric waves in a free homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization are investigated on the basis of the linear theory of elasticity and linear electromechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained through the application of the mechanical and two types of electric boundary conditions at the surface of the cylinder. A convenient method of calculating dispersion curves and phase velocities is discussed, and resulting curves are presented for propagating and evanescent waves for the piezoelectric ceramic material PZT-4 for non-axisymmetric modes of circumferential wave number m=1. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the strength of the electromechanical coupling.

Analysis of non-axisymmetric wave propagation in a homogeneous piezoelectric solid circular cylinder of transversely isotropic material

A study concerning the propagation of free non-axisymmetric waves in a homogeneous piezoelectric cylinder of transversely isotropic material with axial polarization is carried out on the basis of the linear theory of elasticity and linear electro-mechanical coupling. The solution of the three dimensional equations of motion and quasi-electrostatic equation is given in terms of seven mechanical and three electric potentials. The characteristic equations are obtained by the application of the mechanical and two types of electric boundary conditions at the surface of the piezoelectric cylinder. A novel method of displaying dispersion curves is described in the paper and the resulting dispersion curves are presented for propagating and evanescent waves for PZT-4 and PZT-7A piezoelectric ceramics for circumferential wave numbers m = 1, 2, and 3. It is observed that the dispersion curves are sensitive to the type of the imposed boundary conditions as well as to the measure of the electro-mechanical coupling of the material.

Effective action of string theory flux compactifications

We discuss four dimensional effective actions of string theory flux compactifications. These effective actions describe four dimensional gravity coupled to overall Kahler modulus of the compactification manifold. We demonstrate the agreement between ten dimensional equations of motion of supergravity with localized branes, and equations of motion derived from the effective action. The agreement is lost however if one evaluates the full effective action on the equations of motion for a subset of the supergravity modes, provided these modes depend on-shell on the Kahler modulus.

제한된 제어입력을 갖는 유연우주구조물에 대한 확장된 LQR

We consider the simultaneous slewing and vibration suppression control problem of an idealized structural model which has a rigid hub with two cantilevered flexible appendages and finite tip masses. The finite clement method(FEM) is used to obtain linear finite dimensional equations of motion for the model. In the linear quadratic regulator(LQR) problem, a simple method is introduced to provide a physically meaningful performance index for space structure models. This method gives us a mathematically minor but physically important modification of the usual energy type performance index. A numerical procedure to solve a time-variant LQR problem with inequality control constraints is presented using the method of particular solutions.

Soliton dynamics in 3D ferromagnets

We study the dynamics of solitons in a Landau–Lifshitz equation describing the magnetization of a three-dimensional ferromagnet with an easy axis anisotropy. We numerically compute the energy dispersion relation and the structure of moving solitons, using a constrained minimization algorithm. We compare the results with those obtained using an approximate form for the moving soliton, valid in the small momentum limit. We also study the interaction and scattering of two solitons, through a numerical simulation of the (3+1)-dimensional equations of motion. We find that the force between two solitons can be either attractive or repulsive depending on their relative internal phase and that in a collision two solitons can form an unstable oscillating loop of magnons.

Motion control of non-fixed base robotic manipulators

Robotic manipulators mounted on spacecraft experience a number of kinematic, dynamic, and control problems because the motion of the spacecraft is affected by the robot motion. In this paper, the general three dimensional equations of motion are derived for an n link manipulator mounted on a non-fixed base object. Instead of performing a single inverse kinematic calculation at the beginning of a movement to determine the required joint setpoints, multiple inverse kinematic updates are done throughout a movement. The updating sequence is determined by an optimal inverse kinematic updating algorithm. This motion control algorithm is based on experimental simulation results performed in Matlab and a set of performance indices that are used as guidelines. Simple PD joint controllers and a special joint trajectory generator are used for servoing the manipulator joints for a planar robot application. The derived motion control techniques incorporate the base motion without base motion control.

Detachment Analysis of Oranges in Shake Harvesting

ABSTRACT THE dynamic response of fruit suspension twigs to induced vibration, in oranges of the Shamouti variety, is studied by the use of a mathematical model. The elastic properties of the fruit-twig system are defined by a nonlinear stiffness matrix which is determined experi-mentally. The stiffness matrix is used for the solution of the three dimensional equations of motion. The am-plitude and frequencies of the spatial components of motion are solved by numerical methods, and the resultant tensile force between fruit and twig is determined as a function of time. This method is used to analyze the influence of parameters as frequencies, amplitudes and di-rections of the forcing motion on fruit detachment and to establish optimal operational conditions. Comparison with detachment experiments have shown the reliability of the proposed method.

A discrete−continuum theory for periodically layered composite materials

A discrete−continuum theory for periodically layered composite materials is presented. Based on a two−term truncated power series expansion of the displacement field about the middle plane of each layer, two−dimensional equations of motion are obtained for the individual layers. After introducing appropriate continuity conditions at the interfaces between neighboring layers, the governing field equations for periodically layered media are derived in the form of a system of differential−difference equations. The accuracy of the theory is examined by applying it to the propagation of plane harmonic waves in an unbounded layered medium and comparing the results with those obtained from theory of elasticity. To illustrate the application of the theory, thickness−twist vibrations of laminated plates are studied. Numerical examples are included and comparison is made with exact solutions. Subject Classification :40.24.

Stopping abilities of ships equipped with controllable pitch propeller1

Recently KHI built three kinds of ship each equipped with a controllable Pitch Propeller (CPP). They are higher-powered ships in comparison with those built before. The ship types are Reefer, Container and Ore/Oil Tanker. As speed and size of ships increase, the necessity of stopping ability has increased. Investigations on the stopping abilities of ships with Fixed Pitch Propeller (FPP) have been reported in detail by many researchers, but those on CPP ships are very rare. As the first step of the investigation on the stopping abilities of ships equipped with CPP, the authors report crash astern test results compare them with those of FPP ships. Furthermore they show the results of computation of the transient phenomena in case of CPP ships by using one dimensional equation of motion and compare them with sea trial results.

Approximate Theory of Torsional Wave Propagation in Elastic, Composite Cylinders

One dimensional equations of motion are obtained for axially symmetric torsional deformation in elastic, composite cylinders. Under consideration are cylinders composed of two materials: a circular inner core surrounded by an annulus of different material properties. These approximate equations were obtained from the variational equations of motion of a linear elastic medium by assuming a set of simple, orthogonal displacement functions. These functions were chosen to give the first two branches of the dispersion diagram for torsional waves in the composite cylinder. The slope of the first branch at the origin of the dispersion diagram is identical with the corresponding slope obtained from the “exact” analysis. Two correction factors are introduced in the approximate equations in order for the second branch to match the exact analysis at two particular points. The dispersion relations obtained from the resulting corrected equations are very accurate through a wide range of frequencies for real wave numbers. Conditions at the end of finite cylinders, sufficient to provide a unique solution, are provided.