Search results for: Space curved

Authors: A. Peveri

Abstract:

The curvature space-time by the presence of material, this deformation must present a pattern of deformation, not random. Space is uniform, elastic and any modification that occurs in one part, causes a change in another.

This deformation exists, must be a constant value and is independent of the observer, and relates the amount of matter, the force caused by the curvature of space and surface space. This unit of space is defined in this study as PIL and represents a constant area of space, deformable in the direction and sense of the center of mass of the body. The PIL is curved and connected to the center of mass of the Earth, to get to that point, through all matter, thus forming part of any place between particles at atomic and subatomic levels. At these levels the space between each particle is flat, unlike the macro where the space curves.

Keywords: Space flat, Space curved, Unit of space, Deformation.

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Authors: Akif Kutlu, Merve Ermis, Nihal Eratlı, Mehmet H. Omurtag

Abstract:

The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.

Keywords: Curved beam, dynamic analysis, elastic foundation, finite element method.

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Authors: Arti Vaish, Harish Parthasarathy

Abstract:

The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.

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Authors: A. Peveri

Abstract:

The interaction of mass will determine the curvature of space-time, may determine that events proceed at different rates of time at each point in space, so each has a corresponding gravitational potential time. So we can find different values ​​of gravity (g), corresponding to different times (t), thus making a "map of time in space." The space-time is curved by present mass, causing a force of attraction towards the body, but if you invest the curvature of space-time, we find that this field is repulsive: Obtaining negative gravitational forces and positive gravitational forces respectively.

Keywords: Space-time, time, positive gravitation, negative gravitation.

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Authors: Carlos Mendez Galindo, Toshiro Hayashikawa, Javier Gil Belda

Abstract:

This paper investigates the effectiveness of the use of seismic isolation devices on the overall 3D seismic response of curved highway viaducts with an emphasis on expansion joints. Furthermore, an evaluation of the effectiveness of the use of cable restrainers is presented. For this purpose, the bridge seismic performance has been evaluated on four different radii of curvature, considering two cases: restrained and unrestrained curved viaducts. Depending on the radius of curvature, three-dimensional non-linear dynamic analysis shows the vulnerability of curved viaducts to pounding and deck unseating damage. In this study, the efficiency of using LRB supports combined with cable restrainers on curved viaducts is demonstrated, not only by reducing in all cases the possible damage, but also by providing a similar behavior in the viaducts despite of curvature radius.

Keywords: Nonlinear dynamic response, seismic design, seismic isolation, unseating prevention system.

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

The mixed convective flow of MHD incompressible, steady boundary layer in heat transfer over a curved stretching sheet due to temperature dependent thermal conductivity is studied. We use curvilinear coordinate system in order to describe the governing flow equations. Finite difference solutions with central differencing have been used to solve the transform governing equations. Numerical results for the flow velocity and temperature profiles are presented as a function of the non-dimensional curvature radius. Skin friction coefficient and local Nusselt number at the surface of the curved sheet are discussed as well.

Keywords: Curved stretching sheet, finite difference method, MHD, variable thermal conductivity.

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Authors: A. Benzian

Abstract:

The generalization of relativistic theory of gravity based essentially on the principle of equivalence stipulates that for all bodies, the grave mass is equal to the inert mass which leads us to believe that gravitation is not a property of the bodies themselves, but of space, and the conclusion that the gravitational field must curved space-time what allows the abandonment of Minkowski space (because Minkowski space-time being nonetheless null curvature) to adopt Riemannian geometry as a mathematical framework in order to determine the curvature. Therefore the work presented in this paper begins with the evolution of the concept of gravity then tensor field which manifests by Riemannian geometry to formulate the general equation of the gravitational field.

Keywords: Inertia, principle of equivalence, tensors, Riemannian geometry.

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Authors: Janis Šliseris, Karlis Rocens

Abstract:

Optimization of rational geometrical and mechanical parameters of panel with curved plywood ribs is considered in this paper. The panel consists of cylindrical plywood ribs manufactured from Finish plywood, upper and bottom plywood flange, stiffness diaphragms. Panel is filled with foam. Minimal ratio of structure self weight and load that could be applied to structure is considered as rationality criteria. Optimization is done, by using classical beam theory without nonlinearities. Optimization of discreet design variables is done by Genetic algorithm.

Keywords: Curved plywood ribs, genetic algorithm, rationalparameters of ribbed panel, structure optimization.

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Authors: S. C. Kattimani

Abstract:

This article deals with the analysis of active constrained layer damping (ACLD) of smart multiferroic or magneto-electro-elastic doubly curved shells. The kinematics of deformations of the multiferroic doubly curved shell is described by a layer-wise shear deformation theory. A three-dimensional finite element model of multiferroic shells has been developed taking into account the electro-elastic and magneto-elastic couplings. A simple velocity feedback control law is employed to incorporate the active damping. Influence of layer stacking sequence and boundary conditions on the response of the multiferroic doubly curved shell has been studied. In addition, for the different orientation of the fibers of the constraining layer, the performance of the ACLD treatment has been studied.

Keywords: Active constrained layer damping, doubly curved shells, magneto-electro-elastic, multiferroic composite, smart structures.

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Authors: Saroj Kumar Sarangi, M. C. Ray

Abstract:

This paper deals with the analysis of active constrained layer damping (ACLD) of doubly curved laminated composite shells using active fiber composite (AFC) materials. The constraining layer of the ACLD treatment has been considered to be made of the AFC materials. A three dimensional energy based finite element model of the smart doubly curved laminated composite shell integrated with a patch of such ACLD treatment has been developed to demonstrate the performance of the patch on enhancing the damping characteristics of the doubly curved laminated composite shells. Particular emphasis has been placed on studying the effect of variation of piezoelectric fiber orientation angle in the constraining AFC layer on the control authority of the ACLD patch.

Keywords: Active constrained layer damping, Active fibercomposites, Finite element modeling, First order shear deformationtheory.

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Authors: Barenten Suciu, Ryoichi Kinoshita

Abstract:

In this paper, an experimental and theoretical study on the bogie pseudo-hunting motion of a reduced-scale model railway vehicle, running on double-curved rails, is presented. Since the actual bogie hunting motion, occurring for real railway vehicles running on straight rails at high travelling speeds, cannot be obtained in laboratory conditions, due to the speed and wavelength limitations, a pseudo- hunting motion was induced by employing double-curved rails. Firstly, the test rig and the experimental procedure are described. Then, a geometrical model of the double-curved rails is presented. Based on such model, the variation of the carriage rotation angle relative to the bogies and the working conditions of the yaw damper are clarified. Vibration spectra recorded during vehicle travelling, on straight and double-curved rails, are presented and interpreted based on a simple vibration model of the railway vehicle. Ride comfort of the vehicle is evaluated according to the ISO 2631 standard, and also by using some particular frequency weightings, which account for the discomfort perceived during the reading and writing activities. Results obtained in this work are useful for the adequate design of the yaw dampers, which are used to attenuate the lateral vibration of the train car bodies.

Keywords: Double-curved rail, octave analysis, lateral vibration, ride comfort, yaw damper, railway vehicle.

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Authors: Rinna Tanaka, Carlos Mendez Galindo, Toshiro Hayashikawa

Abstract:

The results show that the bridge equipped with seismic isolation bearing system shows a high amount of energy dissipation. The purpose of the present study is to analyze the overall performance of continuous curved highway viaducts with different bearing supports, with an emphasis on the effectiveness of seismic isolation based on lead rubber bearing and hedge reaction force bearing system consisted of friction sliding bearing and rubber bearing. The bridge seismic performance has been evaluated on six different cases with six bearing models. The effects of the different arrangement of bearing on the deck superstructure displacements, the seismic damage at the bottom of the piers, movement track at the pier-s top and the total and strain energies absorbed by the structure are evaluated. In conclusion, the results provide sufficient evidence of the effectiveness on the use of seismic isolation on steel curved highway bridges.

Keywords: Curved highway viaducts, non-linear dynamic response, seismic damage.

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Authors: Xing Feng, Yuanbin Li

Abstract:

Oil spills at sea can cause severe marine environmental damage, including bringing huge hazards to living resources and human beings. In situ burning or chemical dispersant methods can be used to handle the oil spills sometimes, but these approaches will bring secondary pollution and fail in some situations. Oil recovery techniques have also been developed to recover oil using oil skimmer equipment installed on ships, while the hydrodynamic process of the oil flowing through the oil skimmer is very complicated and important for evaluating the recovery efficiency. Based on this, a two-dimensional numerical simulation platform for simulating the hydrodynamic process of the oil flowing through the oil skimmer is established based on the Navier-Stokes equations for viscous, incompressible fluid. Finally, the influence of the design of the flow channel in the curved plane oil skimmer on the hydrodynamic process of the oil flowing through the oil skimmer is investigated based on the established simulation platform.

Keywords: Curved plane oil skimmer, flow channel, CFD, VOF.

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Authors: P. D. Pastuszak

Abstract:

The present work is devoted to thermographic studies of curved composite panels (unidirectional GFRP) with subsurface defects. Various artificial defects, created by inserting PTFE stripe between individual layers of a laminate during manufacturing stage are studied. The analysis is conducted both with the use finite element method and experiments. To simulate transient heat transfer in 3D model with embedded various defect sizes, the ANSYS package is used. Pulsed Thermography combined with optical excitation source provides good results for flat surfaces. Composite structures are mostly used in complex components, e.g., pipes, corners and stiffeners. Local decrease of mechanical properties in these regions can have significant influence on strength decrease of the entire structure. Application of active procedures of thermography to defect detection and evaluation in this type of elements seems to be more appropriate that other NDT techniques. Nevertheless, there are various uncertainties connected with correct interpretation of acquired data. In this paper, important factors concerning Infrared Thermography measurements of curved surfaces in the form of cylindrical panels are considered. In addition, temperature effects on the surface resulting from complex geometry and embedded and real defect are also presented.

Keywords: Active thermography, finite element analysis, composite, curved structures, defects.

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Authors: M. Norouzi, M. H. Kayhani, M. R. H. Nobari, M. Karimi Demneh

Abstract:

In this paper, fully developed flow and heat transfer of viscoelastic materials in curved ducts with square cross section under constant heat flux have been investigated. Here, staggered mesh is used as computational grids and flow and heat transfer parameters have been allocated in this mesh with marker and cell method. Numerical solution of governing equations has being performed with FTCS finite difference method. Furthermore, Criminale-Eriksen- Filbey (CEF) constitutive equation has being used as viscoelastic model. CEF constitutive equation is a suitable model for studying steady shear flow of viscoelastic materials which is able to model both effects of the first and second normal stress differences. Here, it is shown that the first and second normal stresses differences have noticeable and inverse effect on secondary flows intensity and mean Nusselt number which is the main novelty of current research.

Keywords: Viscoelastic, fluid flow, heat convection, CEF model, curved duct, square cross section.

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Authors: Jessada Monthasuwan, Charinsak Saetiaw, Chanchai Thongsopa

Abstract:

This paper presents the development and design of the curved rectangular patch arrays antenna for small missile application. This design uses a 0.1mm flexible copper sheet on the front layer and back layer, and a 1.8mm PVC substrate on a middle layer. The study used a small missile model with 122mm diameter size with speed 1.1 Mach and frequency range on ISM 2.4 GHz. The design of curved antenna can be installation on a cylindrical object like a missile. So, our proposed antenna design will have a small size, lightweight, low cost and simple structure. The antenna was design and analysis by a simulation result from CST microwave studio and confirmed with a measurement result from a prototype antenna. The proposed antenna has a bandwidth covering the frequency range 2.35-2.48 GHz, the return loss below -10 dB and antenna gain 6.5 dB. The proposed antenna can be applied with a small guided missile effectively.

Keywords: Rectangular path arrays, small missile antenna.

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Authors: I. Algul, G. Akgun, H. Kurtaran

Abstract:

Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated.

Keywords: Generalized differential quadrature method, doubly curved panels, laminated composite materials, small displacement.

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Authors: Abdullah Madhi Alsharif, Jamal Uddin

Abstract:

A liquid curved jet has many applications in different industrial and engineering processes, such as the prilling process for generating small spherical pellets (fertilizer or magnesium). The liquids used are usually molten and contain small quantities of polymers and therefore can be modelled as non-Newtonian liquids. In this paper, we model the viscoelastic liquid jet by using the Oldroyd- B model. An asymptotic analysis has been used to simplify the governing equations. Furthermore, the trajectory and a linear temporal stability in the presence of gravity and rotation have been determined.

Keywords: gravity, prilling, rotation, viscoelastic jets.

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Authors: Akshoy R. Paul, Pritanshu Ranjan, Ravi R. Upadhyay, Anuj Jain

Abstract:

Aircraft propulsion systems often use Y-shaped subsonic diffusing ducts as twin air-intakes to supply the ambient air into the engine compressor for thrust generation. Due to space constraint, the diffusers need to be curved, which causes severe flow non-uniformity at the engine face. The present study attempt to control flow in a mild-curved Y-duct diffuser using trapezoidalshaped vortex generators (VG) attached on either both the sidewalls or top and bottom walls of the diffuser at the inflexion plane. A commercial computational fluid dynamics (CFD) code is modified and is used to simulate the effects of SVG in flow of a Y-duct diffuser. A few experiments are conducted for CFD code validation, while the rest are done computationally. The best combination of Yduct diffuser is found with VG-2 arranged in co-rotating sequence and attached to both the sidewalls, which ensures highest static pressure recovery, lowest total pressure loss, minimum flow distortion and less flow separation in Y-duct diffuser. The decrease in VG height while attached to top and bottom walls further improves axial flow uniformity at the diffuser outlet by a great margin as compared to the bare duct.

Keywords: Twin air-intake, Vortex generator (VG), Turbulence model, Pressure recovery, Distortion coefficient

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Authors: Irina Eglite, Andrei A. Kolyshkin

Abstract:

Method of multiple scales is used in the paper in order to derive an amplitude evolution equation for the most unstable mode from two-dimensional shallow water equations under the rigid-lid assumption. It is assumed that shallow mixing layer is slightly curved in the longitudinal direction and contains small particles. Dynamic interaction between carrier fluid and particles is neglected. It is shown that the evolution equation is the complex Ginzburg-Landau equation. Explicit formulas for the computation of the coefficients of the equation are obtained.

Keywords: Shallow water equations, mixing layer, weakly nonlinear analysis, Ginzburg-Landau equation

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Authors: Sourabh Agrawal, Ashok K. Jain

Abstract:

Stick models are widely used in studying the behaviour of straight as well as skew bridges and viaducts subjected to earthquakes while carrying out preliminary studies. The application of such models to highly curved bridges continues to pose challenging problems. A viaduct proposed in the foothills of the Himalayas in Northern India is chosen for the study. It is having 8 simply supported spans @ 30 m c/c. It is doubly curved in horizontal plane with 20 m radius. It is inclined in vertical plane as well. The superstructure consists of a box section. Three models have been used: a conventional stick model, an improved stick model and a 3D finite element model. The improved stick model is employed by making use of body constraints in order to study its capabilities. The first 8 frequencies are about 9.71% away in the latter two models. Later the difference increases to 80% in 50th mode. The viaduct was subjected to all three components of the El Centro earthquake of May 1940. The numerical integration was carried out using the Hilber- Hughes-Taylor method as implemented in SAP2000. Axial forces and moments in the bridge piers as well as lateral displacements at the bearing levels are compared for the three models. The maximum difference in the axial forces and bending moments and displacements vary by 25% between the improved and finite element model. Whereas, the maximum difference in the axial forces, moments, and displacements in various sections vary by 35% between the improved stick model and equivalent straight stick model. The difference for torsional moment was as high as 75%. It is concluded that the stick model with body constraints to model the bearings and expansion joints is not desirable in very sharp S curved viaducts even for preliminary analysis. This model can be used only to determine first 10 frequency and mode shapes but not for member forces. A 3D finite element analysis must be carried out for meaningful results.

Keywords: Bearing, body constraint, box girder, curved viaduct, expansion joint, finite element, link element, seismic, stick model, time history analysis.

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Authors: Irina Eglite, Andrei A. Kolyshkin

Abstract:

The effect of small non-parallelism of the base flow on the stability of slightly curved mixing layers is analyzed in the present paper. Assuming that the instability wavelength is much smaller than the length scale of the variation of the base flow we derive an amplitude evolution equation using the method of multiple scales. The proposed asymptotic model provides connection between parallel flow approximations and takes into account slow longitudinal variation of the base flow.

Keywords: shallow water, parallel flow assumption, weaklynonlinear analysis, method of multiple scales

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Authors: Sameerah Jamal, Abdul Hamid Kara, Ashfaque H. Bokhari

Abstract:

Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduction procedures via symmetries, variational structures and conservation laws are more involved than on the well known flat (Minkowski) manifold.

Keywords: Bianchi metric, conservation laws, Milne metric, symmetries.

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Authors: M. E. Shimpi, G. M. Deheri

Abstract:

This article aims to investigate the performance of a magnetic fluid based squeeze film between rotating transversely rough curved porous annular plates incorporating the effect of elastic deformation. The associated stochastically averaged Reynolds type equation is solved to obtain the pressure distribution leading to the calculation of the load carrying capacity. The results suggest that the transverse roughness of the bearing surfaces affects the performance adversely although the bearing systems register a relatively improved performance due to the magnetization. The deformation causes reduced the load carrying capacity while the curvature parameters tend to nominally increase the load carrying capacity. Besides, the adverse effect of porosity, deformation and standard deviation can be minimized to some extent by the positive effect of the magnetization and the curvature parameters in the case of negatively skewed roughness by suitably choosing the rotational inertia and the aspect ratio, which becomes significant when negative variance occurs.

Keywords: Annular plates curved rough surface, deformation, load carrying capacity, rotational inertia, magnetic fluid, squeeze film.

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Authors: N. Subramanian, C. Murugesan

Abstract:

The double difference sequence space I2 (M, of fuzzy numbers for both 1 < p < oo and 0 < p < 1, is introduced. Some general properties of this sequence space are studied. Some inclusion relations involving this sequence space are obtained.

Keywords: Orlicz function, solid space, metric space, completeness

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Authors: P. Kamphikul, P. Krachodnok, R. Wongsan

Abstract:

This paper presents the gain improvement of a sector antenna for mobile phone base station by using the new technique to enhance its gain for microstrip antenna (MSA) array without construction enlargement. The curved woodpile Electromagnetic Band Gap (EBG) has been utilized to improve the gain instead. The advantages of this proposed antenna are reducing the length of MSAs array but providing the higher gain and easy fabrication and installation. Moreover, it provides a fan-shaped radiation pattern, wide in the horizontal direction and relatively narrow in the vertical direction, which appropriate for mobile phone base station. The paper also presents the design procedures of a 1x8 MSAs array associated with U-shaped reflector for decreasing their back and side lobes. The fabricated curved woodpile EBG exhibits bandgap characteristics at 2.1 GHz and is utilized for realizing a resonant cavity of MSAs array. This idea has been verified by both the Computer Simulation Technology (CST) software and experimental results. As the results, the fabricated proposed antenna achieves a high gain of 20.3 dB and the half-power beam widths in the E- and H-plane of 36.8 and 8.7 degrees, respectively. Good qualitative agreement between measured and simulated results of the proposed antenna was obtained.

Keywords: Gain Improvement, Microstrip Antenna Array, Electromagnetic Band Gap, Base Station.

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Authors: Zhiguo Ren, Lilong Cai

Abstract:

This paper present an effective method to accurately reconstruct and measure the 3D curve edges of small industrial parts based on stereo vision. To effectively fit the curve of the measured parts using a series of line segments in the images, a strategy from coarse to fine is employed based on multi-scale curve fitting. After reconstructing the 3D curve of a hole through a curved surface, its axis is adjusted so that it is parallel to the Z axis with least squares error and the dimensions of the hole can be calculated on the XY plane easily. Experimental results show that the presented method can accurately measure the dimensions of round holes through a curved surface.

Keywords: Stereo Vision, 3D Round Hole Measurement, Curve Fitting, 3D Curve Reconstruction, Least Squares Error.

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Authors: Prakash Persad, Kelvin Loutan, Jr., Trichelle Seepersad

Abstract:

The Finite Element Method is commonly used in the analysis of flexible manipulators to predict elastic displacements and develop joint control schemes for reducing positioning error. In order to preserve simplicity, regular geometries, ideal joints and connections are assumed. This paper presents the dynamic FE analysis of a 4- degrees of freedom open chain manipulator, intended for striking a curved 3D surface percussion musical instrument. This was done utilizing the new MultiBody Dynamics Module in COMSOL, capable of modeling the elastic behavior of a body undergoing rigid body type motion.

Keywords: Dynamic modeling, Entertainment robots, Finite element method, Flexible robot manipulators, Multibody dynamics, Musical robots.

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Authors: Enerit Saçdanaku, Idriz Haxhiu

Abstract:

In this study was monitored the population of the European Pond Turtle, Emys orbicularis (Linnaeus, 1758) in the area of Narta Lagoon, Vlora Bay (Albania), from August to October 2014. A total of 54 individuals of E. orbicularis were studied using different methodologies. Curved Carapace Length (CCL), Plastron Length (PL) and Curved Carapace Width (CCW) were measured for each individual of E. orbicularis and were statistically analyzed. All captured turtles were separated in seven different size – classes based on their carapace length (CCL). Each individual of E. orbicularis was marked by notching the carapace (marginal scutes). Form all individuals captured resulted that 37 were females (68.5%), 14 males (25.9%), 3 juveniles (5.5%), while 18 individuals of E. orbicularis were recaptured for the first and some for the second time.

Keywords: Emys orbicularis, female, juvenile, male, population, size – classes.

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Authors: Muhammad Naveed, Yang Caixia

Abstract:

The need for national space legislation is pivotal, particularly in light of the fact that in recent years space activities have grown immensely both in volume and diversity. Countries are progressively developing capabilities in space exploration and scientific discoveries, market their capabilities to manufacture satellites, provide launch services from their facilities and are looking to privatize and commercialize their space resources. Today, nations are also seeking to comprehend the technological and financial potential of the private sector and are considering to share their financial burdens with them and to limit their exposures to risks, but they are lagging behind in legal framework in this regard. In the perspective of these emerging developments, it is therefore, felt that national space legislation should be enacted with the goal of building and implementing a vibrant and transparent legal framework at the national level to hasten investments and to ensure growth in this capital intensive - highly yield strategic sector. This study looks at (I) the international legal framework that governs space activities; (II) motivation behind making national space laws; and (III) the need for national space legislation. The paper concludes with some recommendations with regards to the conceivable future direction for national space legislation, in particular space empowered sub-areas for countries.

Keywords: International conventions, national legislation, space faring nation, space law.

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