Direct Integration Technique Research Articles

A note on Classification of Proper Teleparallel Homothetic Vector Field in Spherically Symmetric Static Space-times in the Teleparallel Theory of Gravitation using Diagonal Tetrads

In this paper a classification of proper teleparallel homothetic vector field in spherically symmetric static space-times is given using the direct integration technique. From the above study we show that the above space-times do not admit proper teleparallel homothetic vector fields.

Finite Element Formulation for the Large-Amplitude Vibrations of FG Beams

Abstract On the basis of Euler-Bernoulli beam theory, the large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The von Karman type nonlinear strain-displacement relationship is employed where the ends of the beam are constrained to move axially. The material properties are assumed to be graded in the thickness direction according to the power-law and sigmoid distributions. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law index, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible.

Integration of Ni<sub>2</sub>Si/Si Nanograss Heterojunction on n-MOSFET to Realize High-Sensitivity Phototransistors

We report a top-down fabrication technique for direct integration of Ni 2 Si/Si heterojunction arrays on n-type MOSFET gate terminal to realize sensitive field-effect phototransistors (PTs). It was observed that exposing gate area to light (λ = 655 nm) leads to significant modulation of threshold voltage (V TH ) of PT in comparison with a conventional MOSFET. By analyzing optical absorption spectra of Ni 2 Si/Si nanostructures on SiO 2 of this novel PT and planar Ni 2 Si/poly-Si on SiO 2 of conventional transistors, we concluded that, nanostructures strongly improve light absorption. This results in higher optically generated electron-hole pairs in which excess holes induce an electric field on the transistor channel and help the threshold happen at lower voltages. To recognize the appropriate operating point of such nanostructure-based PT, effect of V GS on the sensitivity of drain current was investigated. Experimental results show that device sensitivity (S) is related to gate-source voltage via a homographic like function. Theoretical analysis shows S ∝ 1/(V GS - V TH ) for high V GS , which has been confirmed by experimental data. In addition, external quantum efficiency and photoresponsivity of PT as functions of gate voltage were studied. The achieved results suggest that this device would be a promising candidate for fabricating low-power PTs based on silicide nanostructures.

A note on proper projective symmetry in cylindrical symmetric non-static space-times

In this paper a study of the most general form of cylindrical symmetric non-static space-times is given using direct integration and algebraic techniques. In this study we deal with the cases in which all eigenvalues of the Riemann tensor are different. From this study we show that when the cylindrical symmetric non-static space-times admit proper projective symmetry, it turns out to be a special class of the space-like flat Friedmann-Robertson-Walker model.

Proper projective symmetry in Bianchi type I space-times

A study of the most general form of Bianchi type I space-times is given by using the direct integration and algebraic techniques. In this study we deal with the cases where all the eigenvalues of the Riemann tensor are different. From the above study we have shown that, when the Bianchi type I space-times admit proper projective symmetry, it turns out to be a special class of flat Friedmann Robertson-Walker model.

In-plane and out-of-plane nonlinear dynamics of an axially moving beam

In the present study, the nonlinear forced dynamics of an axially moving beam is investigated numerically taking into account the in-plane and out-of-plane motions. The nonlinear partial differential equations governing the motion of the system are derived via Hamilton’s principle. The Galerkin scheme is then introduced to these partial differential equations yielding a set of second-order nonlinear ordinary differential equations with coupled terms. This set is transformed into a new set of first-order nonlinear ordinary differential equations by means of a change of variables. A direct time integration technique is conducted upon the new set of equations resulting in the bifurcation diagrams of Poincaré maps of the system. The dynamical characteristics of the system are investigated for different system parameters and presented through use of time histories, phase-plane portraits, Poincaré sections, and fast Fourier transforms.

Large-amplitude free vibrations of functionally graded beams by means of a finite element formulation

The large-amplitude free vibration analysis of functionally graded beams is investigated by means of a finite element formulation. The Von-Karman type nonlinear strain–displacement relationships are employed where the ends of the beam are constrained to move axially. The effects of the transverse shear deformation and rotary inertia are included based upon the Timoshenko beam theory. The material properties are assumed to be graded in the thickness direction according to the power-law distribution. A statically exact beam element which devoid the shear locking effect with displacement fields based on the first order shear deformation theory is used to study the geometric nonlinear effects on the vibrational characteristics of functionally graded beams. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique in order to obtain the nonlinear vibration frequencies of functionally graded beams with different boundary conditions. The influences of power-law exponent, vibration amplitude, beam geometrical parameters and end supports on the free vibration frequencies are studied. The present numerical results compare very well with the results available from the literature where possible. Some new results for the nonlinear natural frequencies are presented in both tabular and graphical forms which can be used for future references.

Equivalent reduced model technique development for nonlinear system dynamic response

The dynamic response of structural systems commonly involves nonlinear effects. Often times, structural systems are made up of several components, whose individual behavior is essentially linear compared to the total assembled system. However, the assembly of linear components using highly nonlinear connection elements or contact regions causes the entire system to become nonlinear. Conventional transient nonlinear integration of the equations of motion can be extremely computationally intensive, especially when the finite element models describing the components are very large and detailed.In this work, the equivalent reduced model technique (ERMT) is developed to address complicated nonlinear contact problems. ERMT utilizes a highly accurate model reduction scheme, the System equivalent reduction expansion process (SEREP). Extremely reduced order models that provide dynamic characteristics of linear components, which are interconnected with highly nonlinear connection elements, are formulated with SEREP for the dynamic response evaluation using direct integration techniques. The full-space solution will be compared to the response obtained using drastically reduced models to make evident the usefulness of the technique for a variety of analytical cases.

A Note on Classification of Teleparallel Conformal Vector Fields in Cylindrically Symmetric Static Space-Times in the Teleparallel Theory of Gravitation

In this paper we explored teleparallel conformal vector fields in cylindrically symmetric static space-times in the teleparallel theory of gravitation by using the direct integration technique. It turns out that the dimension of teleparallel conformal vector fields are 8, 9, 10 or 11. The case VI in which the space-time becomes conformally flat admits eleven independent teleparallel conformal vector fields.

Proper projective symmetry in special non-static plane symmetric Lorentzian manifolds

In this paper a study on proper projective symmetry in special non-static plane symmetric space-times is given by using real eigenvalues and eigenbivectors of the Riemann tensor, direct integration and algebraic techniques. It is shown that when the above space-times admit proper projective collineations they become a very special class of spacelike or timelike version of the FRW k = 0 model.

Mathematical Modeling of a Moving Planar Payload Pendulum on Flexible Portal Framework

Mathematical modeling of a moving planar payload pendulum on elastic portal framework is presented in this paper. The equations of motion of such a system are obtained by modeling the portal frame using finite element in conjunction with moving finite element method and moving planar payload pendulum by using Lagrange’s equations. The generated equations indicate the presence of nonlinear coupling between dynamics of portal framework and the payload pendulum. The combinational direct numerical integration technique, namely Newmarkand fourth-order Runge-Kutta method, is then proposed to solve the coupled equations of motion. Several numerical simulations are performed and the results are verified with several benchmarks. The results indicate that the amplitude and frequency of the payload pendulum swing angle are greatly affected by flexibility of structure and the cable in term of carriage speed.

Nonlinear finite element vibration analysis of double-walled carbon nanotubes based on Timoshenko beam theory

The large-amplitude free vibration analysis of double-walled carbon nanotubes embedded in an elastic medium is investigated by means of a finite element formulation. A double-beam model is utilized in which the governing equations of layers are coupled with each other via the van der Waals interlayer forces. The Von Karman type nonlinear strain-displacement relationships are employed where the ends of the nanotube are constrained to move axially. The effects of the transverse shear deformation and rotary inertia are included based upon the Timoshenko beam theory. A superconvergent beam element which devoid the shear locking effect with displacement fields based on the first order shear deformation theory is used to study the geometric nonlinear effects on the vibrational characteristics of these beam-modeled nanotubes. In this kind of beam element, the interpolating functions are obtained using the exact solution of the static analysis of the beam. The finite element method is employed to discretize the nonlinear governing equations, which are then solved by the direct numerical integration technique to obtain the nonlinear vibration frequencies of double-walled carbon nanotubes with different boundary conditions. The effects of material constant of the surrounding elastic medium and the geometric parameters on the vibrational behavior are investigated. For a double-walled carbon nanotube with different boundary conditions between inner and outer tubes, the nonlinear frequencies are obtained apparently for the first time. The present numerical results are validated by comparing the linear and nonlinear frequencies of double-walled carbon nanotubes with those available in the literature where possible. This comparison illustrates that the present scheme yields very accurate results in predicting the nonlinear frequencies.

Collective Micro-Optics Technologies for VCSEL Photonic Integration

We describe the main recent technological approaches that associate micro-optical elements to VCSELs in order to control their output beam and to improve their photonic integration. These approaches imply either a hybrid assembly or a direct integration technique. They are compared with regards to their tolerance to alignment errors and to their ease of implementation onto arrays of devices at a wafer level. In particular, we detail the integration techniques we have developed for self-aligned polymer microlens fabrication for beam collimation and short distance beam focusing. Finally, designs to achieve active micro-optics or to exploit novel nanophotonic effects are discussed.

A Note on Classification of Cylindrically Symmetric Non-static Space–Times According to Their Teleparallel Killing Vector Fields in the Teleparallel Theory of Gravitation

In this paper, we explored the conservation laws of cylindrically symmetric non-static space–times by using direct integration technique. This classification also covers non-static plane symmetric space–times, static cylindrically symmetric space–times and plane symmetric static space–times. In this paper, we will only present the results of non-static cylindrically symmetric and non-static plane symmetric space–times. The results of static cylindrically symmetric space–times and plane static space–times can be found in Shabbir and Khan (Mod Phys Lett A 25:525, 2010). It turns out that the non-static cylindrically symmetric space–times admit four, five, or seven conservation laws. It is important to note that the above space–times admit at least one or at the most four extra conservation laws.

A note on teleparallel Killing vector fields in Bianchi type VIII and IX space—times in teleparallel theory of gravitation

In this paper we classify Bianchi type VIII and IX space—times according to their teleparallel Killing vector fields in the teleparallel theory of gravitation by using a direct integration technique. It turns out that the dimensions of the teleparallel Killing vector fields are either 4 or 5. From the above study we have shown that the Killing vector fields for Bianchi type VIII and IX space—times in the context of teleparallel theory are different from that in general relativity.

A Note on Classification of Spatially Homogeneous Rotating Space-Times According to Their Teleparallel Killing Vector Fields in Teleparallel Theory of Gravitation

In this paper we classify spatially homogeneous rotating space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields is 5 or 10. In the case of 10 teleparallel Killing vector fields the space-time becomes Minkowski and all the torsion components are zero. Teleparallel Killing vector fields in this case are exactly the same as in general relativity. In the cases of 5 teleparallel Killing vector fields we get two more conservation laws in the teleparallel theory of gravitation. Here we also discuss some well-known examples of spatially homogeneous rotating space-times according to their teleparallel Killing vector fields.

Classification of Teleparallel Homothetic Vector Fields in Cylindrically Symmetric Static Space-Times in Teleparallel Theory of Gravitation

In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times.

Classification of Kantowski–Sachs and Bianchi Type III Space-Times According to Their Killing Vector Fields in Teleparallel Theory of Gravitation

In this paper we classify Kantowski–Sachs and Bianchi type III space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields are 4 or 6, which are the same in numbers as in general relativity. In case of 4 the teleparallel Killing vector fields are multiple of the corresponding Killing vector fields in general relativity by some function of t. In the case of 6 Killing vector fields the metric functions become constants and the Killing vector fields in this case are exactly the same as in general relativity. Here we also discuss the Lie algebra in each case.

CLASSIFICATION OF BIANCHI TYPE I SPACETIMES ACCORDING TO THEIR PROPER TELEPARALLEL HOMOTHETIC VECTOR FIELDS IN THE TELEPARALLEL THEORY OF GRAVITATION

In this paper we explored teleparallel homothetic vector fields in Bianchi type I spacetimes in the teleparallel theory of gravitation using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11 which are same in numbers as in general relativity. In the cases of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice of the spacetimes. In the case of 11 teleparallel homothetic vector fields all the torsion components are zero. The homothetic vector fields of general relativity are recovered in this case and the spacetime become Minkowski.

A note on proper affine vector fields in non-static plane symmetric space-times

Themost general form of non-static plane symmetric space-times is considered to study proper affine vector fields by using holonomy and decomposability, the rank of the 6 × 6 Riemannmatrix and direct integration techniques. Studying proper affine vector fields in each nonstatic case of the above space-times it is shown that very special classes of the above space-times admit proper affine vector fields. We also discuss the Lie algebra in each case.