Method Of Initial Values Research Articles

Slope Deflection Method in Nonlocal Axially Functionally Graded Tapered Beams

In this study, the slope deflection method was presented for structures made of small-scaled axially functionally graded beams with a variable cross section within the scope of nonlocal elasticity theory. The small-scale effect between individual atoms cannot be neglected when the structures are small in size. Therefore, the theory of nonlocal elasticity is used throughout. The stiffness coefficients and fixed-end moments are calculated using the method of initial values. With this method, the solution of the differential equation system is reduced to the solution of the linear equation system. The given transfer matrix is unique and the problem can be easily solved for any end condition and loading. In this problem, double integrals occur in terms of the transfer matrix. However, this form is not suitable for numerical calculations. With the help of Cauchy’s repeated integration formula, the transfer matrix is given in terms of single integrals. The analytical or numerical calculation of single integrals is easier than the numerical or analytical calculation of double integrals. It is demonstrated that the nonlocal effect plays an important role in the fixed-end moments of small-scaled beams.

Beetle Antennae Search Strategy for Neural Network Model Optimization with Application to Glomerular Filtration Rate Estimation

The determination of weights is very important for neural network models. Nevertheless, the traditional feedforward neural networks usually use the method of random initial values to determine the weights of the neural networks, such a method would make the related neural network models possess unstable performance in accuracy. Therefore, in order to improve the prediction accuracy and efficiency of neural networks, a novel neural network model based on beetle antennae search (BAS) and weights and structure policy (WASP) is proposed and applied to the estimation of glomerular filtration rate (GFR). Through a series of numerical experiments, it is proved that the accuracy of the proposed neural network model for GFR estimation is higher than that of the model without BAS algorithm optimization. In addition, compared with the traditional one-step method, the method proposed in this article is more than 300% higher in the three performance indicators of MSE, MAE, and MAPE.

Buckling Analysis of a Bi-Directional Strain-Gradient Euler–Bernoulli Nano-Beams

Investigated herein is the buckling of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. Since the transport matrix cannot be calculated analytically, the problem was examined with the help of an approximate transport matrix (matricant). This method can be easily applied with buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on gradient elasticity theory. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The diagrams and tables of the solutions for different end conditions and various values of the parameters are given and the results are discussed.

An investigation of static bending of a bi-directional strain-gradient Euler–Bernoulli nano-beams with the method of initial values

Investigated herein is the static bending of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. To the best of the researchers’ knowledge, in the literature, there is no study carried out into gradient elasticity theory for bending analysis of bi-directional strain-gradient Euler–Bernoulli (BDSGEB) nanostructures with arbitrary functions. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The transfer matrix for beams is given analytically. For an initial value problem, the transport matrix is unique. The diagrams of the solutions for different end conditions and various values of the parameters are given and the results are discussed.

An investigation of free vibrations of a strain gradient Timoshenko beams with the method of initial values

Investigated herein is the free vibrations of beams based on the strain gradient Timoshenko beam theory with the method of initial values. For the vibration of strain-gradient Timoshenko beam (SGTB), the sixth-order ordinary differential equation and three boundary conditions at each end have been obtained by using the Hamilton principle. The effect of the characteristic length on the frequencies of free vibrations is shown. The frequencies of the SGTB are compared to the frequencies of the strain gradient Euler beam (SGEB), classical Timoshenko beam (CTB) and classical Euler beam (CEB). It has been observed that the high-frequency values of conventional and strain-gradient beams are very different. This result can be used to determine the value of the material characteristic length for a nanobeam for which lengthscale effects are believed to be dominant.

Buckling Analysis of Nanobeams Based on Nonlocal Timoshenko Beam Model by the Method of Initial Values

Investigated herein is the buckling of nanobeams based on a nonlocal Timoshenko beam model by the method of initial values within the framework of nonlocal elasticity. Since the nonlocal Timoshenko beam theory is of higher order than the nonlocal Euler–Bernoulli beam theory, it is known to be superior in predicting the small-scale effect. The buckling determinants and critical loads for bars with various kinds of supports are presented. The Carry-Over matrix (Transverse Matrix) is presented and the priorities of the method of initial values are depicted. To the best of the researchers’ knowledge, this is the first work that investigates the buckling of nonlocal Timoshenko beam with the method of initial values.

Improvement of convergence behavior for adaptive feed-forward control with initial values design in hard disk drives

This paper introduces an improvement method of convergence behavior for adaptive feed-forward control in hard-disk-drives (HDDs). To increase a data capacity of HDDs, head-positioning-control system must compensate for any disturbances which worsen the positioning accuracy. Especially, it is important to compensate for external disturbances in the head positioning system of 2.5 type HDDs. Previous studies proposed an adaptive feed-forward control method to compensate for the external disturbances. However, the control method have problems with respect to convergence in the adaptive algorithm. To overcome the problems, we have developed design method of initial values for the adaptive feed-forward control by using data-driven design method. The initial values designed by proposed method can improve the convergence behavior for the adaptive algorithm.

Stability analysis of gradient elastic beams by the method of initial value

The buckling of a bar is studied analytically on the basis of a simple linear theory of gradient elasticity in the frame of the method of initial values. The method of initial values provides the values of the displacements and stress resultants throughout the bar once the initial displacements and initial stress resultants are known. We use probably for the first time the method of initial values to get critical loads of a strain gradient beam under completely different boundary conditions at the two end faces of the beam. Exact carryover matrix is presented for the classical beam and gradient beam analytically. The first mode shapes of classical beam and gradient beam are plotted. The method of initial values is also applied to the beams with variable cross-section. The priorities of the method of initial values are depicted. The variational approach gives a sixth-order ordinary differential equation for a beam in buckling. The additional boundary conditions are used to obtain critical loads. It is observed that critical loads increase dramatically for increasing values of the gradient coefficient.

Task Allocation in Distributed Artificial Intelligence using Boids Model

Decentralized multi-agent approach is a promising research field particularly in the area of performance improvement by handling task allocation and communication time. Some recent research has focused on developing the learning process to be better suited for specific problems; other efforts had proven that a generalized solution is better off especially when there is no global controller. This paper presents a better suited multimembered evolution strategy to agent reasoning with an improved method of pre-assigning initial values to agents. We show through computer experiments that agents using the presented method reach a stable state in a faster pace than other multi-agent systems, although after a stable state is reached the improvement -we are presenting- effect will be a little limited until the system reaches an unstable state again.

Free vibrations of a strain gradient beam by the method of initial values

We extend the application of the method of initial values (also known as the transfer matrix method) to find frequencies of free vibrations of a strain-gradient-dependent Euler–Bernoulli beam (EBB) under different boundary conditions at the two end faces of the beam. For the classical EBB, we find the exact matricant or the carry-over matrix but it is numerically evaluated for the strain-gradient-dependent EBB. For the numerically evaluated matricant, it is found that ten iterations give converged values of the first six frequencies for the classical and the strain-gradient-dependent EBB. For the strain-gradient EBB, the sixth-order ordinary differential equation for the lateral deflection and three boundary conditions at each end have been derived by using the Hamilton principle. The material characteristic length is found to noticeably affect frequencies of free vibrations. Thus, the difference between frequencies of the classical and the strain-gradient-dependent EBB can be used to determine the value of the material characteristic length for a nanobeam for which length scale effects are believed to be dominant.

Nonlocal Effects in Curved Single-Walled Carbon Nanotubes

Carbon nanotubes are molecular structures of graphitic carbons, which are envisioned as hollow cylindrical bars with outstanding properties. They are the most popular ones among the stiffest and strongest fibers, and have remarkable electronic properties and many more unique characteristics. They are widely used in nanotechnological applications. In this article, a single-walled curved carbon nanotube loaded perpendicular to its plane is investigated by using the method of initial values within the framework of nonlocal elasticity. The principal matrix required for the applicability of the method of initial values is presented. The results indicate that nonlocal effects could be significant for curved carbon nanotubes.

The initial values method for buckling of nonlocal bars with application in nanotechnology

In this work, the buckling of a bar is investigated by using the method of initial values within the framework of nonlocal elasticity. The principal matrix required for the applicability of the method of initial values is presented. The critical loads for bars with various kind of supports are found. As is well known that nanotechnology is the engineering of functional systems at the molecular scale. Carbon nanotubes are molecular-scale tubes which are figured as hollow cylindrical bars of graphitic carbon at molecular scale with outstanding properties. They are among the stiffest and strongest fibers known, and have remarkable electronic properties and many other unique characteristics. They are widely used in nanotechnological applications. The results are used to display that nonlocal effects could be significant in buckling of carbon nanotubes.

Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment, axial and shear force

Natural circular frequencies of piles partially embedded in the soil whose upper ends are semi-rigid connected are calculated using the method of initial values, the transfer matrix, the small-displacement theory and the Winkler model. It is assumed that the behavior of the material is linear-elastic, and that the axial force along the pile length and the modulus of subgrade reaction to be constant. The semi-rigid connections of the upper ends of the piles are modeled by elastic rotational springs. The transfer matrices are obtained due to the boundary conditions of the piles. Natural circular frequencies and relative stiffness of the piles are calculated for a non-trivial solution of a linear homogeneous system of equations obtained due to the terms of the transfer matrices of the piles, the stiffnesses of the linear-elastic rotational springs and ratio of embedded length of the pile to total length of the pile; the results are presented in graphs.

Euler Critical Force Calculation for Laced Columns

The paper presents a method of solving the buckling problem of laced column as a statically indeterminate structure without analyzing determinants of high order. The flexural and torsional buckling problems of laced column are reduced to the two-point boundary value problem for a difference equation system. The value of Euler critical load is determined as a result of analyzing the fourth order determinant for column with any degree of static indeterminacy. The solution is based on the method of initial values. Stability of columns with any types of lattice (crosswise, serpentine, with batten struts); with any number of lattice panels and with variable lattice spacing can be examined by this manner. The analogy between the flexural and torsional buckling of the laced column is established. It enables one to use the same relations for consideration of both kinds of buckling. The obtained numerical results show that the Euler critical loads calculated by this method can be substantially differed from those based on the approximated Engesser's approach. A PC program for checking stability of laced column by designer can be developed on the basis of the present method.

The analytical calculation of circular rods of variable cross-section by the initial values method

In this work, the stress resultants and displacements (due to in-plane loading) of circular rods with variable cross-sections are calculated by using the initial values method. The principal matrix and its inverse required for the applicability of the method of initial values are obtained. The expression of the solution of a circular-rod loaded by both continuous and singular loads is given in a compact form. Irrespective of the number of singular loads and the degree of redundancy the system of algebraic equations to be solved contains no more than three variables as shown. Two examples exhibiting the advantages and priorities of the method are solved in full detail. The program Mathematica is used throughout.

Selection method of initial guess values for surface temperature estimation from the satellite data

Abstract For the estimation of sea surface temperature on the basis of linearized inversion of the radiative transfer equation (Rodgers method), the selection method of the initial guess values of sea surface temperature and atmospheric condition is proposed. The selection method uses the temporal statistics of air temperature profile and precipitable water profiles as an atmospheric models. The satellite observed brightness temperature is calculated from the atmospheric models and some surface models, and the atmospheric model and surface model which makes the difference between the calculated and the observed radiance minimize is selected as the initial guess values. The sea surface temperature estimation from MOS-1/VTIR data shows a good correspondence to the sea truth data.

3本ロールの動剛性

In case that we discuss the accuracy of the Bourdon tube pressure gauge, it is supposed that errors of the shape and dimension of the Bourdon tube which arise from manufacturing process, especially the errors of the radius and the thickness, are respectively one of a primary factor which has influence upon the accuracy. But the relation between these errors and the dynamic rigidity of the bender has not been found before. In this paper we regard the bender as a structure which consists of three rollers and the Bourdon tube, and by means of F. E. M. we analyzed how the dynamic rigidity of the roller system would have influence on the errors of the Bourdon tube in the manufacturing process. From the nature of the subject we also considered the Eigenvalue problem and its acceleration technique, especially the Origin Shift Method and estimation of initial values to the number of the Origin Shift, etc.

Some mathematical problems in the theory of the stability of parallel flows

By applying the method of initial values to the theory of stability of shear flows, Case has recently found certain results which are in apparent conflict with those obtained by the theory of normal modes. It is shown how these differences may be reconciled. Some new features in the theory of normal modes are also brought out. The relative merits of the two theories are compared.