Effect of Non-Homogeneity on Thermally Induced Vibration of Orthotropic Visco-Elastic Rectangular Plate of Linearly Varying Thickness

The analysis presented here is to study the effect of non-homogeneity on thermally induced vibration of orthotropic visco-elastic rectangular plate of linearly varying thickness. Thermal vibrational behavior of non-homogeneous rectangular plates of variable thickness having clamped boundary conditions on all the four edges is studied. For non–homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the method of separation of variables, the governing differential equation is solved. An approximate but quite convenient frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Time period and deflection at different points for the first two modes of vibration are calculated for various values of temperature gradients, non- homogeneity constant, taper constant and aspect ratio. Comparison studies have been carried out with non-homogeneous visco-elastic rectangular plate to establish the accuracy and versatility.

Effect of Foundation and Non-Homogeneity on the Vibrations of Polar Orthotropic Parabolically Tapered Circular Plates

The effect of Pasternak foundation and non-homogenity on the axisymmetric vibrations of polar orthotropic parabolically varying tapered circular plates has been analyzed on the basis of classical plate theory. Ritz method has been used to find the numerical solution of the specified problem. The efficiency of the Ritz method depends on the choice of basis function based upon deflection of polar orthotropic plates. The effects of different plate parameters viz. elastic foundation, non-homogeneity, taper parameter and that of orthotropy on fundamental, second and third mode of vibration have been studied for clamped and simply-supported boundary conditions. Mode shapes for specified plates have been drawn for both the boundary conditions. Convergence and comparison studies have been carried out for specified plates.

DYNAMIC FRACTURE MECHANICS ANALYSIS FOR COMPOSITE MATERIAL WITH MATERIAL NON-HOMOGENEITY IN THICKNESS DIRECTION

The problem considered here is the response of a non-homogeneouscomposite material containing some cracks subjected to dynamicloading. It is assumed that the composite material is or- thotropicand all material properties depend only on the coordinate y (alongthe thickness direcion). In the analysis, the elastic region isdivided into a number of plies of infinite length. The materialproperties are taken to be constants for each ply. By utilizing theLaplace transform and Fourier transform technique, the generalsolutions for plies are derived.

Natural vibration and critical velocity of translating Timoshenko beam with non-homogeneous boundaries

In most practical engineering applications,the translating belt wraps around two fixed wheels.The boundary conditions of the dynamic model are typically specified as simply supported or fixed boundaries.In this paper,non-homogeneous boundaries are introduced by the support wheels.Utilizing the translating belt as the mechanical prototype,the vibration characteristics of translating Timoshenko beam models with nonhomogeneous boundaries are investigated for the first time.The governing equations of Timoshenko beam are deduced by employing the generalized Hamilton's principle.The effects of parameters such as the radius of wheel and the length of belt on vibration characteristics including the equilibrium deformations,critical velocities,natural frequencies,and modes,are numerically calculated and analyzed.The numerical results indicate that the beam experiences deformation characterized by varying curvatures near the wheels.The radii of the wheels play a pivotal role in determining the change in trend of the relative difference between two beam models.Comparing the results unearths that the relative difference in equilibrium deformations between the two beam models is more pronounced with smaller-sized wheels.When the two wheels are of equal size,the critical velocities of both beam models reach their respective minima.In addition,the relative difference in natural frequencies between the two beam models exhibits nonlinear variation and can easily exceed 50%.Furthermore,as the axial velocities increase,the impact of non-homogeneous boundaries on modal shape of translating beam becomes more significant.Although dealing with non-homogeneous boundaries is challenging,beam models with non-homogeneous boundaries are more sensitive to parameters,and the differences between the two types of beams undergo some interesting variations under the influence of non-homogeneous boundaries.

Robust adaptive radar beamforming based on iterative training sample selection using kurtosis of generalized inner product statistics

In engineering application,there is only one adaptive weights estimated by most of traditional early warning radars for adaptive interference suppression in a pulse reputation interval(PRI).Therefore,if the training samples used to calculate the weight vector does not contain the jamming,then the jamming cannot be removed by adaptive spatial filtering.If the weight vector is constantly updated in the range dimension,the training data may contain target echo signals,resulting in signal cancellation effect.To cope with the situation that the training samples are contaminated by target signal,an iterative training sample selection method based on non-homogeneous detector(NHD)is proposed in this paper for updating the weight vector in entire range dimension.The principle is presented,and the validity is proven by simulation results.

Non-homogeneous SiGe-on-insulator formed by germanium condensation process

Ge condensation process of a sandwiched structure of Si/SiGe/Si on silicon-on-insulator （SOI） to form SiGe-on- insulator （SGOI） substrate is investigated. The non-homogeneity of SiGe on insulator is observed after a long time oxidation and annealing due to an increased consumption of silicon at the inflection points of the corrugated SiGe film morphology, which happens in the case of the rough surface morphology, with lateral Si atoms diffusing to the inflection points of the corrugated SiGe film. The transmission electron microscopy measurements show that the non-homogeneous SiGe layer exhibits a single crystalline nature with perfect atom lattice. Possible formation mechanism of the non-homogeneity SiGe layer is presented by discussing the highly nonuniform oxidation rate that is spatially dependent in the Ge condensation process. The results are of guiding significance for fabricating the SGOI by Ge condensation process.

Study the Effect of Thermal Gradient on Transverse Vibration of Non-Homogeneous Orthotropic Trapezoidal Plate of Parabolically Varying Thickness

The present paper deals with the effect of linearly temperature on transverse vibration of non-homogeneous orthotropic trapezoidal plate of parabolically varying thickness. The deflection function is defined by the product of the equations of the prescribed continuous piecewise boundary shape. The non homogeneity of the plate is characterized by taking linear variation of the Young's modulus and parabolically variation of the density of the material. The non homogeneity is assumed to arise due to the variation in the density of the plate material and it is taken as parabolically. Rayleigh Ritz method is used to evaluate the fundamental frequencies. The equations of motion, governing the transverse vibrations of orthotropic trapezoidal plates, are derived with boundary condition clamped-simply supported-clamped-simply supported. Frequencies corresponding to first two modes of vibration are calculated for the trapezoidal plate for various combinations of the parameters of the non-homogeneity, thermal gradient, taper constant and for different values of the aspect ratios and shown by figures. All The results presented here are entirely new and are not found elsewhere. Comparison can only be made for homogeneous plates, and in that cases the results have been compared with those found in the existing literatures and are in excellent agreement.

Study of Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Parabolically Thickness Variation in Both Directions

The present analysis demonstrates the thermal effect on vibrations of a symmetric, non-homoge- neous trapezoidal plate with parabolically varying thickness in both directions. The variation in Young’s modulus and mass density is the main cause for the occurrence of non-homogeneity in plate’s material. In this consideration, density varies linearly in one direction. The governing differential equations have been derived by Rayleigh-Ritz method in order to attain fundamental frequencies. With C-S-C-S boundary condition, a two term deflection function has been considered. The effect of structural parameters such as taper constants, thermal gradient, aspect ratio and non-homogeneity constant has been investigated for first two modes of vibration. The obtained numerical results have been presented in tabular and graphical form.

Study of Temperature Behaviour on Thermally Induced Vibration of Non-Homogeneous Trapezoidal Plate with Bi-Linearly Varying Thickness

The main aim of the present work is to study the linear temperature behaviour of a non-homogeneous trapezoidal plate whose thickness varies linearly in both directions. The temperature behaviour considered linear along the length of the plate. Non-homogeneity in plate arises due to variation in density along the length of the plate. The two-term deflection function with clamped-simply supported-clamped-simply supported boundary condition is taken into consideration. The effect of structural parameters such as taper constants, thermal gradient, non-homogeneity constant and aspect ratio has been studied. Rayleigh-Ritz method is used to solve the governing differential equations and to obtain the fundamental frequencies for the first two modes of vibration. Results are presented in graphical form.

Interval grey number sequence prediction by using non-homogenous exponential discrete grey forecasting model

This paper aims to study a new grey prediction approach and its solution for forecasting the main system variable whose accurate value could not be collected while the potential value set could be defined. Based on the traditional nonhomogenous discrete grey forecasting model（NDGM）, the interval grey number and its algebra operations are redefined and combined with the NDGM model to construct a new interval grey number sequence prediction approach. The solving principle of the model is analyzed, the new accuracy evaluation indices, i.e. mean absolute percentage error of mean value sequence（MAPEM） and mean percent of interval sequence simulating value set covered（MPSVSC）, are defined and, the procedure of the interval grey number sequence based the NDGM（IG-NDGM） is given out. Finally, a numerical case is used to test the modelling accuracy of the proposed model. Results show that the proposed approach could solve the interval grey number sequence prediction problem and it is much better than the traditional DGM（1,1） model and GM（1,1） model.

Large scale shaking table model test and analysis on seismic response of utility tunnel in non-homogeneous soil

Underground utility tunnels are the most fundamental and reliable lifeline network in urban cities,and are widely constructed throughout the world.In urban areas,most utility tunnels usually encounter the non-homogeneity of subsoil condition due to various construction effects.Studies have shown that the damage mechanism of shallow underground structures mainly depends on the inhomogeneity of the subsoil conditions.This would become a considerable factor for the stability of the underground utility tunnel structures.However,this type of research still needs to establish the vulnerable seismic design.In this study,a series of shaking table tests were conducted on non-homogenous soils to investigate the performance of seismic interaction between utility tunnels,surrounding soils and interior pipelines.The dynamic responses measured from the test account for the boundary condition of non-homogeneous soils,the internal forces,displacement of tunnel joints,the dynamic characteristics on interior pipelines and the reasonable spring stiffness with damping in the seismically isolated gas pipeline model inside the tunnel.The vulnerability of underground utility tunnel in non-homogeneous soil zone and the mechanism of the stability of interior facilities are the main topics discussed in this paper.

Immersed Interface Finite Element Methods for Elasticity Interface Problems with Non-Homogeneous Jump Conditions

In this paper,a class of new immersed interface finite element methods (IIFEM) is developed to solve elasticity interface problems with homogeneous and non-homogeneous jump conditions in two dimensions.Simple non-body-fitted meshes are used.For homogeneous jump conditions,both non-conforming and conforming basis functions are constructed in such a way that they satisfy the natural jump conditions. For non-homogeneous jump conditions,a pair of functions that satisfy the same non-homogeneous jump conditions are constructed using a level-set representation of the interface.With such a pair of functions,the discontinuities across the interface in the solution and flux are removed;and an equivalent elasticity interface problem with homogeneous jump conditions is formulated.Numerical examples are presented to demonstrate that such methods have second order convergence.

ELASTODYNAMIC SOLUTION OF A NON-HOMOGENEOUS ORTHOTROPIC HOLLOW CYLINDER

A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure.

Solution to 1-D consolidation of non-homogeneous soft clay

In this work, semi-analytical methods were used to solve the problem of 1-D consolidation of non-homogeneous soft clay with spatially varying coefficients of permeability and compressibility. The semi-analytical solution was programmed and then verified by comparison with the obtained analytical solution of a special case. Based on the results of some computations and comparisons with the 1-D homogeneous consolidation (by Terzaghi) and the 1-D non-linear consolidation theory (by Davis et al.) of soft clay, some diagrams were prepared and the relevant consolidation behavior of non-homogeneous soils is discussed. It was shown that the result obtained differs greatly from Terzaghi’s theory and that of the non-linear consolidation theory when the coefficients of permeability and compressibility vary greatly.

Development of Optimal Maintenance Policies for Offshore Wind Turbine Gearboxes Based on the Non-homogeneous Continuous-Time Markov Process

Gearbox in offshore wind turbines is a component with the highest failure rates during operation. Analysis of gearbox repair policy that includes economic considerations is important for the effective operation of offshore wind farms. From their initial perfect working states, gearboxes degrade with time, which leads to decreased working efficiency. Thus, offshore wind turbine gearboxes can be considered to be multi-state systems with the various levels of productivity for different working states. To efficiently compute the time-dependent distribution of this multi-state system and analyze its reliability, application of the nonhomogeneous continuous-time Markov process(NHCTMP) is appropriate for this type of object. To determine the relationship between operation time and maintenance cost, many factors must be taken into account, including maintenance processes and vessel requirements. Finally, an optimal repair policy can be formulated based on this relationship.

Free vibration analysis of non-homogeneous orthotropic plates resting on Pasternak elastic foundation by Rayleigh-Ritz method

Free vibration analysis of non-homogeneous orthotropic plates resting on a Pasternak type of elastic foundation is investigated. A set of admissible orthogonal polynomials are generated with Gram-Schmidt orthogonalization procedure and adopted in the Rayleigh-Ritz method. Accuracy and applicability of the method are examined by comparison of the results for different boundary conditions and material types with those available in literature. It is found that this method has good accuracy regardless of type of boundary condition and yields very accurate results even with low number of terms of orthogonal polynomials for the first mode of vibration. For higher modes of vibration, higher terms of orthogonal polynomials should be used. The effects of foundation parameter, density and non-homogeneity parameters on natural frequency are examined. It is concluded that natural frequency of plates are more sensitive to shearing layer coefficient rather than Winkler coefficient and density parameter has weakening effect on natural frequency.

Bayesian Reliability——Growth Analysis for Statistical of Diverse Population Based on Non-homogeneous Poisson Process

New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aiming at the test process which is high expense and small sample-size in the development of complex system, the specific methods are studied on how to process the statistical information of Bayesian reliability growth regarding diverse populations. Firstly, according to the characteristics of reliability growth during product development, the Bayesian method is used to integrate the testing information of multi-stage and the order relations of distribution parameters. And then a Gamma-Beta prior distribution is proposed based on non-homogeneous Poisson process（NHPP） corresponding to the reliability growth process. The posterior distribution of reliability parameters is obtained regarding different stages of product, and the reliability parameters are evaluated based on the posterior distribution. Finally, Bayesian approach proposed in this paper for multi-stage reliability growth test is applied to the test process which is small sample-size in the astronautics filed. The results of a numerical example show that the presented model can make use of the diverse information synthetically, and pave the way for the application of the Bayesian model for multi-stage reliability growth test evaluation with small sample-size. The method is useful for evaluating multi-stage system reliability and making reliability growth plan rationally.

Element nodal computation-based radial integration BEM for non-homogeneous problems

This paper presents a new strategy of using the radial integration boundary element method （RIBEM） to solve non-homogeneous heat conduction and thermoelasticity problems. In the method, the evaluation of the radial in-tegral which is used to transform domain integrals to equivalent boundary integrals is carried out on the basis of elemental nodes. As a result, the computational time spent in evaluating domain integrals can be saved considerably in comparison with the conventional RIBEM. Three numerical examples are given to demonstrate the correctness and computational efficiency of the proposed approach.

Lipschitz estimates for commutator of fractional integral operators on non-homogeneous metric measure spaces

In this paper, the authors establish the(L^p(μ), L^q(μ))-type estimate for fractional commutator generated by fractional integral operators Tα with Lipschitz functions(b ∈ Lipβ(μ)),where 1 < p < 1/(α + β) and 1/q = 1/p-(α + β), and obtain their weak(L^1(μ), L^(1/(1-α-β))(μ))-type. Moreover, the authors also consider the boundedness in the case that 1/(α+β) < p < 1/α,1/α≤ p ≤∞ and the endpoint cases, namely, p = 1/(α + β).

FORMULA OF GLOBAL SMOOTH SOLUTION FOR NON-HOMOGENEOUS M-D CONSERVATION LAW WITH UNBOUNDED INITIAL VALUE

In this article, we prove the existence and obtain the expression of its solution formula of global smooth solution for non-homogeneous multi-dimensional（m-D） conservation law with unbounded initial value; our methods are new and essentially different with the situation of bounded initial value.