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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

Impact Noise of Non-homogeneous Floors： Analysis of Different Input Parameters for Computational Modeling Predictions

Floor systems with non-homogeneous slabs have more complex means of propagation than homogeneous systems, with more variables to be considered in predictions by theoretical models. For those slabs, it is necessary to understand the differences of each material composing each subsystem, and the connection types between the elements of each one of this subsystem. Some floors integrating lightweight elements without structural purposes, are broadly used in several countries in precast slabs. The predictions based on computer modelling for building systems can be influenced by the input parameters related to connections between the elements of the floor system. In building structures, the analysis of radiation due to element vibrations may be represented by wave propagation relationships as a one-dimensional system, a two-dimensional system or a three-dimensional solid. In these floors, the modelling of the interaction between elements can be basically a face, a line or a point connection. In addition, the choice of the connection type can determine the vibration transmission amongst all the floor elements. This study focuses on the differences that can be obtained in the induced vibration response due to an impact source on non-homogeneous slabs. It also presents some examples of modelling options for several floor systems, considering input parameters for different connection types.

WEAK TYPE INEQUALITIES FOR FRACTIONAL INTEGRAL OPERATORS ON GENERALIZED NON-HOMOGENEOUS MORREY SPACES

We obtain weak type （1, q） inequalities for fractional integral operators on generalized non-homogeneous Morrey spaces. The proofs use some properties of maximal operators. Our results are closely related to the strong type inequalities in [13, 14, 15].

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.

THRESHOLD RESULT FOR SEMILINEAR PARABOLIC EQUATIONS WITH INDEFINITE NON-HOMOGENEOUS TERM

In this paper, we study the threshold result for the initial boundary value problem of non-homogeneous semilinear parabolic equations {μt-△μ=g（μ）＋λf（x）,（x,t）∈Ω×（0,T）,μ=0,（x,t）∈ Ω×[0,T）,μ（x,0）=μ0（x）≥0,x∈Ω.By combining a priori estimate of global solution with property of stationary solution set of problem （P）, we prove that the minimal stationary solution Uλ（x） of problem （P） is stable, whereas, any other stationary solution is an initial datum threshold for the existence and nonexistence of global solution to problem （P）.

Isogeometric Boundary Element Method for Two-Dimensional Steady-State Non-Homogeneous Heat Conduction Problem

The isogeometric boundary element technique(IGABEM)is presented in this study for steady-state inhomogeneous heat conduction analysis.The physical unknowns in the boundary integral formulations of the governing equations are discretized using non-uniform rational B-spline(NURBS)basis functions,which are utilized to build the geometry of the structures.To speed up the assessment of NURBS basis functions,the Bezier extraction´approach is used.To solve the extra domain integrals,we use a radial integration approach.The numerical examples show the potential of IGABEM for dimension reduction and smooth integration of CAD and numerical analysis.

Vertical dynamic response characteristics of single pile in non-homogeneous soil layers

A computational method and a mechanical model for evaluating the vertical dynamic harmonic response characteristics of a single pile embedded in non-homogeneous soil layers and subjected to harmonic loadings were established based on a certain assumption and the improved dynamic model of beam-on-Winkler foundation by using the principle of soil dynamics and structure dynamics. Both non-homogeneity of soil strata and softening effect of soil layer around the pile during vibration were simultaneously taken into account in the proposed computational model. It is shown through the comparative study on a numerical example that the numerical results of dynamic response of the single pile computed by the proposed method are relatively rational and can well agree with the numerical results computed from the well-known software of finite element method. Finally the parametric studies were conducted for a varied range of main parameters to discuss the effects of relevant factors on dynamic responses of the single pile embedded in non-homogeneous layered soils excited by harmonic loading with different frequencies.

Deposition Morphology of Non-homogeneous Debris Flow and Its Energy Characteristics

Non-homogeneous two-phase debris flows are widely found in the western mountainous regions of China. To investigate the characteristics of the debris flow deposition process related to the morphology and extent of the debris fan, a series of physical experiments were carried out using an experimental flume. Some useful relationships were obtained to link the flow velocity with the geometric characteristics of deposition morphology and the corresponding area or volume. Based on these, some expressions about energy dissipation process in both the transport-deposition zone and deposition zone are presented, and improved equations describing solidliquid two-phase energy transformations in the specific deposition zone are also established. These results provide a basis for further investigating the underlying mechanisms of non-homogeneous debris flows, based upon which effective disaster control measures can be undertaken.

The Existence of Positive Solutions of p-Laplacian Non-homogeneous Multi-point Boundary Value Problems

We study the following nonlinear m-point p-Laplacian boundary value problem with non-homogenous condition: (Φp(u′)′)+f(t, u, u′)=0, 0<t<1, u′(0)=0, u(1)-Σ m-2 i=1 kiu(ξi)=λ, where Φp(s)=|s|p-2 s, p>1, λ>0, ki≥0(i = 1, 2, ··· , m-2), 0<ξ1<ξ2< ··· <ξm-2<1,0 < Σm-2 i=1 ki<1. Under sufficient conditions, we show that there exists a positive number λ* such that the problem has at least one positive solution for 0 < λ < λ and no solution for λ > λ*. The proof is based on the Schauder fixed point theorem and upper-lower technics.

Thermal Effect on Free Vibration of Non-Homogeneous Orthotropic Visco-Elastic Rectangular Plate of Parabolically Varying Thickness

A simple model presented here is to study the thermal effect on vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness having clamped boundary conditions on all the four edges. For non-homogeneity of the plate material, density is assumed to vary linearly in one direction. Using the separation of variables method, the governing differential equation has been solved for vibration of non-homogeneous orthotropic viscoelastic rectangular plate. An approximate frequency equation is derived by using Rayleigh-Ritz technique with a two-term deflection function. Results are calculated for time period and deflection at different points, for the first two modes of vibration, for various values of temperature gradients, non-homogeneity constant, taper constant and aspect ratio and shown by graphs.