On the dynamic vibrations of an elastic beam in frictional contact with a rigid obstacle

Existence and uniqueness results are established for weak formulations of initial-boundary value problems which model the dynamic behavior of an Euler-Bernoulli beam that may come into frictional contact with a stationary obstacle. The beam is assumed to be situated horizontally and may move both horizontally and vertically, as a result of applied loads. One end of the beam is clamped, while the other end is free. However, the horizontal motion of the free end is restricted by the presence of a stationary obstacle and when this end contacts the obstacle, the vertical motion of the end is assumed to be affected by friction. The contact and friction at this end is modelled in two different ways. The first involves the classic Signorini unilateral or nonpenetration conditions and Coulomb's law of dry friction; the second uses a normal compliance contact condition and a corresponding generalization of Coulomb's law. In both cases existence and uniqueness are established when the beam is subject to Kelvin-Voigt damping. In the absence of damping, existence of a solution is established for a problem in which the normal contact stress is regularized.The work of the last two authors was supported in part by Oakland University Research Fellowships.     

Vertical vibrations of elastic foundation resting on saturated half-space

This paper is mainly concerned with the dynamic response of an elastic foun- dation of finite height bounded to the surface of a saturated half-space.The foundation is subjected to time-harmonic vertical loadings.First,the transform solutions for the governing equations of the saturated media are obtained.Then,based on the assumption that the contact between the foundation and the half-space is fully relaxed and the half- space is completely pervious or impervious,this dynamic mixed boundary-value problem can lead to dual integral equations,which can be further reduced to the Fredholm integral equations of the second kind and solved by numerical procedures.In the numerical exam- ples,the dynamic compliances,displacements and pore pressure are developed for a wide range of frequencies and material/geometrical properties of the saturated soil-foundation system.In most of the cases,the dynamic behavior of an elastic foundation resting on the saturated media significantly differs from that of a rigid disc on the saturated half-space. The solutions obtained can be used to study a variety of wave propagation problems and dynamic soil-structure interactions.     

Shear creep and recovery of a technical polystyrene

The torsional creep and recoverable bahaviour of a technical polystyrene is reported over seven orders of magnitude of the value of the compliance from 10^–8 to 10^–1 Pa^–1 and over more than seven decades in time. The results for the recoverable compliance J_R (t) reveal a dispersion region seen between the glass transition and the steady-state recoverable compliance J_e. The limiting value of the final dispersion J_e = 4.7 · 10^–4 Pa^–1 indicates a broad molecular-weight distribution. The steady-state recoverable compliance J_e is independent of the temperature. The temperature dependence of the final dispersion was found to be indistinguishable from that of viscous flow. However, this temperature dependence differs significantly from that of the glass-rubber transition. A proposal has been made for the construction of creep compliance and recoverable compliance over an extended time scale.     

A variational principle in a geometrically nonlinear theory of heterogeneous viscoelastic shells

The use of the hereditary theory for shells heterogeneous across their thickness is considered. A variational method is formulated for calculating thin anisotropic shells made of a material whose deformation behavior can be described by relations of the linear theory of viscoelasticity. In order to transform the corresponding functional into a form suitable for shells, some assumptions related to concepts of the theory of thin shells are introduced. In the capacity of Euler equations, physical relations, nonlinear equilibrium equations, and nonlinear boundary conditions are derived. The state equations are deduced for a multilayered shell. Translated from Mekhanika Kompozitnykh Materialov, Vol. 45, No. 2, pp. 231–240, March–April, 2009.     

A mixed variational formulation of a contact problem with adhesion

A mathematical model describing the contact between a viscoplastic body and a deformable foundation is analyzed under small deformation hypotheses. The process is quasistatic and in normal direction the contact is with adhesion, normal compliance, memory effects and unilateral constraint. We derive a mixed-variational formulation of the problem using Lagrange multipliers. Finally, we prove the unique weak solvability of the contact problem.     

Tutorial on evaluation of type I and type II errors in chemical analyses: From the analytical detection to authentication of products and process control

Uncertainty is inherent in all experimental determinations. Nevertheless, these measurements are used to make decisions including the performance of the own measurement systems. The link between the decision and the true implicit system that generates the data (measurement system, production process, category of samples, etc.) is a representation of this uncertainty as a probability distribution. This representation leads to the probabilistic formalization of the possibility of making errors. In the context of regulations established by official agencies, it is important to use these statistical decision methods in some cases because the own norm makes them mandatory and, in general, because this is the way of reasonably evaluating whether a working hypothesis is rejected on the basis of the experimental data.The aim of the present tutorial is to introduce some ideas and basic methods for the critical analysis of experimental data. With this goal, the basic elements of the Neyman-Pearson theory of hypothesis testing are formally introduced in connection with the common problems in chemical analysis and, if this is the case, their relation to the norms of regulatory agencies. The notion of decision with ‘enough quality’ is modelled when explicitly considering: (1) the null, H₀, and alternative, H₁, hypotheses. (2) The significance level of the test, which is the probability, α, of rejecting H₀ when it is true, and the power of the test, 1 − β, β being the probability of accepting H₀ when it is false. (3) The difference between H₀ and H₁ that has to be detected with experimental data. (4) The needed sample size. These four concepts should be explicitly defined for each problem and, under the usual assumption of normal distribution of the data, the mathematical relations among these concepts are shown, which allow the analyst to design a decision rule with pre-set values of α and β.To illustrate the unifying character of this inferential methodology, several situations are exposed along the tutorial: the design of a hypothesis test to decide on the performance characteristics of analytical methods, the capability of detection of both quantitative and qualitative analytical methods (including its generalization to the case of multivariate and/or multiway signals), the analytical sensitivity with multivariate signals, the class-modelling and the process control.     

锻压操作机夹持长棒料随动过程动态受力分析

研究了锻压操作机夹持长棒料锻件锻压随动过程中夹钳的受力状态。利用拉格朗日方程及有限元方法建立了包含操作机及其锻件的总体动力学方程。操作机系统建立为端部悬挂质量弹簧的Euler-Bernoulli梁模型,随动过程中因为梁上节点位移激励引起操作机系统的瞬态振动。计算结果与LS-DYNA显式有限元模型结果进行了比对,吻合良好。结果表明,对于长棒料锻件,液压机锻压的位置对操作机的动态受力有着十分显著的影响。     

一种工程实用的分数指数黏弹性固体模型

从热力学对模型的限制出发,提出了一种工程实用的、新固体流变模型-分数指数模型,它可与实验结果很好吻合,具有简单实用、计算速度快、自相谐调的优点,克服了目前固体模型收敛速度太慢、计算量太大的严重缺点,可以广泛应用于线性或非线性黏弹性被子示问题的计算之中。