A quasistatic viscoplastic contact problem with normal compliance,unilateral constraint,memory term and friction

The goal of this paper is to deal with a mathematical model which describes the quasistatic frictional contact between a viscoplastic body and a foundation. The contact is modeled with normal compliance, unilateral constraint and memory term. We present the classical formulation of the problem together with the list of assumptions on the data. Then we derive the variational–hemivariational formulation of the model and we prove its unique weak solvability. The proof is based on a recent abstract result of a class of history-dependent variational–hemivariational inequalities.     

On constructing normal and non-normal Cayley graphs

Bamberg and Giudici (2011) showed that the point graphs of certain generalised quadrangles of order $(q?1,q+1)$, where $q=p^k$ is a prime power with $p\ge 5$, are both normal and non-normal Cayley graphs for two isomorphic groups. We call these graphs BG-graphs. In this paper, we show that the Cayley graphs obtained from a finite number of BG-graphs by Cartesian product, direct product, and strong product also possess the property of being normal and non-normal Cayley graphs for two isomorphic groups.     

A microslip friction model with normal load variation induced by normal motion

A two-dimensional microslip friction model with normal load variation induced by normal motion is presented in this paper. The model is a distributed parameter model, which characterizes the stick-slip-separation of the contact interface and determines the resulting friction force, including its time variance and spatial distribution, between two elastic structures. When the relative motion is simple harmonic motion, the stick-slip-separation transition angles associated with any point in the contact area can be analytically determined within a cycle of motion. In addition, if the relative motion is given, stick-slip-separation transition boundaries inside the contact area and their time variances can be determined. Along with an iterative multi-mode solution approach utilizing harmonic balance method (HBM), the developed model can be employed to determine the forced response of frictionally constrained structures. In the approach, the forced response is constructed in terms of the free mode shapes of the structure; consequently, it can be determined at any excitation frequency and for any type of normal load distribution. Two examples, a one-dimensional beam like damper and a more realistic blade to ground damper, are employed to illustrate the predictive abilities of the developed model. It is shown that while employing a single mode model, transition boundaries for the beam like damper agrees with the results given in the literature, the developed method identifies the phase difference along the slip to stick transition boundary when a multi-mode model is employed. Moreover, while partial slip is illustrated in the two examples, typical softening and hardening effects, due to separation of the contact surface, are also predicted for the blade to ground damper.     

结构可靠度的当量正态PFSORM算法

对结构功能函数为相关非正态随机变量构成情况 ,使用PFSORM算法确定结构二次可靠指标须使用随机变量的条件分布函数及其反函数。工程实践中随机变量的条件分布函数及其反函数常不易确定。基于此 ,本文提出当量正态PFSORM算法 ,仅需要随机变量的分布函数、分布密度函数及其相关系数即可     

双频内共振系统的Normal Form及其简化

讨论双频内共振系统的 Normal Form及其降维问题.利用发展的 Normal Form直接方法,导出了任意双频内共振系统 Normal Form的一般形式.指出 Poincare共振项分为内共振项和非内共振性两类,并定义了内共振项的阶.提出了一种普遍适用的降维变换,并证明了该变换可将任意双频内共振系统的 Normal Form方程降到3维.应用举例表明,该变换不仅适用于半单问题,也适于非半单问题（即强:1:1内共振系统）.     

A note on uniqueness of the normal form for quasi-integrable systems

We provide a simple argument that at non-resonant actions the normal form for a quasi-integrable Hamiltonian system, as defined by von Zeipel-Poicaré and Lie perturbation algorithms, is unique.

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Sommario Si fornisce una semplice dimostrazione dell'unicità della forma normale di un sistema hamiltoniano quasi-integrabile, come definito dagli algoritmi perturbativi di VonZeipel-Poincarè e Lie.

     

Non-linear systems under parametric white noise input: Digital simulation and response

Monte Carlo technique is constituted of three steps. Therefore, improving such technique in practice means, improving the procedure used in one of the three following steps: (i) sample paths of the stochastic input process, (ii) calculation of the outputs corresponding to the generated input samples by using methods of classical dynamics and (iii) estimating statistics of the output process from sample outputs related to the previous step. For linear and non-linear systems driven by parametric impulsive inputs such as normal or non-normal white noises, a general integration method requires a considerable reduction of the integration step when the impulse occurs, treating the impulse as a physical one, by means of a window function of finite duration. This makes Monte Carlo simulation very prohibitive from a computational time point of view. While knowing the exact jump value of the response at impulse occurring that is expressed by a numerical series, the aforementioned problem is overcome because there is no need to reduce the integration step saving computational time, reliability being equal as shown by means of a numerical example.     

Enhancement of Anammox performances in an ABR at normal temperature by the low-intensity ultrasonic irradiation

A lab-scale ultrasound enhancing Anammox reactor (ABR_U) was established and irradiated once a week by ultrasound with the optimal parameter (frequency of 25.0 kHz, intensity of 1.00 W cm⁻² and exposure time of 36.0 s) obtained by response surface methodology (RSM). ABR_U and the controlled Anammox reactor (ABR_C) without ultrasonic treatment were operated in parallel. The start-up time of Anammox process in ABR_U (59 d) was shorter than that in ABR_C (69 d). At the end of the nitrogen load-enhancing period, NLR (0.500 kg N m⁻³ d⁻¹) and NRR (0.430 kg N m⁻³ d⁻¹) in ABR_U were both higher than NLR (0.400 kg N m⁻³ d⁻¹) and NRR (0.333 kg N m⁻³ d⁻¹) in ABR_C. The results of RTQ-PCR demonstrated that the specific low-intensity ultrasound irradiation improved the enrichment levels of AnAOB in mature sludge. SEM images and the observation of the macroscopic morphology of mature sludge showed that the ultrasound irradiation strengthened the formation of Anammox granular sludge, thereby improved the interception capacity and impact load resistance of the reactor, and enhanced the nitrogen removal performance in ABR_U. The ultrasonic enhanced Anammox reactor based on an ABR with the optimal parameters can promote the rapid start-up and efficient and stable operation of the Anammox process at normal temperature (around 25.0 °C).     

An experimental study of the first normal stress difference — shear stress relationship in simple shear flow for concentrated shear thickening suspensions

For many polymeric solutions in a simple shear flow a plot of the logarithm of the first normal stress difference N ₁ against the logarithm of the shear stress , for a range of temperatures results in a linear relationship. For such polymer solutions these plots yield a straight line of slope very close to 2 when measured at low shear rates. This relationship is tested against a polymer solution (polyacrylamide in a 50/50 mixture of glycerol/water), a polymer melt (polyethylene), and three concentrated suspensions. These are Superclay (supplied by English China Clays, Cornwall, U.K.) in water, polyvinylchloride in dioctylphthalate and polystyrene latex in water, at volume concentrations of 40% 48%, and 60%, respectively. It was found that the log N ₁ — log relationship is applicable to the polymer solution and melt over a significant range of shear rates and temperatures. In the cases of concentrated suspensions the relationship holds to the point of onset of the shear thickening behaviour. Beyond this point a different relationship exists, however, flow instabilities are apparent. A comment on the contribution of N ₁ and N ₂ to the flow instabilities is made.     

Finite Groups with Unique n-Maximal Subgroup

The aim of this note is to classify the finite groups with unique n-maximal subgroup.