Exact controllability of a spherical cap: Numerical implementation of HUM

This paper deals with the numerical implementation of the exact boundary controllability of the Reissner model for shallow spherical shells (Ref. 1). The problem is attacked by the Hilbert uniqueness method (HUM, Refs. 2–4), and we propose a semidiscrete method for the numerical approximation of the minimization problem associated to the exact controllability problem. The numerical results compare well with the results obtained by a finite difference and conjugate gradient method in Ref. 5.This work was done when the first two authors were at CNR-IAC, Rome, Italy as Graduate Students.     

应用振幅矢量法讨论夫琅和费单缝衍射光强分布

本文提供了夫琅和费单缝衍射（简称衍射，下同）光强计算公式，与一般文献中的理论公式相比，不但完全等效，而且计算简便精确，对衍射光强分布的实际应用及实验测量￣［３］具有一事实上的参考价值。     

三线摆振动周期与角振幅的关系

本根据机械能守恒定律推出了三线摆的振动周期和角振幅的关系，并据该关系式讨论了角振幅对周期的影响以及角振幅的确定。     

Effect of viscous damping on power transmissibility for the vibration isolation of building services equipment

Vibration isolation plays an important role in both the vibration and noise control of building services equipment. To evaluate vibration isolation performance, the force transmissibility method is commonly adopted. However, increasing the damping effect in the force transmissibility method reduces both the resonance peak value and the isolation performance in the “isolation region”. The limitation of the method is that the transmitted displacement of a floor structure and the interaction of mounting points are neglected. To include the floor displacement and the interaction of mounting points, Mak and Su recently proposed the power transmissibility method to assess the performance of vibration isolation. In this paper, the effect of viscous damping on power transmissibility is investigated. A practical procedure for experimentally determining the damping ratio is also given.     

Distribution of Particles Which Produces a “Smart” Material

If A _q(β, α, k) is the scattering amplitude, corresponding to a potential , where D⊂ℝ³ is a bounded domain, and is the incident plane wave, then we call the radiation pattern the function , where the unit vector α, the incident direction, is fixed, β is the unit vector in the direction of the scattered wave, and k>0, the wavenumber, is fixed. It is shown that any function , where S ² is the unit sphere in ℝ³, can be approximated with any desired accuracy by a radiation pattern: , where ∊ >0 is an arbitrary small fixed number. The potential q, corresponding to A(β), depends on f and ∊, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density of the number of small acoustically soft particles D _m⊂ D, 1≤ m≤ M, distributed in an a priori given bounded domain D⊂ℝ³. The geometrical shape of a small particle D _m is arbitrary, the boundary S _m of D _m is Lipschitz uniformly with respect to m. The wave number k and the direction α of the incident upon D plane wave are fixed. It is shown that a suitable distribution of the above particles in D can produce the scattering amplitude , at a fixed k>0, arbitrarily close in the norm of L ²(S ²× S ²) to an arbitrary given scattering amplitude f(α ', α), corresponding to a real-valued potential q∊ L ²(D), i.e., corresponding to an arbitrary refraction coefficient in D. MSC: 35J05, 35J10, 70F10, 74J25, 81U40, 81V05, 35R30. PACS: 03.04.Kf.     

Obtaining Fourier series graphically from large amplitude oscillatory shear loops

Large amplitude oscillatory shear (LAOS) flow has been used to characterize the nonlinear viscoelasticity of polymer melts and solutions. Results are frequently reported with shear stress versus strain loops, or with shear stress versus shear rate loops. A Fourier analysis of the stress response to LAOS is often desired for comparison with theory, or for quantitative comparison between resins. A method is presented which employs the discrete Fourier transform to obtain the Fourier series coefficients from LAOS loops.     

Studying the Effect of the Spatial Frequency and Amplitude of Corrugation on the Stress–Strain State of Cylindrical Shells

An approach developed earlier to solve two-dimensional static problems for noncircular cylindrical shells is used to analyze the effect of the spatial frequency and amplitude of corrugation on the stress–strain state of shells. The results of the analysis are presented in the form of plots and tables     

The effect of dynamical self-orientation and its applicability for identification of natural frequencies

The effect of dynamical self-orientation and its applicability for the identification of natural frequencies of the investigated systems is demonstrated in this paper. Unidirectional vibration exciter is fixed to the investigated systems via a pivot link and can rotate around it. It is shown that the exciter changes its orientation in the steady state motion mode when the frequency of excitation sweeps over the fundamental frequency of the examined system. Approximate analytical analysis of the discrete system illustrates the basic principle of the effect of dynamical self-orientation. Numerical analysis of both the discrete and different continuous elastic systems confirms the applicability of the effect of self-orientation for the identification of natural frequencies.     

垂直激励圆柱形容器中的表面波特性研究

利用奇异摄动理论的两时间变量展开法，研究了垂直强迫激励圆柱形容器中的单一水表面驻波模式。假设流体是无粘、不可压且运动是无旋的，在忽略了表面张力的影响下，得到一个具有立方项以及底部驱动项影响的非线性振幅方程。对上述方程进行了数值计算，并研究了特定(3，4)模式的表面驻波结构和特性，如驻波的节点分布及随某些参数的变化规律等，从计算的等高线的图象来看，和以往的实验结果相当吻合。     

Flexible Wiper System Dynamic Instabilities: Modelling and Experimental Validation

The optimization of wiper systems under various conditions and the creation of a product which is as robust as possible are the main objectives for an equipment supplier. However, in certain conditions, instabilities can appear and generate wiping defects due to the rubber-glass contact. To improve wiping quality and to reduce the number of test stages for design, this study proposes a wiper system modeling method. The wiper system is represented by a rigid blade holder on which a rubber blade is fitted. This rigid blade system is used on a flat test bench at constant wiping velocity. The model is based on modal synthesis methods and will be validated through comparison with experimental tests under various conditions. The right correlation obtained allows the same modelling method to be applied to the new generation of flexible wiper blades which take account of the degree of freedom of the wiper blade flexions. So, a new computation tool will be developed and validated through experimentation on a specific test bench.