Transient vibration of an infinite string bearing a concentrated mass and supported by elastic-viscous suspensions

The transient transverse vibration of a string, bearing a concentrated mass and supported by elastic-viscous suspensions a constant distance apart, is investigated. The vibration is excited either by an instantaneous impulsive force or a constant force suddenly applied to the concentrated mass. In the first case a formal Fourier transformation of the Dirac impulse function is employed. In the second case the action of the constant force is regarded as a succession of actions of instantaneous pulses.     

Wave scattering by an array of periodic barriers

The 2D scattering of a plane harmonic wave obliquely incidenton an array of perforated barriers is investigated. The geometrygeneralises that previously considered and is subject only tothe requirement of periodicity along the barriers. By partitioninga matrix-valued integral operator into a combination of anothersuch operator and a matrix system, the interactions betweenthe barriers are decoupled. This approach, which extends theusual wide-spacing approximation so as to include a finite numberof evanescent modes, leads to structural simplicity and computationalsaving without compromising accuracy. The couplings betweenthe individual barriers arise naturally through a sequence oftransfer matrices without the need to postulate a matching procedure.Numerical results obtained by using a variational approach aregiven to confirm the efficiency of the method and to give examplesof the scattering process. In particular, the phenomenon ofBragg resonance that occurs in the case of equally spaced, identicalbarriers is examined.     

Arranging apples in an array

Departing from a real-world problem we consider a greedy algorithm which either finds a 0–1 matrix with prescribed row and column sums or terminates with the conclusion that no such matrix exists.The problem has been pending in the literature for about 30 years. Our proof of the validity of the algorithm is established along with an account of earlier findings and appears to be considerably simpler than any other proof hitherto proposed. Various open questions conclude the paper.Dedicated to Peter Naur on the occasion of his 60th birthday     

振动钻削微小孔中钻头寿命与振动参数的二次回归试验研究

本文采用正交组合设计的试验方法，对振动钻削微小孔加工中钻头寿命与轴向振动参数之间的非线性关系进行了二次回归试验，得到了最优回归方程。用回归方程给出的最佳振动参数钻孔，钻头寿命提高了９６．３％     

Discretisation of an infinite delay equation

In this paper, a Banach phase space containing and contained in is defined with which existence of a solution and convergence of a discrete scheme are proved for an infinite delay differential equation.

     

Vibration optimization of an infinite circular AT-cut quartz resonator with ring electrodes

This paper presents the thickness-shear (TSh) vibration modes of an infinite circular AT-cut quartz resonator with ring electrodes. By application of 2D scalar differential equations derived by Tiersten and Smythe, we obtain the resonant frequencies and vibration amplitude distributions of thickness-shear modes in the resonator. The theoretical results have been verified in commercial FEM software COMSOL. Through numerical examples, we illustrate that the distribution of displacement fields in the center part of the ring electrode is adjustable. Furthermore, we optimize the size of the electrodes and the mass ratio of the electrode to the plate, in order to achieve a nearly uniform displacement distribution and mass sensitivity of the resonator. These results can be a theoretical guidance for design and optimization of sensors based on quartz resonators.     

膜与不可压缩有界流体接触时的自由振动

圆形膜与流体接触时的振动被广泛应用于工业中．推导了圆形膜在与不可压缩有界流体接触时,非对称自由振动的自振频率．鉴于膜在不可压缩、非粘性流体中振动引起的小振幅,采用速度势函数来描述流体场．使用两种方法来推导系统的自由振动频率．它们包括变分法及一种近似解法——Rayleigh商法．在用两种方法求得的自由振动频率值之间具有良好的相关性．最后,研究了流体的深度、质量密度以及径向张力对耦合系统自由振动频率的影响．     

具有振动边值的扩散方程Dirichlet问题

本文以上（下）连续函数作为扩散方程u_t=1/2Δu+cu 在Ｄ内的Ｄｉｒｉｃｈｌｅｔ问题边值函数，讨论了振动边值的Ｄｉｒｉｃｈｌｅｔ问题，并用概率方法证明解的存在性、唯一性和稳定性，把古典Ｄｉｒｉｃｈｌｅｔ问题边值条件减弱到最一般情形     

梁振动方程的一种新解法

本文运用广义差分法建立了梁振动方程一种新解法,并对其稳定性进行了讨论     

周边固支圆板非线性热弹耦合振动分析

导出了轴对称圆板非线性热弹耦合自由振动基本方程,对周边固支圆板运用伽辽金法求解,得出振幅随时间变化的数值解.将热弹耦合与非热弹耦合情况进行对比,发现振幅较小时,热弹耦合效应使板的固有频率相对于无热弹耦合情形提高;振幅较大时,热弹耦合效应使固有频率降低.最后比较了不同热弹耦合参数对应的振动情况.     

Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model

A mathematical model is proposed to investigate the dynamic response of an inclined single-walled carbon nanotube (SWCNT) subjected to a viscous fluid flow. The tangential interaction of the inside fluid flow with the equivalent continuum structure (ECS) of the SWCNT is taken into account via a slip boundary condition. The dimensionless equations of motion describing longitudinal and lateral vibrations of the fluid-conveying ECS are obtained in the context of nonlocal elasticity theory of Eringen. The unknown displacement fields are expressed in terms of admissible mode shapes associated with the ECS under simply supported conditions with immovable ends. Using Galerkin method, the discrete form of the equations of motion is derived. The time history plots of the normalized longitudinal and transverse displacements as well as the nonlocal axial force and bending moment of the midspan point of the SWCNT are provided for different levels of the fluid flow speed, small-scale parameter, and inclination angle of the SWCNT. The effects of small-scale parameter, inclination angle, speed and density of the fluid flow on the maximum dynamic amplitude factors of longitudinal and transverse displacements as well as those of nonlocal axial force and bending moment of the SWCNT are then studied in some detail.     

半球壳振动的有限元法分析

本文建立了用有限元法分析球壳的动力学方程.计算分析了不同边界条件下壳体的振动频率.     

基于导纳方法的大型空间结构被动减振研究

以导纳方法研究空间桁架或框架结构的振动,建立了适合分析各种边界条件下均匀梁的机械导纳的通用计算方法,然后通过导纳函数求解各结构单元传递或损耗的功率,通过对损耗功率较大的单元来增加结构的阻尼特征。根据导纳分析结果,可以寻找阻尼单元的最优位置,对结构进行局修改。     

Factoring an infinite abelian group by lacunary cyclic subsets

It was proved in Corrádi and Szabó (Math Pannonica 5:275–280, 1994) that if a finite abelian group of odd order is factored into a direct product of lacunary cyclic subsets, then at least one of the factors must be a subgroup. The paper extends this result for certain infinite torsion groups.      

弹性振动点观测反馈控制古典解的存在性

本文运用有界线性算子的积分半群理论证明弹性振动点观测反馈控制方程古典解的存在性     

Boundedness of imaginary powers of the stokes operator in an infinite layer

In this article we prove the existence of bounded purely imaginary powers of the Stokes operator , which is defined on the space of solenoidal vector fields < q < , where is an infinite layer. It is a consequence of a special representation of the resolvent of the Stokes operator in terms of the Stokes operator on , a composition of a trace and a Poisson operator – a singular Green operator – and a negligible part.     

轴向变速运动粘弹性弦线横向振动的复模态Galerkin方法

在考虑初始张力和轴向速度简谐涨落的情况下,利用含预应力三维变形体的运动方程,建立了轴向变速运动弦线横向振动的非线性控制方程,材料的粘弹性行为由Kelvin模型描述．利用匀速运动线性弦线的模态函数构造了变速运动非线性弦线复模态Galerkin方法的基底函数,并借助构造出来的基底函数研究了复模态Galerkin方法在轴向变速运动粘弹性弦线非线性振动分析中的应用．数值结果表明,复模态Galerkin方法相比实模态Galerkin方法对变系数陀螺系统有较高的收敛速度．