Finite impulse response utilizing the principle of superposition

A critical parameter in any finite impulse response (FIR) design is the impulse response length, which must be optimized for the given design specifications in order to reduce the size of the filter. To this end, many design algorithms have been introduced, such as Remez exchange, linear programming, and least mean squares. A new algorithm has been derived that is simple, efficient, and accurate for the design of arbitrary filter specifications and requires fewer computations than many other FIR approaches. This paper provides the definition of the basic functions used for the design process. An overview of the design process is given and the design technique used to design filters with tailored passband and stopband responses to yield a near-optimum time length is presented. This design can be very useful when compensating for the effects of a second transducer or other second order effects in surface acoustic wave (SAW) devices. The effects of monotonically increasing sidelobes on the impulse response length are discussed and illustrated. The addition of arbitrary phase response to the filter design process is discussed. The results of the current FIR approach are discussed and compared with other design techniques.     

A superposition method of reflected wave for moving string vibration with nonclassical boundary

A reflected wave superposition method is proposed for an axially traveling string with classical and nonclassical boundaries, based on the reflection of the propagating wave on both sides of the string, combining its initial conditions and the continuity conditions in order to obtain the expressions for the reflected wave. The reflection process, in three phases, is deduced and a determinate expression for the transverse vibration is obtained. The correctness and superiority of the proposed method is verified by comparison with the Newmark-β method for an axially moving string with a fixed and a spring-dashpot boundary.     

Damped response of an axially excited rotating liquid bridge in zero-gravity

Summary The response of a solidly rotating finite liquid bridge due to axial excitation exhibits for frictionless liquid at the resonances singularities. For the experimenter in a spacelabmission the actual resonance amplitude is of quite some importance. For this reason damping, that has to be measured in ground tests, has been introduced into the results of the response.Notation a radius of the liquid bridge - h length of the liquid bridge - I ₀,I ₁ modified Besselfunctions - J ₀,J ₁ Besselfunctions - r, ,z polar coordinates - t time - excitation amplitude - elliptic case - hyperbolic case - abbreviation - damping factor of liquid - (z, t) free surface displacement - =² – ² surface tension - surface tension - liquid density - ₀ rotational speed of liquid bridge - forcing frequency of axial excitation - natural frequency of liquid bridge With 2 Figures     

参数激励非线性压电梁的振动稳定性

研究了参数激励压电梁的振动稳定性,考虑非线性阻尼的影响,采用Hamilton变分原理推导结构运动方程,采用多尺度法求解稳态响应幅值。通过数值算例分析了电压、轴向力以及非线性阻尼等因素对定常解稳定性的影响。通过分析可见,外加电压与压电层上下表面电势差的差值△V主要影响自变量σ／ω的取值区间,对定常解的稳定性影响较小;梁所承受的轴力越小,定常解稳定区间越大;非线性阻尼的常数项和二次项系数越大,定常解稳定区间越大。     

窄带随机噪声参激作用下强非线性系统的响应

将改进的L-P(ModifiedLindstedt-Poincare)方法和随机多尺度法结合起来,研究了窄带随机噪声参激作用下强非线性VanderPol-Duffing系统的响应、稳定性和分叉问题。文中首先由改进的L-P方法引入变换参数,然后用多尺度法分离了系统的快变量,求出了最大Lyapunov指数的解析表达式,得到了系统几乎必然稳定的充分必要条件,讨论了系统的参数对稳定性的影响,分析了系统在1/2亚谐共振区的性态。理论分析与数值计算表明:在一定条件下系统将发生随机跳跃,且随着随机激励带宽的增大,扩散的极限环的宽度将逐渐增大。数值模拟结果表明:MLP方法结合随机多尺度法研究强非线性随机系统的响应、稳定性和分叉问题是有效的。     

Nonlinear transversal vibration of an axially moving viscoelastic string on a viscoelastic guide subjected to mono-frequency excitation

In this paper, the nonlinear transversal vibration of an axially moving viscoelastic string on a viscoelastic guide subjected to a mono-frequency excitation is considered. The model of the viscoelastic guide is a parallel combination of springs and viscous dampers. The governing equation of motion is developed using Hamilton’s principle. Applying the method of multiple scales to the governing partial differential equation, the solvability condition and approximate solutions are derived. Three cases, namely primary, subharmonic and superharmonic resonances are studied and appropriate analytical solutions are obtained. The effect of mean value velocity, force amplitude, guide stiffness and viscosity coefficient of the string on the frequency-response and bifurcation points is investigated. Findings are in good agreement with results extracted from numerical modeling.     

Applicability of the time–temperature superposition principle in modeling dynamic response of a polyurea

This paper addresses the applicability of the Time–Temperature Superposition Principle in the dynamic response of a polyurea polymer at high strain rates and different temperatures. Careful and extensive measurements in the time domain of the relaxation behavior and subsequent deduction of a master-relaxation curve establish the mechanical behavior for quasistatic deformations over a time range of 16 decades. To examine its validity in a highly dynamic environment, experiments with the aid of a split Hopkinson (Kolsky) pressure bar are carried out. The use of a two-material pulse shaper allows for stress equilibrium across the specimen during the compression process, to concentrate on the initial, small deformation part that characterizes linearly viscoelastic behavior. This behavior of polyurea at high strain rates and different temperatures is then investigated by comparing results from a physically fully three-dimensional (axisymmetric) numerical model, employing the quasistatically obtained properties, with corresponding Hopkinson bar measurements. The experimentally determined wave history entering the specimen is used as input to the model. Experimental and simulation results are compared with each other to demonstrate that the Time–Temperature Superposition Principle can indeed provide the requisite data for high strain rate loading of viscoelastic solids, at least to the extent that linear viscoelasticity applies with respect to the polyurea material.     

On the principle of superposition for stress intensity factors

The principle of superposition as applied for stress intensity factors for different types of loading will be discussed. Using an energy formulation, it will be shown that stress intensity factors for different loading types are additive provided all loading types tend to open the crack. Negative part contributions to the stress intensity factor may also be superimposed if the associated loads tend to close the crack along the entire crack front.     

移动质量作用下轴向运动悬臂梁振动特性分析

将弹炮发射系统简化为移动质量作用下的轴向运动悬臂梁系统,推导了轴向运动梁的振动方程,采用修正的Galerkin法离散求解该偏微分方程,得到以模态坐标表示的二阶时变常微分方程组,通过Newmark-β法对方程组进行了求解。计算结果表明,移动质量载荷主要使梁的一阶模态受到激励,移动质量的大小和运动速度对悬臂梁的振动响应影响较大,在移动质量作用下梁的伸缩运动都处于不稳定状态;在移动质量脱离悬臂梁后,梁的轴向收缩运动使得梁的瞬时振动频率不断减小,振动位移逐渐衰减,而振动速度逐渐增大,梁的运动处于不稳定状态,伸展时梁的自由振动规律相反。     

轴向高速运动梁的热冲击动力学响应及控制

研究了轴向高速运动、两端自由梁的热冲击下横向振动响应及控制,采用Hamilton原理得到了受热冲击和控制力的轴向运动高速梁的横向振动方程和边界条件.运用修正的伽辽金法得到了求解系统响应的近似方程.数值仿真给出了速度2马赫时,系统的二阶模型在热冲击下的响应,发现响应较大.运用LQR法设计了最优控制器,其中采用加权系数法选择Q,R矩阵,比较了系统的无控制与有控制下的位移响应,结果表明控制效果良好.     

轴向运动黏弹性夹层板的多模态耦合横向振动

基于薄板小挠度理论和Kelvin-Voigt黏弹性本构方程, 建立了轴向运动黏弹性夹层板横向振动控制方程, 研究了其横向振动特性。采用一阶和二阶Galerkin截断得到夹层板横向振动的特征方程, 讨论了两种夹心层所占总厚度比率下轴向运动速度对其横向振动特性的影响。研究表明: 在未超过临界速度前, 无论一阶还是二阶截断, 在定性描述系统特征上二者相同, 但一阶截断不适合描述轴向运动速度超过临界速度的情形; 对四边简支黏弹性夹层板, 临界速度和发生耦合模态颤振的速度随着夹心层比率的减少逐渐增大。     

Steady-state voltammetric response of the nanopore electrode

The steady-state voltammetric response of the truncated conical-shaped glass nanopore electrode is presented. Analytical theory, finite-element simulations, and experimental measurement of the diffusive flux of a redox molecule through the pore orifice demonstrate that the steady-state current decreases rapidly as the pore depth increases and then asymptotically approaches a constant value when the pore depth is approximately 50x larger than the pore orifice. The asymptotic limit of the steady-state current is only a function of the pore orifice radius and the cone angle of the pore and has a finite value for all cone angles greater than zero. Experimental confirmation of the predicted dependence on pore depth is obtained using nanopore electrodes with 100-1000 nm orifice radii, by measuring the steady-state voltammetric current corresponding to the oxidation of ferrocene in acetonitrile solutions containing an excess of supporting electrolyte.     

Numerical study of the remittances of axially excited chiral sculptured zirconia thin films

The transmission and reflection spectra from a right-handed chiral sculptured zirconia thin film are calculated using the coupled wave theory and the Bruggeman homogenization formalism in conjunction with the experimental data for the relative dielectric constant of zirconia thin film. The dielectric dispersion function effect on these spectra appeared in wavelengths shorter than the Bragg wavelength. In wavelengths larger than the Bragg wavelength, the dispersion of the dielectric function can be ignored. The results achieved in this work are consistent with the experimental data [Wu, Q.; Hodgkinson, I.J.; Lakhtakia, A. Opt. Eng. 2000, 39, 1863]. A shift towards shorter wavelengths is observed for the Bragg peak with increasing void fraction, which is in agreement with the theoretical work of Lakhtakia [Microw. Opt. Technol. Lett. 2000, 24, 239]. Sorge et al. [Opt. Express 2006, 14, 10550] also found this effect in their experimental results on TiO₂ chiral thin films, while they also found that unlike our results the intensity of the reflectance of the Bragg peak decreases with increasing void fraction. This difference between our theoretical work and Sorge et al.'s experimental work can be related to the structural difference between the idealized theoretical model for chiral films and that obtained in experimental work. In the latter, as Sorge et al. have pointed out the experimental films exhibit a large amount of scattering due to the highly complex and non-ideal structure that the individual chiral elements exhibit.     

The energetics and the stability of axially moving strings undergoing planar motion

Free coupled planer vibration of an axially moving string is investigated from the point of view of energetics. The time-rate of the total mechanical energy associated with the vibration is calculated for axially accelerating strings with ends moving in a prescribed way. The result shows that the energy is not conserved for a string moving in a constant axial speed and constrained by two fixed ends. For such a string, it is proved that there exists a conserved quantity that remains a constant during the coupled planar vibration. An approximate conserved quantity is derived from the conserved quantity in the neighborhood of the straight equilibrium configuration. The approximate conserved quantity is applied to verify the Lyapunov stability of the straight equilibrium configuration.     

轴向运动粘弹性夹层梁热力耦合振动频率分析

研究了温度场与位移场相互耦合时,轴向运动粘弹性夹层梁的横向振动特性。基于Euler-Bernouli梁理论和Kelvin粘弹性材料本构关系,建立了轴向运动粘弹性夹层梁横向振动控制方程;考虑材料变形与传热的相互影响,得到相应的热力耦合状态下轴向运动粘性夹层梁的耦合控制方程。采用Galerkin截断得到相应的热力耦合动力系统。用数值方法分析了相关热参数对梁振动频率的影响。     

Stochastic analysis of the critical velocity of an axially moving cracked elastic plate

In this study, a probabilistic analysis of the critical velocity for an axially moving cracked elastic and isotropic plate is presented. Axially moving materials are commonly used in modelling of manufacturing processes, like paper making and plastic forming. In such systems, the most serious threats to runnability are instability and material fracture, and finding the critical value of velocity is essential for efficiency. In this paper, a formula for the critical velocity is derived under constraints for the probabilities of instability and fracture. The significance of randomness in different model parameters is investigated for parameter ranges typical of paper material and paper machines. The results suggest that the most significant factors are variations in the crack length and tension magnitude.     

Prediction of long-term viscoelastic behavior of amorphous resin based on the time-temperature superposition principle

This paper deals with the prediction of long-term viscoelastic behavior of amorphous resin at a temperature below the glass transition temperature T _g from measuring the short-term viscoelastic behavior at elevated temperatures based on the time-temperature superposition principle (TTSP) with vertical shift as well as horizontal shift. The long-term creep compliance as well as short-term and medium-term creep compliances were measured at elevated temperatures. The master curves of creep compliance can be constructed from measured data by shifting vertically as well as horizontally. The master curves of creep compliance constructed from measured data by short-term and medium-term creep tests agree well with those measured by long-term creep tests. Furthermore, the horizontal and vertical shift factors obtained from constructing the master curve are independent of the time period of creep tests. Therefore, the long-term viscoelastic behavior at a temperature below T _g can be predicted accurately from measuring the short-term viscoelastic behavior at elevated temperatures based on the TTSP with vertical shift as well as horizontal shift.     

Instability and treatments of the coupled discrete element and lattice Boltzmann method by the immersed moving boundary scheme

The immersed moving boundary (IMB) scheme has been extensively used to couple the discrete element method (DEM) with the lattice Boltzmann method (LBM). In the literature, only the formulation of IMB for lattice nodal cells covered by a single-solid particle was given. The treatment of situations where a nodal cell is covered by two or more solid particles is seldom discussed. It is found that some numerical instability can occur for such situations due to an inappropriate computation of the weighting function in the IMB formulation. This work presents an enhanced treatment that can resolve the issue and validates it using some benchmark tests. Furthermore, to avoid the extra costs associated with the treatment and simplify the complicated procedure introduced, a simplified IMB scheme is proposed. The accuracy of both enhanced and simplified IMB schemes are validated by test cases including single-particle sedimentation, two-particle drafting-kissing-tumbling phenomenon, and multiple-particle sedimentation. Then, the robustness of both schemes is examined and discussed using a specially designed flow past cylinders test. The simplified IMB scheme is proved to be robust and sufficiently accurate and simpler and more effective than the enhanced scheme.