Eigenfrequency of a Helmholtz resonator at the wall of a rectangular duct

The eigenfrequency of a Helmholtz resonator fixed at the wall of a rectangular duct is estimated. Special attention is given to determining the attached length of the resonator neck as viewed from the duct. The dependences of the attached neck length and the eigenfrequency on the duct configuration are analyzed. Theoretical results are compared with the data of numerical calculations performed by the finite-element method.     

Acoustics of a blocked duct with flow

An analysis is given for flow and acoustical motion of fluid in a duct, aimed at describing some features of the blowing mechanism of a woodwind instrument. The latter is simulated by a rigid rectangular duct, open at one end and nearly closed off at the other, where a local section of the side wall can undergo transverse displacement. It is supposed that such a piston-like oscillation superposes an acoustical perturbation on a steady flow through the duct. The principal results of the calculations, in which it is presupposed that the displacement amplitude is small compared to the piston width, which is in turn small compared with the duct width and wavelength, are contained in estimates for the natural frequencies and optimum flow speeds to excite these modes.     

Radiation impedance of a piston in a waveguide

The radiation of a piston in a rectangular waveguide whose wall is a baffle for the piston is considered. Simple asymptotic formulas for the real and imaginary parts of the piston radiation impedance are derived.     

Attractive Casimir forces in a closed geometry

We study the Casimir force acting on a conducting piston with arbitrary cross section. We find the exact solution for a rectangular cross section and the first three terms in the asymptotic expansion for small height to width ratio when the cross section is arbitrary. Though weakened by the presence of the walls, the Casimir force turns out to be always attractive. Claims of repulsive Casimir forces for related configurations, like the cube, are invalidated by cutoff dependence.     

On the attached length of orifices

The attached length of orifices in reactive mufflers has been estimated based on numerical calculations by the finite-element method. The numerical results for a diaphragm in a duct are compared with the theoretical data obtained by Rayleigh, Fock, Karal, and Ingard. The dependence of the attached length on the diaphragm thickness is given. The results obtained are generalized for the case in which the orifice is a Helmholtz resonator neck. The effect of the resonator length on the attached length of the neck is analyzed.     

STUDY ON THE RADIATION ACOUSTIC FIELD OF RECTANGULAR RADIATORS IN FLEXURAL VIBRATION

In this paper, the radiation acoustic field of a rectangular radiator in flexural vibration is studied. The radiator is a rectangular thin plate in flexural vibration with simply supported boundary conditions. Based on the theory of Rayleigh integral, the acoustic pressure distribution of the radiator in its far field is obtained analytically and the near acoustic field of the radiator is also computed numerically. In the near field, the three-dimensional acoustic pressure distribution is obtained. In the far field, the two- and three-dimensional acoustic pressure distribution patterns are calculated. The dependence of the radiation acoustic pressure of the radiator on the vibrational order of the plate in flexural vibration is analyzed. It is demonstrated that the radiation acoustic pressure along the central axis of the radiator is always zero in the near and far acoustic fields, and the radiation near acoustic field and the far acoustic field are both directional. This is different from the acoustic field generated by an oscillating piston. On the other hand, when the vibrational order is increased, the acoustic pressure distribution of the radiator becomes complex.     

弯曲振动矩形板辐射阻抗的计算

本文推导了四边简支矩形板的辐射阻抗表达式, 利用高斯数值积分方法, 计算了其相对辐射阻抗的数值解. 由不同模态下相对辐射阻抗与频率以及不同长宽比对应的相对辐射阻抗与频率的关系可知, 在中低频段, 模态越低, 辐射阻抗越大, 也就意味着辐射声功率和同振质量越大; 对于一定面积和模态的矩形板, r (r=a/b, 长与宽之比)值越接近1, 即越接近正方形, 辐射阻和辐射抗越大. 本文的方法能对其他复杂边界条件下的、无振动解析解的矩形板的辐射阻抗数值量级大小提供一个参考, 也可由计算弯曲振动的阻抗自然地过渡到活塞振动阻抗的计算.     

The radiation impedance of a rectangular piston

The radiation impedance of a rectangular piston is expressed as the Fourier transform of its impulse response, which is obtained from the recent work of Lindermann [1]. The analytical evaluation of the transform is performed and new integral expressions are presented for both the radiation resistance and reactance. The integrals are readily evaluated in terms of elementary functions at both the low and high frequency limits. The integrals are also expressed as series of Bessel functions which are valid for all frequencies and aspect ratios. Numerical results are presented to illustrate the behavior of the radiation resistance and reactance as a function of the aspect ratio of the piston and a normalized frequency parameter. Additional numerical results are then presented to illustrate the accuracy of the analytical expressions for the radiation resistance and reactance at low and high frequencies. Finally, numerical results are presented to illustrate the application and accuracy of using standard FFT algorithms to evaluate the radiation resistance and reactance directly from the impulse responses.     

一种精确计算毫米波矩形微带天线贴片元物理尺寸的新方法

为了使矩形微带天线的实际谐振频率和设计频率相一致,矩形贴片元物理尺寸的精确计算是非常重要的。文中在腔模理论的基础上,计入辐射损耗,提出了一种精确计算毫米波矩形微带天线贴片元物理尺寸的新方法,并利用该方法计算设计了四元毫米波矩形微带贴片天线,仿真和实测结果证实了该方法的有效性。     

On the radiation impedance of a rectangular piston

Single integral representations for the resistive and reactive components of the radiation impedance appropriate to a rectangular piston are established, thereby enabling a systematic refinement of estimates at both short and long wavelengths. Comparisons with previous analyses are made explicit as well as extensions and corrections thereto.     

Acoustic radiation impedance of rectangular pistons on prolate spheroids

The self and mutual radiation impedances for rectangular piston(s) arbitrarily located on a rigid prolate spheroidal baffle are formulated. The pistons are assumed to vibrate with uniform normal velocity and the solution is expressed in terms of a modal series representation in spheroidal eigenfunctions. The prolate spheroidal wave functions are obtained using computer programs that have been recently developed to provide accurate values of the wave functions at high frequencies. Results for the normalized self and mutual radiation resistance and reactance are presented over a wide frequency range for different piston sizes and spheroid shapes.     

Simulation of hydrodynamic phenomena attendant on the flame front propagation in a tube behind a piston

The propagation of a propane-air flame in a model internal combustion chamber, a tube with one or two pistons, is studied experimentally. Situations are simulated in which the flame front moves in a semiopen flat or cylindrical tube between two pistons or between a piston and the closed end of the tube. The time dependence of the flame front position and acceleration is obtained for the case of the variable tube length and combustible mixture volume. Self-oscillation conditions for the flame front and piston are determined. A relation between their amplitude-frequency characteristics is found. It is established that the piston paradox motion effect, i.e., the motion of the piston toward the flame front, depends on the length of the tube. It is demonstrated that the piston effect is related to the formation of a “tulip” flame. An explanation to the observed hydrodynamic phenomena is given.     

双光栅绕射辐射器件谐振系统Q值分析与结构优化

对双光栅绕射辐射器件谐振系统的Q值特性进行了分析,研究了谐振系统结构参数对Q值的影响及其优化措施。结果表明,双光栅绕射辐射器件谐振结构的Q值受矩形槽宽度和球面开放腔长度的影响最为明显。与奥罗管相比,双光栅绕射辐射器件中光栅的引入对Q值的影响要小得多,且光栅齿宽和齿深的增加都会导致谐振系统Q值降低。     

Propagation and radiation of sound in a finite length duct

An analysis has been carried out to investigate sound transmission in an unflanged circular duct of finite length. A new formulation for calculating the generalized radiation impedance of the opening of a finite length duct with a spinning source inside is presented. The effect of interference between the duct apertures at its two ends is identified in the calculations of radiation impedance, reflection coefficient, and the far field radiation pattern. The results show that the degree of interference between the two ends reduces for high frequency waves and/or for long ducts. Further, the interference effects on the far field for spinning sound are more serious than those for non-spinning sound.     

Effect of flow on quasi-one-dimensional acoustic wave propagation in a variable area duct of finite length

The general equation for the velocity potential of quasi-one-dimensional acoustic wave motion in a variable area, finite duct with one-dimensional flow is derived by using a perturbation technique. The non-linear second-order partial differential equation is linearized and then solved, by either a power series expansion method or the Runge-Kutta fourth-order method, for harmonic time dependence. The boundary condition taken at the duct mouth is that of matching the impedance of the duct sound field to that of the radiation field at the duct opening. Three axial Mach number variations along the duct axis are considered and the results obtained are compared with those for the case of constant Mach number, to determine the influence of the axial velocity gradient on sound propagation. The effect of flow on the radiation impedance is also considered.     

聚焦部分相干涡旋光束作用于不同折射率瑞利粒子上的辐射力

 使用聚焦部分相干高斯谢尔涡旋光束,对不同折射率的瑞利粒子的辐射力做了分析,着重研究了相关长度和束腰宽度对辐射力和俘获稳定性的影响。结果表明：相关长度和束腰宽度分别存在临界值,相干长度小于等于其临界值或束腰宽度大于等于其临界值时,可利用其俘获相对折射率大于1的微粒;而在相关长度大于其临界值或束腰宽度小于其临界值时,可利用其俘获相对折射率小于1的微粒。对俘获稳定性的分析表明,需选择适当的相关长度和束腰宽度才能稳定俘获瑞利粒子。     

Anomalous band formation in arrays of terahertz nanoresonators

We investigate band formation in one-dimensional periodic arrays of rectangular holes which have a nanoscale width but a length of 100 μm. These holes are tailored to work as resonators in the terahertz frequency regime. We study the evolution of the electromagnetic response with the period of the array, showing that this dependence is not monotonic due to both the oscillating behavior of the coupling between holes and its long-range character.     

Finite-temperature Casimir effect in piston geometry and its classical limit

We consider the Casimir force acting on a d-dimensional rectangular piston due to a massless scalar field with periodic, Dirichlet and Neumann boundary conditions and an electromagnetic field with perfect electric-conductor and perfect magnetic-conductor boundary conditions. The Casimir energy in a rectangular cavity is derived using the cut-off method. It is shown that the divergent part of the Casimir energy does not contribute to the Casimir force acting on the piston, thus renders an unambiguously defined Casimir force acting on the piston. At any temperature, it is found that the Casimir force acting on the piston increases from −∞ to 0 when the separation a between the piston and the opposite wall increases from 0 to ∞. This implies that the Casimir force is always an attractive force pulling the piston towards the closer wall, and the magnitude of the force gets larger as the separation a gets smaller. Explicit exact expressions for the Casimir force for small and large plate separations and for low and high temperatures are computed. The limits of the Casimir force acting on the piston when some pairs of transversal plates are large are also derived. An interesting result regarding the influence of temperature is that in contrast to the conventional result that the leading term of the Casimir force acting on a wall of a rectangular cavity at high temperature is the Stefan–Boltzmann (or black-body radiation) term which is of order T ^d+1, it is found that the contributions of this term from the two regions separating the piston cancel with each other in the case of piston. The high-temperature leading-order term of the Casimir force acting on the piston is of order T, which shows that the Casimir force has a nontrivial classical ℏ→0 limit. Explicit formulas for the classical limit are computed.     

Impedance of the microstrip line for magnetostatic backward volume waves

We study excitation of magnetostatic backward volume waves on the microstrip line. The relation between the current density in the line and the normal component of the magnetic induction is found. The impedance of the line per unit length, i.e., its reactance and radiation resistance per unit length, is represented as a functional of the current density. The dependence of the operating-wave radiation resistance on the transverse size of the line and the width of the dielectric gap is studied. The radiation resistances of multistrip array and meander-type converters of magnetostatic backward volume waves are calculated     

对史密斯-帕塞尔自由电子激光光栅的研究

为了研究史密斯-帕塞尔自由电子激光的输出频率和光栅槽深、光栅槽长、光栅槽宽的关系,对于基于矩形光栅的史密斯-帕塞尔自由电子激光利用粒子模拟软件进行模拟和理论分析。首先,利用粒子模拟软件模拟对于基于矩形光栅的史密斯-帕塞尔自由电子激光进行了研究,发现史密斯-帕塞尔自由电子激光的输出频率随光栅槽深、光栅槽长、光栅槽宽的增大而减少。接着,对史密斯-帕塞尔自由电子激光的光栅槽进行了理论分析,发现每个光栅槽都可以等效为一个LC谐振电路,并发现在史密斯-帕塞尔自由电子激光中存在两种辐射,一种是史密斯-帕塞尔辐射,另一种是LC振荡辐射。最后,对光栅槽的LC振荡辐射进行了估算,发现史密斯-帕塞尔自由电子激光输出频率的模拟值与光栅槽的LC振荡辐射估算值的数量级均为102 GHz,且变化规律上一致。据此推测决定史密斯-帕塞尔自由电子激光输出频率的应该是光栅槽,而不是谐振腔。