Vibration analysis of polar orthotropic discs using the transfer matrix method

The well known transfer matrix scheme of Ehrich for calculating the vibration characteristics of uniform and varying thickness discs is extended to include polar orthotropic material behaviour. The exact deflection equations for an annular element of material are used in the solution. Comparisons with alternative solutions in the literature show excellent agreement for both annular and complete discs of uniform and varying thickness profile.     

Vibration analysis of liquid-filled pipelines with elastic constraints

In this paper, a transfer matrix method (TMM) in frequency domain considering fluid-structure interaction of liquid-filled pipelines with elastic constraints is proposed. The time-domain equations considering fluid-structure interaction, are transformed into frequency domain by Laplace transformation, and then twelve fourth-order ordinary differential equations and two second-order ordinary differential equations are deduced from the frequency-domain equations. The results of the fourteen frequency-domain equations are assembled into a transfer matrix, which represents the motion of a single pipe section. Combined with point matrices that describe specified boundary conditions, an overall transfer matrix for liquid-filled pipeline system can be assembled. Using the method, all the pipeline with no and rigid constraints can be easily calculated by simply setting the stiffness of the restraining springs from zero to a large number. Taking into account the longitudinal vibration, transverse vibration and torsional vibration, the proposed method can be used to analyze the pipelines with bends. Several numerical examples with different constraints are presented here to illustrate the application of the proposed method. The results are validated by measured and simulation data. Through the numerical examples, it is shown that the proposed method is efficient.     

Sylvester theorem and the multichannel transfer matrix method for arbitrary transverse potential profile inside a wave guide

Based on the Sylvester and Frobenius theorems, we drastically enhance the feasibility of the transfer-matrix approach to deal with problems involving a large number of propagating and interfering modes, which require the solution of coupled differential equations and the evaluation of functions of matrix variables. We report closed formulas for the spectral decomposition of this type of functions. As specific example, besides the calculation of simple and well-known 1D one channel transfer matrices, we derive the multi-channel transfer matrix for an electron gas in the presence of a transverse electric field.     

A study of stepped acoustic resonator with transfer matrix method

Transfer matrix method was applied in the study of stepped acoustic resonators. Transfer matrix method was more competent in comparison with analytic method to investigate the acoustic properties of stepped acoustic resonator, especially multi-step acoustic resonator. With the help of the numerical solution, the resonance frequencies, the phase angles and the radiation impedances of stepped acoustic resonators which consisted of one to five sub-tubes were studied theoretically and experimentally. The numerical solutions were in excellent agreement with the experimental results.     

利用转移矩阵方法求解一维散射问题

利用转移矩阵方法,求解粒子通过任意势垒的透射系数及反射系数,并给出粒子的概率密度分布曲线.     

Vibration analysis of plates of arbitrary shape—A new approach

The so-called finite strip method combined with the deflection contour method has proved highly successful in the analysis of bending of thin elastic plates of arbitrary shape. Here the same technique is used to obtain the fundamental frequency of plates of arbitrary shape. The method of approach is much simpler than the conventional finite element method since it requires less programming effort and a reduction in both memory space and time on the computer. Several representative plate problems of irregular boundaries are treated by the proposed method. For all cases, comparison of the results are made with other known solutions and the agreement appears to be excellent.     

用时间平均全息方法分析扬声器的振形

简述由时间平均全息法拍摄扬声器振形的基本原理、方法和实验装置。     

Vibration of doubly curved shallow shells with arbitrary boundaries

The first comprehensive study of shallow shell vibrations subjected to as many as 21 possible boundary conditions is presented. Thin shallow shell theory is used. Relatively accurate results for natural frequencies of doubly-curved shallow shells have been obtained. These can be used for benchmarking by researchers as well as reference data for practicing engineers. The Ritz method is used to solve for natural vibrations of these shells with arbitrary boundary conditions. Natural frequencies are presented for various shell curvatures including spherical, cylindrical and hyperbolic paraboloidal shells.     

Analysis of a right-angle conical reflector resonator by the transfer matrix method

A resonator with a right-angle conical reflector has been proposed to produce high-power CO₂ laser beams. To analyze eigenfields of the right-angle conical reflector resonator, this paper adopts and demonstrates the transfer matrix method. In this paper, the mode-fields and corresponding losses are described as eigenvectors and eigenvalues of a transfer matrix according to the self-reproducing principle of laser field. By solving the transfer matrix for eigenvectors and eigenvalues, we obtain field distributions and losses of the dominant eigenmodes. The calculation results reveal that the right-angle conical reflector resonator could be used for a high-power CO₂ laser to achieve low-order modes. However, the beam quality is reduced due to the residual blind-hole, which is in accord with the experimental result.     

A transfer matrix analysis of quaternary diffusion

A transfer matrix method (TMM), developed recently by Ram-Mohan and Dayananda, has been employed for the first time to generate error function solutions for quaternary diffusion in solid–solid metallic diffusion couples. The method was validated with the aid of a hypothetical couple with known quaternary interdiffusion coefficients and applied to two experimental Cu–Ni–Zn–Mn quaternary couples annealed at 775°C. Quaternary interdiffusion coefficients were determined by the Dayananda analysis from the concentration profiles of the couples over selected composition ranges in the diffusion zone and employed for the subsequent TMM calculation of error function solutions. For the hypothetical test couple, identical sets of constant interdiffusion coefficients were determined on either side of the Matano plane and utilized for the calculation of concentration profiles by TMM. For the experimental Cu–Ni–Zn–Mn couples, interdiffusion coefficients determined over selected regions in the diffusion zone were employed for the TMM generation of the concentration profiles.     

The analytical transfer matrix method for quantum reflection

In this paper, the analytical transfer matrix method (ATMM) is applied to study the properties of quantum reflection in three systems: a sech$^{2}$ barrier, a ramp potential and an inverse harmonic oscillator. Our results agree with those obtained by Landau and Lifshitz [Landau L D and Lifshitz E M 1977 \wx{Quantum Mechanics (Non-relativistic Theory)}{} (New York: Pergamon)], which proves that ATMM is a simple and effective method for quantum reflection.     

Energy eigenvalues from an analytical transfer matrix method

A detailed procedure based on an analytical transfer matrix method is presented to solve bound-state problems. The derivation is strict and complete. The energy eigenvalues for an arbitrary one-dimensional potential can be obtained by the method. The anharmonic oscillator potential and the rational potential are two important examples. Checked by numerical techniques, the results for the two potentials by the present method are proven to be exact and reliable.     

Photon path length analysis of radiative heat transfer in planar layers with arbitrary temperature distributions

The internal source analytical technique is extended to predict the radiative heat transfer for a layer having an arbitrary temperature distribution. By combining a number of internal sources distributed at various optical depths in the layer and weighting them appropriately, a nonisothermal layer is modeled. Heat flux and intensity distributions within layers having a single internal source are presented. The distributions are found to present trends unique to the internal source problem. Isothermal layers are modeled and compare very well with published results. Increased accuracy is attained for all cases and particularly for larger optical depths and smaller albedos by increasing the number of internal sources. The technique is applied to a nonisothermal layer having a temperature distribution similar to that for a hot medium with a cold boundary region. The effect of the boundary region on the normalized heat flux leaving the layer is seen to collapse to a single line for small layer optical thicknesses and large albedos, the slope of which is governed by the temperature ratio T_max/T_min.     

Discrete time transfer matrix method for dynamics of multibody system with real-time control

By taking the control and feedback parameters into account in state vectors, defining new state vectors and deducing new transfer equations and transfer matrices for actuator, controlled element and feedback element, a new method named as the discrete time transfer matrix method for controlled multibody system (CMS) is developed to study dynamics of CMS with real-time control in this paper. This method does not need the global dynamics equations of system. It has the modeling flexibility, low order of system matrix, high computational efficiency, and is efficient for general CMS. Compared with the ordinary dynamics methods, the proposed method has more advantages for dynamics design and real-time control of a complex CMS. Adopting the PID adaptive controller and modal velocity feedback control on PZT actuators, and applying the proposed method and ordinary dynamics method, respectively, the tip trajectory tracking for a flexible manipulator is carried out. Formulations of the method as well as numerical simulation are given to validate the proposed method.     

传递矩阵法预报时空随机激励下任意薄壳腔体内部噪声

利用结构有限元结合声有限元及边界元方法,建立了任意薄壳腔体弹性壳板振动与内外声场的耦合模型,并计算了激励力与壳板振动和内部声场之间的传递矩阵;湍流边界层脉动压力具有时空随机面激励特性,引入整体形状函数矩阵,进一步推导弹性壳板广义节点力功率谱密度函数矩阵与随机面分布激励力功率谱密度函数的关系,再利用声振耦合传递矩阵,得到弹性壳板振动和内部声场功率谱密度函数与广义节点力功率谱密度函数矩阵的关系,形成随机分布激励下任意薄壳腔体结构振动及内部声场的计算方法。以典型的内外均有声介质且一面为弹性矩形板的矩形腔声振耦合模型为例,计算了弹性壳板振动和内部声场功率谱密度函数,并与解析方法进行了比较,两者基本吻合,偏差分别为1 dB和2 dB左右。传递矩阵法不受腔体结构及其内部区域形状的制约,具有良好的适用性。     

Transfer matrix method for internal noise prediction of an arbitrary shell-cavity structure induced by temporal-spatial random surface excitation

Combining structural finite element method(FEM),acoustic finite element and boundary element methods,a model of elastic shell vibration of an arbitrary shell-cavity structure coupled with internal and external sound fields is built.In addition,the transfer matrices from the excitation force to vibration of the shell and internal sound field are calculated.As the fluctuating pressure of turbulent boundary layer(TBL) is a temporal-spatial random surface excitation,the overall shape function matrix is introduced,and then the relationship between power spectral density matrix of the generalized nodal force of the elastic shell and power spectral density of the temporal-spatial random surface excitation is derived.Utilizing the vibro-acoustic coupled transfer matrix,relationships between the power spectral densities of vibration of the elastic shell/internal sound field and the power spectral density matrix of the generalized nodal force are obtained.Thus,the calculation method of vibration and internal sound field of an arbitrary shell-cavity structure induced by temporal-spatial random surface excitation is established.A typical vibro-acoustic coupled model of a rectangular cavity with acoustic media internally and externally,and with elastic rectangular plate on one side,is taken as example.The vibration of the elastic shell and power spectral density of the internal sound field are calculated and compared with the analytical method.The two results generally agree with the analytical one,with deviations of about 1 dB and 2 dB,respectively.The transfer matrix method has good adaptability which is not restricted by the shell-cavity structure and the shape of the inner region.     

The three-measurement two-calibration method for measuring the transfer matrix

Extensive use of transfer matrices (TMs) is made in determining the acoustic properties of a duct and in in-duct acoustic propagation models in the automotive industry and for musical acoustics purposes. The experimental apparatuses of classical TM measurement methods feature two measurement heads. Two microphones are flush with the walls of each head. The pressure signals are processed following the transfer function method constructed on an analytical model of acoustic propagation in measurement heads. The present paper aims at presenting a measurement method based on a three-microphone experimental apparatus and on its acoustic calibration through two reference measurements: the three-measurement two-calibration method for measuring the TM (3M2C-TM). Two microphones are flush with the measurement head walls and one is in the cap closing one side of the measured duct. 3M2C-TM proved essential for an accurate measurement of the four TM elements of two different ducts: a cylindrical duct and an expansion chamber.     

夹心式压电超声换能器串并联传输矩阵设计法

将压电环片等效为一有源六端网络,考虑预应力螺栓对系统建模的影响,并将其等效为一机械四端网络,基于串并联传输矩阵法,建立了Langevin换能器的总体网络模型,导出其总传输矩阵,进而推算出换能器的共振频率。结果显示该方法比普遍采用的Langevin换能器传输矩阵设计法有更高的参量计算精度。此方法也为分析换能器其它电学参数提供了方便。