Vibro-acoustic analysis of complex systems

A general method is presented for predicting the ensemble average steady-state response of complex vibro-acoustic systems that contain subsystems with uncertain, or random, properties. The method combines deterministic and statistical techniques to produce a non-iterative hybrid method that incorporates equations of dynamic equilibrium and power balance. The method is derived explicitly without reference to statistical energy analysis (SEA); however, it is seen that the wave approach to SEA can be viewed as a special case of the proposed method. The proposed method provides a flexible way to account for necessary deterministic details in a vibro-acoustic analysis without requiring that an entire system be modeled deterministically. The method therefore provides a potential solution to the mid-frequency problem (in which a system is neither entirely deterministic nor entirely statistical). The application of the method is illustrated with a numerical validation example.     

Accuracy enhancement of fatigue damage counting using design sensitivity analysis

Recent studies have suggested fatigue damage counting of a linear elastic system using only the output data; design sensitivity analysis based on the transmissibility function was studied in order to identify the most sensitive response location under intact conditions. The design sensitivity index was derived to be proportional to the response energy at the measured point through reformulation of the previous equation for the sensitivity index. The accuracy of the damage counting method can be enhanced with design sensitivity analysis by selecting the location with the maximum response energy; the method is optimally robust against unexpected noise in the output data. Simulation and testing of a notched simple specimen under uniaxial excitation were used to verify that sensitivity analysis enhances the accuracy of the predicted damage counting.     

Vibro-acoustic response of an infinite, rib-stiffened, thick-plate assembly using finite-element analysis

The vibration of and sound radiation from an infinite, fluid-loaded, thick-plate assembly stiffened periodically with ribs are investigated numerically using finite-element analysis. First, numerical simulations are compared to the analytical solutions presented recently for this particular problem [Hull and Welch, J. Sound Vib. 329, 4192-4211 (2010)]. It is shown that the solutions reported in this reference are partially incorrect because the number of modes was not chosen correctly. Subsequently, the numerical model is used to study the effect of repeated and equally spaced void inclusions on the vibro-acoustic response of the system.     

Shape design sensitivity analysis for the radiated noise from the thin-body

Many industrial applications generally use thin-body structures in their design. To calculate the radiated noise from vibrated structure including thin bodies, the conventional boundary element method (BEM) using the Helmholtz integral equation is not an effective resolution. Thus, many researchers have studied to resolve the thin-body problem in various physical fields. No major study in the design sensitivity analysis (DSA) fields for thin-body acoustics, however, has been reported.A continuum-based shape DSA method is presented for the radiated noise from the thin-body. The normal derivative integral equation is employed as an analysis formulation. And, for the acoustic shape design sensitivity formulation, the equation is differentiated directly by using material derivative concept. To solve the normal derivative integral equation, the normal velocities on the surface should be calculated. In the acoustic shape sensitivity formulation, not only the normal velocities on the surface are required but also derivative coefficients of the normal velocities (structural shape design sensitivity) are also required as the input. Hence, the shape design sensitivity of structural velocities on the surface, with respect to the shape change, should be calculated. In this research, the structural shape design sensitivities are also obtained by using a continuum approach. And both a modified interpolation function and the Cauchy principle value are used to regularize the singularities generated from the acoustic shape design sensitivity formulation.A simple annular disk is considered as a numerical example to validate the accuracy and efficiency of the shape design sensitivity equations derived in this research. The commercial BEM code, SYSNOISE, is utilized to confirm the results of the developed in-house code based on a normal derivative integral equation. To validate the calculated design sensitivity results, central finite difference method (FDM) is employed. The error between FDM and the analytical result are less than 3%. This comparison demonstrates that the proposed design sensitivities of the radiated pressure are very accurate.     

Vibro-acoustic analysis of a rectangular-like cavity with a tilted wall

In this paper, a fully coupled vibro-acoustic model is developed to characterize the structural and acoustic coupling of a flexible panel backed by a rectangular-like cavity with a slight geometrical distortion, which is introduced through a tilted wall. The combined integro-modal approach is used to handle the acoustic pressure inside the irregular-shaped cavity. Based on the model proposed, the distortion effect on the vibro-acoustic behavior of the coupled system is investigated using the averaged sound pressure level inside the enclosure and the averaged quadratic velocity of the vibrating plate. Simulations are conducted to examine the distortion effect on acoustic natural frequencies, acoustic pressures and structural responses. Effects of the wall inclination on coupling coefficients are also assessed, and an index is proposed to quantify the degree of variation of coupling strength.     

Multilayer thin film thickness measurement using sensitivity separation method

This paper, for the first time, proposed a new sensitivity separation (SS) method for measuring thicknesses of multilayer thin-film stack with high efficiency and accuracy. Through the analysis of the relationship between the film parameters and the mean misfit error (MSE), a parameter called sensitivity is defined. With this parameter, an estimated rational thickness is assigned to a layer with lower sensitivity first, and then the layer thickness with high sensitivity is further obtained by optimization techniques. This method will greatly reduce the searching range and increase the iterating efficiency. It is a pretreatment method and it can be used with other optimization methods. Both theory and simulation results are provided in detail. The uncertainty problems are discussed and examples are given to verify the effectiveness of this method.     

Classification of flaw severity using pattern recognition for guided wave-based structural health monitoring

In this paper, the authors present a formal classification routine to characterize flaw severity in an aircraft-grade aluminum plate using Lamb waves. A rounded rectangle flat-bottom hole is incrementally introduced into the plate, and at each depth multi-mode Lamb wave signals are collected to study the changes in received signal due to mode conversion and scattering from the flaw. Lamb wave tomography reconstructions are used to locate and size the flaw at each depth, however information about the severity of the flaw is obscured when the flaw becomes severe enough that scattering effects dominate. The dynamic wavelet fingerprint is then used to extract features from the raw Lamb wave signals, and supervised pattern classification techniques are used to identify flaw severity with up to 80.7% accuracy for a training set and up to 51.7% accuracy on a series of validation data sets extracted from independent plate samples.     

Vibro-acoustic analysis procedures for the evaluation of the sound insulation characteristics of agricultural machinery cabins

Over the last few years, customer demands regarding acoustic performance, along with the tightening of legal regulations on noise emission levels and human exposure to noise, have made the noise and vibration properties into important design criteria for agricultural machinery cabins. In this framework, both experimental analysis procedures for prototype testing as well as reliable numerical prediction tools for early design assessment are compulsory for an efficient optimization of the cabin noise and vibration comfort.This paper discusses several numerical approaches, which are based on the finite element and boundary element method, in terms of their practical use for airborne sound insulation predictions. To illustrate the efficiency and reliability of the various vibro-acoustic analysis procedures, the numerical procedures are applied for the case of a harvester driver's cabin and validated with experimental results.     

Vibro-acoustic response and sound transmission loss analysis of functionally graded plates

This paper presents analytical studies on the vibro-acoustic and sound transmission loss characteristics of functionally graded material (FGM) plates using a simple first-order shear deformation theory. The material properties of the plate are assumed to vary according to power law distribution of the constituent materials in terms of volume fraction. The sound radiation due to sinusoidally varying point load, uniformly distributed load and obliquely incident sound wave is computed by solving the Rayleigh integral with a primitive numerical scheme. Displacement, velocity, acceleration, radiated sound power level, radiated sound pressure level and radiation efficiency of FGM plate for varying power law index are examined. The sound transmission loss of the FGM plate for several incidence angles and varying power law index is studied in detail. It has been found that, for the plate being considered, the sound power level increases monotonically with increase in power law index at lower frequency range (0–500 Hz) and a non-monotonic trend is appeared towards higher frequencies for both point and distributed force excitations. Increased vibration and acoustic response is observed for ceramic-rich FGM plate at higher frequency band; whereas a similar trend is seen for metal-rich FGM plate at lower frequency band. The dBA values are found to be decreasing with increase in power law index. The radiation efficiency of ceramic-rich FGM plate is noticed to be higher than that of metal and metal-rich FGM plates. The transmission loss below the first resonance frequency is high for ceramic-rich FGM plate and low for metal-rich FGM plate and further depends on the specific material property. The study has found that increased transmission loss can be achieved at higher frequencies with metal-rich FGM plates.     

Suspended stripline low pass filters design using the TLM method

This work presents the design of a Suspended Stripline Low-Pass filter using an Electromagnetic simulation software based on tridimensional TLM method. The filter design procedure is shown and discussed, as well as the optimization using the TLM. Theoretical, simulated and experimental results are compared.     

Exact wave-based Bloch analysis procedure for investigating wave propagation in two-dimensional periodic lattices

This paper presents an exact, wave-based approach for determining Bloch waves in two-dimensional periodic lattices. This is in contrast to existing methods which employ approximate approaches (e.g., finite difference, Ritz, finite element, or plane wave expansion methods) to compute Bloch waves in general two-dimensional lattices. The analysis combines the recently introduced wave-based vibration analysis technique with specialized Bloch boundary conditions developed herein. Timoshenko beams with axial extension are used in modeling the lattice members. The Bloch boundary conditions incorporate a propagation constant capturing Bloch wave propagation in a single direction, but applied to all wave directions propagating in the lattice members. This results in a unique and properly posed Bloch analysis. Results are generated for the simple problem of a periodic bi-material beam, and then for the more complex examples of square, diamond, and hexagonal honeycomb lattices. The bi-material beam clearly introduces the concepts, but also allows the Bloch wave mode to be explored using insight from the technique. The square, diamond, and hexagonal honeycomb lattices illustrate application of the developed technique to two-dimensional periodic lattices, and allow comparison to a finite element approach. Differences are noted in the predicted dispersion curves, and therefore band gaps, which are attributed to the exact procedure more-faithfully modeling the finite nature of lattice connection points. The exact method also differs from approximate methods in that the same number of solution degrees of freedom is needed to resolve low frequency, and arbitrarily high frequency, dispersion branches. These advantageous features may make the method attractive to researchers studying dispersion characteristics, band gap behavior, and energy propagation in two-dimensional periodic lattices.     

A study on the applications of the acoustic design sensitivity analysis of vibrating bodies

The determination of the sensitivity of the acoustical characteristics of vibrating systems with respect to the variation of the design parameters predicting these characteristics is a necessary and important step of the acoustic design and optimization process. Acoustic design sensitivity analysis includes the computation and evaluation of the sensitivity information required for this procedure. In this study, a boundary element code performing the sensitivity analysis of the acoustic pressure by using the matrix sensitivities with respect to different design variables has been developed. The effect of the precision of boundary element discretization on the acoustic pressure sensitivity is examined via this code. The formulation is applied to a multi-source system and the dimension sensitivity analysis of near field pressures of two-dilating-spherical source is performed. The last application is devoted to a real sound source: a washing machine sitting on the floor. Sensitivity of the field pressures to the machine’s dimensions (size), surface velocity and frequency is examined on the bases of the boundary element model of the machine and half-space condition. The impacts of these variables are compared; and a limiting speed for the machine responding both the acoustical and operational requirements is determined.     

Proton therapy analysis using the Monte Carlo method

The range and straggling data obtained from the transport of ions in matter (TRIM) computer program were used to determine the trajectories of monoenergetic 60 MeV protons in muscle tissue by using the Monte Carlo technique. The appropriate profile for the shape of a proton pencil beam in proton therapy as well as the dose deposited in the tissue were computed. The good agreements between our results as compared with the corresponding experimental values are presented here to show the reliability of our Monte Carlo method.     

Experimental determination of sensitivity of piezoquartz microweighing using an electrochemical method

The sensitivity of a piezoquartz microweighing device was determined experimentally using an electrochemical method working in a real time mode. The results obtained confirmed the linearity of the dependence of the piezoquartz generator’s basic frequency drift on the mass of an applied metal for a wide measurement range.     

Energy flow analysis and design sensitivity of structural problems at high frequencies

The design sensitivity formulation of an energy finite element method is presented using the direct differentiation and adjoint variable methods. The continuum method is used to derive the design sensitivity equation of the energy flow equation, whereas the discrete method is used to calculate the variation of the coupling relation. For design variables, material property, panel thickness, and structural shape are taken into account, in addition to the structural damping factor. The design variable's effect on the power transfer coefficient is discussed in detail. Even if the system matrix equation is not symmetric, the adjoint problem is solved using the same factorized matrix from response analysis. Design sensitivity results calculated from the proposed method are compared to the finite difference sensitivity results with a good agreement.     

基于特征值灵敏度分析的超高速摄影仪转镜设计

利用数值分析方法,通过建立转镜特征值灵敏度分析模型,根据模态分析计算生成转镜特征值灵敏度循环执行文件,选用Monte Carlo法拉丁超立方抽样对转镜结构尺寸参数在其概率密度分布函数内进行抽样计算,统计分析得到反应转镜结构尺寸与特征值之间的Spearman秩相关系数。根据数值分析结果,修改镜体外接圆半径,并对修改前后的转镜分别进行模态数值分析和试验,结果显示转镜1阶模态增大101.8%,1阶临界转速达到8.7105 r/m,说明根据转镜特征值灵敏度数值分析结果优化转镜结构尺寸是一种实用、有效的方法。     

Asymmetric MRI magnet design using a hybrid numerical method

Two-dimensional 1H/13C polarization inversion spin exchange at the magic angle experiments were applied to single crystal samples of amino acids to demonstrate their potential utility on oriented samples of peptides and proteins. High resolution is achieved and structural information obtained on backbone and side chain sites from these spectra. A triple-resonance experiment that correlates the 1H-13Calpha dipolar coupling frequency with the chemical shift frequencies of the alpha-carbon, as well as the directly bonded amide 15N site, is also demonstrated. In this experiment the large 1H-13Calpha heteronuclear dipolar interaction provides an independent frequency dimension that significantly improves the resolution among overlapping 13C resonances of oriented polypeptides, while simultaneously providing measurements of the 13Calpha chemical shift, 1H-13C dipolar coupling, and 15N chemical shift frequencies and angular restraints for backbone structure determination.