Experimental analysis of the vibrational characteristics of the human skull

Analytical models of the human skull structure have generally been constructed so as to characterize the gross geometric features and material properties; however, a model should also have accurate frequency response characteristics since these are essential for collision and head injury analyses. An experimental investigation was conducted to identify the dynamic characteristics of freely vibrating human skulls. Resonant frequencies and associated mode shapes in the frequency band from 20 Hz to 5000 Hz were delineated for two dry human skulls. Osteometrically, one skull corresponds to a 50th percentile male (skull 1) and the second is representative of a 5th percentile female skull (skull 2). Digital Fourier analysis techniques were used to identify the resonant frequencies and corresponding mode shapes of each skull. Eleven resonant frequencies were identified for skull 1, with the lowest being 1385 Hz. In contrast, skull 2 exhibited only 6 resonant frequencies with the first being 1641 Hz. Nine mode shapes were identified for skull 1, but only 5 modes were recognized for skull 2. The vibrational pattern of the human skull, as indicated by its mode shapes in this limited study, seems to be a unique property of a particular skull. Skull satures did not appear to influence the modal pattern.     

X-ray imaging characterization of femoral bones in aging mice with osteopetrotic disorder

Aging mice with a rare osteopetrotic disorder in which the entire space of femoral bones are filled with trabecular bones are used as our research platform. A complete study is conducted with a micro computed tomography (CT) system to characterize the bone abnormality. Technical assessment of femoral bones includes geometric structure, biomechanical strength, bone mineral density (BMD), and bone mineral content (BMC). Normal aging mice of similar ages are included for comparisons. In our imaging work, we model the trabecular bone as a cylindrical rod and new quantitative which are not previously discussed are developed for advanced analysis, including trabecular segment length, trabecular segment radius, connecting node number, and distribution of trabecular segment radius. We then identified a geometric characteristic in which there are local maximums (0.0049, 0.0119, and 0.0147 mm) in the structure of trabecular segment radius. Our calculations show 343% higher in percent trabecular bone volume at distal-metaphysis; 38% higher in cortical thickness at mid-diaphysis; 11% higher in cortical cross-sectional moment of inertia at mid-diaphysis; 42% higher in cortical thickness at femur neck; 26% higher in cortical cross-sectional moment of inertia at femur neck; 31% and 395% higher in trabecular BMD and BMC at distal-metaphysis; 17% and 27% higher in cortical BMD and BMC at distal-metaphysis; 9% and 53% higher in cortical BMD and BMC at mid-diaphysis; 25% and 64% higher in cortical BMD and BMC at femur neck. Our new quantitative parameters and findings may be extended to evaluate the treatment response for other similar bone disorders.     

Whole-lung resonance in a bottlenose dolphin (Tursiops truncatus) and white whale (Delphinapterus leucas)

An acoustic backscatter technique was used to estimate in vivo whole-lung resonant frequencies in a bottlenose dolphin (Tursiops truncatus) and white whale (Delphinapterus leucas). Subjects were trained to submerge and position themselves near an underwater sound projector and a receiving hydrophone. Acoustic pressure measurements were made near the thorax while the subject was insonified with pure tones at frequencies from 16 to 100 Hz. Whole-lung resonant frequencies were estimated by comparing pressures measured near the subject's thorax to those measured from the same location without the subject present. Experimentally measured resonant frequencies for the white whale and dolphin lungs were 30 and 36 Hz, respectively. These values were significantly higher than those predicted using a free-spherical air bubble model. Experimentally measured damping ratios and quality factors at resonance were 0.20 and 2.5, respectively, for the white whale, and 0.16 and 3.1, respectively, for the dolphin.     

Ultrasonic characterization of human cancellous bone using the Biot theory: inverse problem

This paper concerns the ultrasonic characterization of human cancellous bone samples by solving the inverse problem using experimental transmitted signals. The ultrasonic propagation in cancellous bone is modeled using the Biot theory modified by the Johnson et al. model for viscous exchange between fluid and structure. The sensitivity of the Young modulus and the Poisson ratio of the skeletal frame is studied showing their effect on the fast and slow wave forms. The inverse problem is solved numerically by the least squares method. Five parameters are inverted: the porosity, tortuosity, viscous characteristic length, Young modulus, and Poisson ratio of the skeletal frame. The minimization of the discrepancy between experiment and theory is made in the time domain. The inverse problem is shown to be well posed, and its solution to be unique. Experimental results for slow and fast waves transmitted through human cancellous bone samples are given and compared with theoretical predictions.     

Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model

The flexural vibration of the fluid-conveying single-walled carbon nanotube (SWCNT) is derived by the Timoshenko beam model, including rotary inertia and transverse shear deformation. The effects of the flow velocity and the aspect ratio of length to diameter on the vibration frequency and mode shape of the SWCNT are analyzed. Results show that the effects of rotary inertia and transverse shear deformation result in a reduction of the vibration frequencies, especially for higher modes of vibration and short nanotubes. The frequency is also compared with the previous study based on Euler beam model. In addition, if the ratio of length to diameter increased to 60, the influence of the shear deformation and rotary inertia on the mode shape and the resonant frequencies can be neglected. However, the influence is very obvious when the ratio decreased to 20. As the flow velocity of the fluid increases in the vicinity of 2π, the SWCNT reveals the divergence instability. It regains stability when the flow velocity reaches about 9. As the velocity increases further, the SWCNT undergoes a coupled-mode flutter and results in a larger amplitude.     

一种新型微机电系统扫描镜的谐振频率研究

在微光机电系统(MOEMS)技术的基础上,采用绝缘体上硅(SOI)的体硅加工工艺,设计并加工制作了一种新型的静电驱动的谐振式微机电系统(MEMS)扫描镜。介绍了其基本工作原理及结构设计特点;理论计算了圆形和方形两种结构的尺寸扫描镜的谐振频率,并利用ANSYS有限元软件进行仿真;设计并搭建了一个简单易操作的光学测试系统,对研制出的MEMS扫描镜(7.1mm×5.2mm)进行扫描角度测试。利用该器件参数激励的迟滞频率特性,对其谐振频率进行实际测量。同时,为验证其所测谐振频率的准确性,利用激光多普勒测振(LDV)系统对其进行测试。在工作电压10V,方形和圆形扫描镜的驱动频率分别为556Hz和596Hz时,机械扫描角度分别可达到约6°和5°,谐振频率分别约为300Hz和277Hz。并分析误差产生的原因及其结果。     

Compact fiber optic accelerometer

A compact fiber optic accelerometer based on a Michelson interferometer is proposed and demonstrated. In the proposed system, the sensing element consists of two single-mode fibers glued together by epoxy, which then act as a simple supported beam. By demodulating the optical phase shift, the acceleration is determined as proportional to the force applied on the central position of the two single-mode fibers. This simple model is able to calculate the sensitivity and the resonant frequency of the compact accelerometer. The experimental results show that the sensitivity and the resonant frequency of the accelerometer are 0.42 rad/g and 600 Hz, respectively.     

Inverse problems in cancellous bone: estimation of the ultrasonic properties of fast and slow waves using Bayesian probability theory

Quantitative ultrasonic characterization of cancellous bone can be complicated by artifacts introduced by analyzing acquired data consisting of two propagating waves (a fast wave and a slow wave) as if only one wave were present. Recovering the ultrasonic properties of overlapping fast and slow waves could therefore lead to enhancement of bone quality assessment. The current study uses Bayesian probability theory to estimate phase velocity and normalized broadband ultrasonic attenuation (nBUA) parameters in a model of fast and slow wave propagation. Calculations are carried out using Markov chain Monte Carlo with simulated annealing to approximate the marginal posterior probability densities for parameters in the model. The technique is applied to simulated data, to data acquired on two phantoms capable of generating two waves in acquired signals, and to data acquired on a human femur condyle specimen. The models are in good agreement with both the simulated and experimental data, and the values of the estimated ultrasonic parameters fall within expected ranges.     

Low frequency phononic band structures in two-dimensional arc-shaped phononic crystals

The low frequency phononic band structures of two-dimensional arc-shaped phononic crystals (APCs) were studied by the transfer matrix method in cylindrical coordinates. The results showed the first phononic band gaps (PBGs) of APCs from zero Hz with low modes. Locally resonant (LR) gaps were obtained with higher-order rotation symmetry, due to LR frequencies corresponding to the speeds of acoustic waves in the materials. These properties can be efficiently used in a structure for low frequencies that are forbidden, or in a device that permits a narrow window of frequencies.     

固体板背覆薄层特性的低频超声反演方法研究

研究了应用低频超声的反射频谱对固体板厚度及背覆薄层的各特征参数(包括厚度、声速、密度、衰减、声阻抗率、声时)进行反演的方法。从灵敏度函数、目标函数及误差传递方程的角度,对应用反射频谱的谐振频率或幅度谱反演模型系统的单参数和双参数的方法进行了分析讨论。实验使用中心频率为7MHz的探头检测铝板/聚合物薄层样品,在同样的条件下,谐振频率法和幅度谱法反演的单参数反演效果相当,谐振频率方法的双参数反演效果优于幅度谱方法,前者薄层声阻抗率和声时同时反演的平均误差为3.4%和4.7%,而后者没有得到结果。      

In-fiber integrated accelerometer

A compact in-fiber integrated fiber-optic Michelson interferometer based accelerometer is proposed and investigated. In the system, the sensing element consists of a twin-core fiber acting as a bending simple supported beam. By demodulating the optical phase shift, we obtain that the acceleration is proportional to the force applied on the central position of the twin-core fiber. A simple model has been established to calculate the sensitivity and resonant frequency. The experimental results show that such an accelerometer has a sensitivity of 0.09 rad/g at the resonant frequency of 680 Hz.     

Predictions of the modified Biot-Attenborough model for the dependence of phase velocity on porosity in cancellous bone

The modified Biot–Attenborough (MBA) model for acoustic wave propagation in porous media has been found useful to predict wave properties in cancellous bone. The present study is aimed at applying the MBA model to predict the dependence of phase velocity on porosity in cancellous bone. The MBA model predicts a phase velocity that decreases nonlinearly with porosity. The optimum values for input parameters of the MBA model, such as compressional speed c_m of solid bone and phase velocity parameter s₂, were determined by comparing the predictions with previously published measurements in human calcaneus and bovine cancellous bone. The value of the phase velocity parameter s₂ = 1.23 was obtained by curve fitting to the experimental data for 53 human calcaneus samples only, assuming a compressional speed c_m = 2500 m/s of solid bone. The root-mean-square error (RMSE) of the curve fit was 15.3 m/s. The optimized value of s₂ for all 75 cancellous bone samples including 22 bovine samples was 1.42 with a value of 55 m/s for the RMSE of the curve fit. The latter fit was obtained by using of a value of c_m = 3200 m/s. Although the MBA model relies on the empirical parameters determined from experimental data, it is expected that the model can be usefully employed as a practical tool in the field of clinical ultrasonic bone assessment.     

Ultrasonic pulse waves in cancellous bone analyzed by finite-difference time-domain methods

The trabecular frame of cancellous bone has a high degree of porosity, anisotropy and inhomogeneity. The propagation of ultrasonic waves in cancellous bone is significantly affected by the trabecular structure. In this paper, two two-dimensional finite-difference time-domain (FDTD) methods, which were the popular viscoelastic FDTD method for a viscoelastic medium and Biot's FDTD method for a fluid-saturated porous medium, have been applied to numerically analyze the ultrasonic pulse waves propagating through bovine cancellous bone in the directions parallel and perpendicular to the trabecular alignment. The Biot's fast and slow longitudinal waves, which were identified in previous experiments for the propagation parallel to the trabecular orientation, could be analyzed using Biot's FDTD method rather than the viscoelastic FDTD method. For the single wave propagation in the perpendicular direction, on the other hand, the viscoelastic FDTD result was found to be in more good agreement with the experimental result.     

Observations on a principal components analysis of head-related transfer functions.

A recent principal components analysis (Kistler and Wightman, 1992) has shown that the transfer functions of the human external ear, for a wide range of source locations, can be expressed as weighted sums of a small number of basis vectors. Directional transfer functions obtained in this laboratory, using substantially different measurement techniques, yielded principal component basis vectors that are remarkably similar to those reported by Kistler and Wightman. When this subject population was divided in half according to the overall physical sizes of subjects, basis vectors computed for the subpopulation of smaller subjects were shifted systematically to higher frequencies relative to those computed for the subpopulation of larger subjects.     

Application of Biot's theory to ultrasonic characterization of human cancellous bones: determination of structural, material, and mechanical properties

This paper is devoted to the experimental determination of distinctive macroscopic structural (porosity, tortuosity, and permeability) and mechanical (Biot-Willis elastic constants) properties of human trabecular bones. Then, the obtained data may serve as input parameters for modeling wave propagation in cancellous bones using Biot's theory. The goal of the study was to obtain experimentally those characteristics for statistically representative group of human bones (35 specimens) obtained from a single skeletal site (proximal femur). The structural parameters were determined using techniques devoted to the characterization of porous materials: electrical spectroscopy, water permeametry, and microcomputer tomography. The macroscopic mechanical properties, Biot-Willis elastic constants, were derived based on the theoretical consideration of Biot's theory, micromechanical statistical models, and experimental results of ultrasonic studies for unsaturated cancellous bones. Our results concerning structural parameters are consistent with the data presented by the other authors, while macroscopic mechanical properties measured within our studies are situated between the other published data. The discrepancies are mainly attributed to different mechanical properties of the skeleton frame, due to strong structural anisotropy varying from site to site. The results enlighten the difficulty to use Biot's theory for modeling wave propagation in cancellous bone, implying necessity of individual evaluation of input parameters.     

Resonant Response of Rectangular/kFM Cantilever in Liquid

Dynamic characteristics of atomic force microscopy （AFM） cantilevers can be influenced by their working media. We perform an experimental study on the resonant responses of rectangular AFM cantilevers with different sizes immersed in various viscous fluids. The measured resonance frequencies in liquids are used to valldate several theoretical models. Comparison shows the analytical model proposed by Sader [J. Appl. Phys. 84 （1998） 64] can give the best agreement with the experimental results with the maximum relative error nearly 16% for all the cantilevers in different liquids. The ratio between the resonant frequencies in air and water is almost independent of the cantilever length, which is consistent with the theoretical analyses.     

Estimation of critical and viscous frequencies for Biot theory in cancellous bone

The use of Biot theory for modelling ultrasonic wave propagation in porous media involves the definition of a "critical frequency" above which both fast and slow compressional waves will, in principle, propagate. Critical frequencies have been evaluated for healthy and osteoporotic cancellous bone filled with water or marrow, using data from the literature. The range of pore sizes in bone gives rise to a critical frequency band rather than a single critical frequency, the mean of which is lower for osteoporotic bone than normal bone. However, the critical frequency is a theoretical concept and previous researchers considered a more realistic "viscous frequency" above which both fast and slow waves may be experimentally observed. Viscous frequencies in bone are found to be several orders of magnitude greater than calculated critical frequencies. Whereas two waves may well be observed at all ultrasonic frequencies for water-filled cancellous bone at 20 degrees C, it is probable megahertz frequencies would be needed for observation of two waves in vivo.     

Resonant modes due to anion interstitials and anion vacancies in fluorites

The resonant modes due to anion interstitials and anion vacancies in fluorites are computed on the basis of a Green's function formalism. The Green's functions are calculated on the basis of shell model fitted to the phonon dispersion curves of the respective crystals. The force constant changes are calculated by finding the relaxations of the different host atoms and then using the short range potential due to Catlow and Norgett. The calculated frequencies of the resonant mode due to anion interstitials in BaF₂; shows good agreement with the experimental results. The results discussed in a comparative fashion for the three crystals CaF₂, SrF₂; and BaF₂; along with the possibility of their experimental detection.     

Coaxial Waveguide Slot Bridge Cell for Liquid Substances Study

The experimental method suggested suppose the studying of energy characteristics of slot bridge (SB) cells in the multi mode operating regime based on the preliminary numerical investigation of scattering resonant characteristics of SB (solution of boundary value problem and investigation of eigen frequencies and relevant field modes). The configuration of experimental model of SB cell is computed accordingly to required frequency band and preliminary information about dielectric parameters of materials chosen for tests. Ethanol scattering characteristics of SB cell are computed by software, developed on the base of rigorous solution of the boundary value problem, providing numerical data with any required accuracy.     

Polytopes vibrations within Coxeter group symmetries

We are considering polytopes with exact reflection symmetry group G in the real 3-dimensional Euclidean spaceR³. By changingone simple element of the polytope (position of one vertex or length of an edge), one canretain the exact symmetry of the polytope by simultaneously changing other correspondingelements of the polytope. A simple method of using the symmetry of polytopes in order todetermine several resonant frequencies is presented. Knowledge of these frequencies, or atleast their ratios can be used for control of some principal changes of the polytopes.