Biomedical subjects

S I Rokhlin

Publications and source records attributed to S I Rokhlin.

11 recordsLinked to original sources

PubMed2004

Modulated angle beam ultrasonic spectroscopy for evaluation of imperfect interfaces and adhesive bonds.

An experimental method incorporating high frequency pulsed angle beam ultrasonic measurements modulated by low frequency vibrations of a bonded structure is described. This method uses parametric/nonlinear mixing between high and low frequencies to characterize adhesive degradation. It is demonstrated that good quality (undamaged) bonds exhibit little dependence of ultrasonic signature on the overlay of low frequency vibration loads; however, environmentally degraded or imperfect bonds exhibit strong modulation of the resonance frequency of the ultrasonic signal reflected from the bond. The results are interpreted using a model for normal and oblique wave interaction with two nonlinear interfaces separated by an adhesive layer under quasi-static stress modulation.

Journal Article↗

PubMed2003

Beam and phase effects in angle-beam-through-transmission method of ultrasonic velocity measurement.

The accuracy of a plane wave approximation for phase velocity measurements in isotropic and anisotropic material using the angle-beam-through-transmission method has been investigated numerically and experimentally. In this method the velocity is measured in different propagation directions as a function of incidence angle. The effect of two factors on the measurement accuracy have been discussed: intrinsic phase shift of the transmitted signal through a fluid-solid interface and beam diffraction due to the finite beam size of receiver and transmitter. It is shown that the interface-induced phase shift can introduce an error in time delay measurements of the shear wave after the first critical angle and that this time delay error can be accurately corrected for. Numerical results obtained by a time-domain beam model show that except at the critical angles, the finite width of the transmitter and receiver only affects the amplitudes of the transmitted signals and has almost no effect on the measured zero-cross time delay; therefore the plane wave approximation for obtaining phase velocity from the measured time delay data by this method and the plane wave interface-induced phase correction are fully applicable.

Journal Article↗

PubMed2003

Inverse ultrasonic determination of imperfect interfaces and bulk properties of a layer between two solids.

A method for determination of the complete set of physical, geometrical, and interfacial properties of an isotropic layer embedded between two known solids is discussed. These properties are: Lamé elastic moduli, density and thickness of the layer, and complex normal and transverse interfacial stiffnesses between the layer and the substrates. The properties are combined in the form of eight nondimensional parameters, which are determined from experimental reflection spectra at two incident angles: normal and oblique. The conditions for simultaneous determination of bulk layer properties and the interface normal and transverse springs with losses and the stability of the inversion method against data scatter are addressed. The inversion model is validated by experiment on normal and angular ultrasonic reflectivity from a layer between two semispaces in dry mechanical contact and from an environmentally degraded adhesive joint. The layer properties were measured independently, showing good agreement with the reconstructed results.

Journal Article↗

PubMed2003

Ultrasonic wave interaction with multidirectional composites: modeling and experiment.

Phenomena of wave transmission through a multidirectional composite laminate immersed in a fluid have been investigated. Based on a recently-developed recursive stiffness matrix method time-domain beam models have been developed to simulate the problem. Experimental and theoretical results at frequency 2.25 MHz show that the transmission amplitude is highly dependent on lamina orientation and angle of incidence. Large transmission amplitude appears at small (<10 degrees) and large incident angles (45 degrees-60 degrees). At intermediate incident angles (16 degrees-40 degrees) the transmission amplitude is almost zero. At high frequency, the residue epoxy layers between each lamina become important and corresponding resonances may be observed. These transmission phenomena have been interpreted in terms of Floquet waves. It shows that the pass and stop bands of the three Floquet waves obtained from the unit cell stiffness matrix determine the transmission amplitude distribution in frequency, incident angle and rotation angle domains. The effect of random deviation of the laminated structure periodicity has also been assessed. At normal incidence, the variation of the thickness of the epoxy residual layer between composite lamina has little effect on the overall stop and pass band structures but introduces random reverberation and scattering in the pass bands. It is shown that for oblique incidence the transmittivity spectrum of a composite with random lamina lay-up converges with increase of randomness to that of a [0/-45/90/45]2s quasi-isotropic composite. Randomization of lamina lay-up produces a small effect in the transmittivity spectrum for a quasi-isotropic composite.

Journal Article↗

PubMed2002

Determination of embedded layer properties using adaptive time-frequency domain analysis.

A general model for determination of the complete set of acoustical and geometrical properties of an isotropic layer embedded between isotropic or anisotropic multilayered solids is developed. These properties include density, longitudinal and shear elastic moduli, layer thickness, and loss factors, simultaneously determined from two measurements, one at normal and one at oblique incidence. The inversion model is an extension of the method proposed by Lavrentyev and Rokhlin [J. Acoust. Soc. Am. 102, 3467 (1997)] which is applicable to thick substrates. In this new method, the inversion model mimics an experiment by using the same time-domain gating of the signal reflected from the embedded layer. This allows application of this method to layered solids when reflections from different layers overlap in the time domain. The sensitivity of the method, its stability against data scatter, and the effect of the oblique incident angle are evaluated. The effect of plane-wave approximation versus beam approximation in the inverse algorithm is discussed. Experimental results are given to demonstrate examples of adhesive layer property reconstruction.

Journal Article↗

PubMed2002

Floquet wave homogenization of periodic anisotropic media.

A dynamic homogenization method based on Floquet wave theory is developed. The theory is based on the equivalency within the homogenization domain of Floquet waves in a periodic anisotropic medium and plane waves in a dispersive homogeneous anisotropic medium. A simple procedure has been developed to estimate analytically critical angles and the upper frequency bound of this homogenization domain. Using this method, the frequency dependent effective elastic constants are obtained and examples for [0/90] and [0/45/90/-45] composites are given. By comparison with an exact theory, it is shown that the time domain signal propagation in a periodic laminate is well described by the Floquet wave homogenization theory in the homogenization domain. It is also shown that in the static limit the results are identical to those calculated by static homogenization theory (the generalized method of cells). The potential applications of the method are discussed.

Journal Article↗

PubMed2002

Stable recursive algorithm for elastic wave propagation in layered anisotropic media: stiffness matrix method.

An efficient recursive algorithm, the stiffness matrix method, has been developed for wave propagation in multilayered generally anisotropic media. This algorithm has the computational efficiency and simplicity of the standard transfer matrix method and is unconditionally computationally stable for high frequency and layer thickness. In this algorithm, the stiffness (compliance) matrix is calculated for each layer and recursively applied to generate a stiffness (compliance) matrix for a layered system. Next, reflection and transmission coefficients are calculated for layered media bounded by liquid or solid semispaces. The results show that the method is stable for arbitrary number and thickness of layers and the computation time is proportional to the number of layers. It is shown both numerically and analytically that for a thick structure the solution approaches the solution for a semispace. This algorithm is easily adaptable to laminates with periodicity, such as multiangle lay-up composites. The repetition and symmetry of the unit cell are naturally incorporated in the recursive scheme. As an example the angle beam time domain pulse reflections from fluid-loaded multilayered composites have been computed and compared with experiment. Based on this method, characteristic equations for Lamb waves and Floquet waves in periodic media have also been determined.

Journal Article↗

PubMed2002

Floquet wave ultrasonic method for determination of single ply moduli in multidirectional composites.

An inversion method based on Floquet wave velocity in a periodic medium has been introduced to determine the single ply elastic moduli of a multi-ply composite. The stability of this algorithm is demonstrated by numerical simulation. The applicability of the plane wave approximation to the velocity measurement in the double-through-transmission self-reference method has been analyzed using a time-domain beam model. It shows that the finite width of the transmitter affects only the amplitudes of the signals and has almost no effect on the time delay. Using this method, the ply moduli for a multiply composite have been experimentally determined. While the paper focuses on elastic constant reconstruction from phase velocity measurements by the self-reference double-through-transmission method, the reconstruction methodology is also applicable to assessment of data collected by other methods.

Journal Article↗

PubMed2001

An ultrasonic method for determination of elastic moduli, density, attenuation and thickness of a polymer coating on a stiff plate.

An ultrasonic method proposed by us for determination of the complete set of acoustical and geometrical properties of a thin isotropic layer between semispaces (J. Acoust. Soc. Am. 102 (1997) 3467) is extended to determination of the properties of a coating on a thin plate. The method allows simultaneous determination of the coating thickness, density, elastic moduli and attenuation (longitudinal and shear) from normal and oblique incidence reflection (transmission) frequency spectra. Reflection (transmission) from the coated plate is represented as a function of six nondimensional parameters of the coating which are determined from two experimentally measured spectra: one at normal and one at oblique incidence. The introduction of the set of nondimensional parameters allows one to transform the reconstruction process from one search in a six-dimensional space to two searches in three-dimensional spaces (one search for normal incidence and one for oblique). Thickness, density, and longitudinal and shear elastic moduli of the coating are calculated from the nondimensional parameters determined. The sensitivity of the method to individual properties and its stability against experimental noise are studied and the inversion algorithm is accordingly optimized. An example of the method and experimental measurement for comparison is given for a polypropylene coating on a steel foil.

Journal Article↗

PubMed2001

Stable reformulation of transfer matrix method for wave propagation in layered anisotropic media.

The numerical instability problem in the standard transfer matrix method has been resolved by introducing the layer stiffness matrix and using an efficient recursive algorithm to calculate the global stiffness matrix for an arbitrary anisotropic layered structure. For general anisotropy the computational algorithm is formulated in matrix form. In the plane of symmetry of an orthotropic layer the layer stiffness matrix is represented analytically. It is shown that the elements of the stiffness matrix are as simple as those of the transfer matrix and only six of them are independent. Reflection and transmission coefficients for layered media bounded by liquid or solid semi-spaces are formulated as functions of the total stiffness matrix elements. It has been demonstrated that this algorithm is unconditionally stable and more efficient than the standard transfer matrix method. The stiffness matrix formulation is convenient in satisfying boundary conditions for different layered media cases and in obtaining modal solutions. Based on this method characteristic equations for Lamb and surface waves in multilayered orthotropic media have been obtained. Due to the stability of the stiffness matrix method, the solutions of the characteristic equations are numerically stable and efficient. Numerical examples are given.

Algorithms↗

PubMed1992

Equivalent boundary conditions for thin orthotropic layer between two solids: reflection, refraction, and interface waves.

Boundary conditions for an interface between two solids are introduced to model a thin orthotropic interface layer. The plane of symmetry of the layer material coincides with the incidence plane. Boundary conditions relating stresses and displacements on both sides of the interface are obtained from an asymptotic representation of the three-dimensional solutions for an interface layer whose thickness is small compared to the wavelength. The results for anisotropic boundary conditions are a generalization of our previous results [S. I. Rokhlin and Y. J. Wang, J. Acoust. Soc. Am. 89, 505-515 (1991)] for an isotropic viscoelastic layer. The interface boundary conditions obtained contain interface stiffness and inertia and terms involving coupling between normal and tangential stresses and displacements. The applicability of such boundary conditions is analyzed by comparison with exact solutions for reflection. As in the isotropic case, fundamental boundary-layer conditions are introduced containing only one transverse or normal mass or stiffness. It is shown that the solution for more accurate interface boundary conditions, which include two inertia elements and two stiffness elements, can be decomposed into a sum of fundamental solutions. Interface waves along such an interface are considered. Characteristic equations for these waves are obtained in closed form for different types of approximate boundary conditions and the velocities calculated from them are compared to the exact solution. It is shown that retention of the terms describing coupling between normal and transverse stresses and displacements is essential for calculating the velocity of an antisymmetric interface wave.

Acoustics↗