Reflection Of Longitudinal Waves Research Articles

Electromagnentic filed and rotation for fractional derivative order calculus with temperature-dependent on reflection of longitudinal wave under initial stress and three-phase-lag model

The central interest of the present study is to investigate the fractional order calculus in addition to studying impact of temperature dependent properties, electromagnetic field, rotation, and primary pressure on the reflection of plane and secondary vertically waves phenomenon putting in considerations the three-phase-lag model (THPL). The main equations that have been articulated related to the body forces neglecting the outer temperature supplier and the existence of primary pressure, spin, and the dependent on temperature according to THPL theory in its fractional form (Caputo fractional derivatives). The researchers related the boundary conditions with the consideration of the mechanical and Maxwell's stresses and temperature dependent properties. The researchers have made a comparison between the analytical integer and fractional solutions for the problem. The solutions are calculated analytically and are shown by drawings to demonstrate the physical connotation of the wave's reflection phenomenon. The existence of fractional derivative illustrates the degree to which these waves reach can be employed in today's manufacturing. By comparing the existence and non-existence of fractional derivative demonstrating the way the fractional derivative influences these waves.

Strengthening effect of laser shock: convex model with and without reflection

In this paper, the total reflection convex model and non-reflective convex model are established by simulation method, and the influence of shock pressure/laser energy and longitudinal wave reflection on the strengthening effect of laser shock 7050-T7451 aluminum alloy convex model is analyzed, and the relevant experiments are carried out to verify. When the shock pressure is 1500 MPa or the laser energy is 2.71 J, the shock energy is small, and the reflection of longitudinal wave has no effect on the material surface. When the shock pressure is greater than 1500 MPa or the laser energy is greater than 2.71 J, the reflection of longitudinal wave begins to affect the material surface, and the residual stress and deformation in the spot follow the rule that the position of spot edge in the circumferential direction is the largest, and the position of spot edge in the center and generatrix direction is smaller. Combined with the experimental results and simulation analysis, the residual stress distribution and surface integrity were evaluated comprehensively. When the convex model with 1/5 curvature was strengthened by laser shock, 4.82 J laser energy was applied on the surface of 4 mm spot to obtain better strengthening effect.

Strengthening effect of laser shock: concave model with and without reflection

When a laser shock wave is loaded onto the surface of a concave model, many factors affect the laser shock effect, including loading pressure, curvature, surface wave and reflection of longitudinal wave. It is difficult to clarify the mixed effects of these factors, as such. The reflection of longitudinal wave is the most important factor, and the non-reflective concave model can effectively distinguish the influence of longitudinal wave reflection. In this paper, the concave models with and without reflection are established using the ABAQUS software. The effect of loading pressure, curvature, surface wave, and reflection of longitudinal wave on laser shock processing are analyzed. Curvature changes the incident angle of the laser during processing, so the actual pressure on the material surface changes. The results show that the optimal loading pressure is 2000 MPa/4 J when the curvature is 1/5 and the spot radius is 4 mm. The experimental results are consistent with the simulation results, so the simulation results are reliable.

Reflection of Longitudinal Wave in the Micropolar Elasticity with Voids

By considering no more interaction between wryness tensor and change in voids volume fraction in the materials, the reflection problem of plane longitudinal waves at a free boundary of micropolar elastic materials with voids has been investigated. We have obtained the amplitude and energy ratios of reflected waves for the incident longitudinal wave by using appropriate boundary conditions. The effect of void parameters in the nondimensional wavenumber, amplitude and energy ratios are computed numerically for the particular material’s model.

Area of reflection of longitudinal waves in multilayer Fibonacci arrangements

Abstract In this article, we study the total reflection in 1D phonic crystals in quasiperiodic Fibonacci type arrangements of solid/solid layers. It was found that the reflection occurs in an area centered at a normalized frequency of 2π, and an angle of incidence of 61.6° which has not been observed in periodic systems. For studies in arrangements n > 4, the geometric evolution and breakdown of the area of interest is presented, starting from n = 6 arrays, giving rise to the formation of resonances (lR falls), which give rise to transmission and reflection of transverse waves, as well as the widening and formation of relative reflection peaks towards the critical angle. The global matrix method was used to obtain transmission and reflection spectra in quasiperiodic arrangements, when acoustic waves of longitudinal polarization were made. It is concluded that the geometric shape of the reflection zone observed after the critical angle depends on the FS arrangement, and its filling factor [f = a/(a + b)]. The calculations were made in super networks with Pt/Zn, where the first and the last layer are the means: incident and transmitted respectively.

The acoustic waves propagation laws in the force-fit connections for test of the interference fit

Calibrated tuning samples of compression joints with an interference of 29, 72, 126 μm were developed and manufactured. The samples were tested by ultrasonic control with an pulse echo technique. The coefficients of reflection of longitudinal waves from the boundary of the parts of different values of interference are experimentally determined under real operating conditions at frequencies of 2.5, 5 and 10 MHz.

Acoustic Characterization of Patterning Degradation during Wet Etching

Wet etching in photoresist presence is commonly used in MEMS or integrated circuits manufacturing: metal gates [1], or gate oxides patterning [2]. Nonetheless the resist can’t stand a too long exposure to wet chemicals. Indeed, the liquids diffuse through the resist. Then the polymer enters a plasticizing sequence. It swells under the action of polar water and etchant molecules that break the cohesive hydrogen bonds between the polymer chains. The resist stress increases till fractures and blisters appears (figure 1). Hence these phenomena have been characterized by various acoustic means described hereby. First method consists in using a high-frequency echography principle [3]. A ZnO transducer, sputtered on the backside of the silicon wafer emits a 2GHz acoustic wave. The longitudinal wave reflection occurs at the interface between the silicon and the medium on the wafer frontside enabling its characterization by monitoring the transducer electrical impedance (figure 3). In the case of a silicon / air interface, the acoustic wave reflection is total. When air is replaced by water, the reflection is partial and the reflection coefficient value is 0.86. These reflection properties will be modified in the presence of a thin TiN layer coated with a 248nm deep UV resist. As the resist thickness (210 nm) is thin compared with the acoustic wavelengths in the different materials (micrometer range), reflections at each interface cannot be separated (silicon / resist and resist / upper medium) so only one total reflection occurs in the presence of air. Then, the reflection coefficient is measured with water on the resist. Without any resist damage, the reflection coefficient changes from 0.86 to 0.765. This latter value is then modulated by the resist blisters amount due to the modification of the mechanical properties of the silicon / resist interface. Measurements are performed on wafers exposed to SC1 (Standard Clean 1) solutions for different durations (figure 1). The reflection coefficient increases with the blisters apparition (figure 4). By determining the ratio of blisters area on optical microscope images of the resist, the reflection coefficient is theoretically calculated for different blisters mechanical properties (solids, liquids and gas). Experimental and theoretical values perfectly match in the case of gas. This result let us think that gas pockets appeared in the resist during blisters formation. The method sensitivity is excellent and mainly depends on the high contrast between gas and water acoustic impedances. A comparison with two other complementary technics will be made. First, picosecond acoustic will characterize the resist adhesion loss. Its principle is similar to a sonar. The acoustic wave into the sample is supplied by a tunable laser [4], and an echo is generated at each interface enabling its characterization. Finally the scanning acoustic microscopy will monitor the resist blister apparition with a thicker resist. This technic is commonly used to monitor wafer bonding voids in 3D integrated circuits assembly [5]. Conclusion Photoresist degradation occurs during long exposure to wet etching. Resist delamination from substrate and blisters appear after a certain contact duration. This latter is shorter with thin resist, which occurs more and more along the integrated circuits node evolution to maintain photolithography optical requirements. Three acoustic methods have been compared to monitor this degradation. Results show these methods are far better than optical microscopy to detect the resist degradation starting point.

Analytical calculation of in-plane response of plates with concentrated masses to impact and application to pyroshock simulation

In aerospace missions pyroshocks occur due to controlled explosions of ordnance devices enabling the functionality of space modules. These shocks result from deployment mechanisms or opening solar sails and can cause failures of electronic devices and structures. Thus, essential components for assuring the reliability of modules are pyroshock tests for the completion of which strict requirements by the aerospace administrations have to be met. One of them is the definition of a specific acceleration signal and, based on this, the Shock Response Spectrum (SRS) for each part.So far, there is rather empirical than analytical knowledge about producing desired SRS with mechanical impacts and its characteristics due to the variation of input parameters. In this paper a widespread testing procedure for far-field pyroshocks is discussed which is realized by the in-plane impact of a hammer pendulum on a plate including the test specimen. The mechanical model consists of the contact between a rigid sphere and a free deformable rectangular plate with attached masses including subsequent propagation and reflection of longitudinal waves. In order to allow for a prediction of the acceleration field and the corresponding SRS due to the impact the problem is solved semi-analytically by using Hertzian contact theory, the Galerkin-procedure and numerical integration in time domain. The in-plane problem has, to the best of the authors' knowledge, not yet been treated in the literature in the way presented.The results calculated are compared with experimental data showing very good coincidence and allowing for a fast prediction of far-field pyroshock tests due to the impact excitation by a hammer pendulum. Hence, the framework of this paper is an enrichment for the current state of the art considering analytical pyroshock simulation. By better understanding the effect of pyroshocks to one and two dimensional structures a reduction of costs as well as durations for testing procedures seems promising.

Determination of the Cyclic-Tension Fatigue of Extruded Pure Magnesium Using Multiple Ultrasonic Waves

Three acoustic techniques, namely longitudinal wave reflection, vertically-polarized shear wave (SV) reflection, and horizontally polarized shear wave (SH) transmission methods, were used to assess the cyclic-tension fatigue of an extruded pure magnesium. The acoustic velocities were measured by the reflection methods, and found to decrease considerably at the beginning of the fatigue. This suggests that void defects formed at grain boundaries (Coble creep). Decrease in the elastic moduli and increase in the internal frictions revealed decrease in the mechanical and increase in the viscoelastic properties during the fatigue progress, respectively. For SH transmission method, acoustic parameters such as propagation time, amplitude and logarithmic damping ratio were strongly affected by detouring of acoustic waves, accompanied by variation in the residual stress caused by acoustoelasticity, in comparison with the reflection methods. These acoustic results were determined using OM, SEM, Vickers hardness tester, surface roughness tester and XRD. [doi:10.2320/matertrans.M2009432]

Measurement of viscosity and shear wave velocity of a liquid or slurry for on-line process control

An on-line sensor to measure the density of a liquid or slurry, based on longitudinal wave reflection at the solid–fluid interface, has been developed by the staff at Pacific Northwest National Laboratory. The objective of this research is to employ shear wave reflection at the solid–fluid interface to provide an on-line measurement of viscosity as well. Both measurements are of great interest for process control in many industries. Shear wave reflection measurements were conducted for a variety of liquids. By analyzing multiple reflections within the solid (only 0.63 cm thick––similar to pipe wall thickness) we increased the sensitivity of the measurement. At the sixth echo, sensitivity was increased sufficiently and this echo was used for fluid interrogation. Shear wave propagation of ultrasound in liquids is dependent upon the viscosity and the shear modulus. The data are analyzed using the theory for light liquids (such as water and sugar water solutions) and also using the theory for highly viscous liquids (such as silicone oils). The results show that, for light liquids, the shear wave reflection measurements interrogate the viscosity. However, for highly viscous liquids, it is the shear wave modulus that dominates the shear wave reflection. Since the density is known, the shear wave velocity in the liquid can be determined from the shear wave modulus. The results show that shear wave velocities in silicone oils are very small and range from 315 to 2389 cm/s. Shear wave reflection measurements are perhaps the only way that shear wave velocity in liquids can be determined, because the shear waves in liquids are highly attenuated. These results show that, depending on the fluid characteristics, either the viscosity or the shear wave velocity can be used for process control. There are several novel features of this sensor: (1) The sensor can be mounted as part of the wall of a pipeline or tank or submerged in a tank. (2) The sensor is very compact and can be located within the process stream. (3) The sensor can interrogate and characterize very attenuative liquids or slurries because the sensor operation depends upon reflection at the interface between the solid and the fluid, rather than on transmission through a liquid. (4) The sensor performance is not affected by fluid flow rate, entrained air, or vibration.

Depth Measurements of Short Cracks in Perspex with the Scanning Acoustic Microscope

By using a scanning acoustic microscope (SAM) combined with the time-of-flight diffraction technique, the depths of short cracks in perspex have been measured. Perspex was chosen for the work because it is a transparent, isotropic, and acoustically slow material; therefore, it enables one to measure the crack geometry in the light microscope, and it eliminates the involvement of the Rayleigh surface waves and the influence of wave speed anisotropy on the acoustic measurements. Short cracks of different geometries (depth to length ratios of 0.72 and 0.25) were initiated in commercial perspex by bending the specimens slightly and adding a little acetone to the surface bearing a tensile stress while at 20°C and 50°C, respectively. The SAM was operated in a short pulse mode capable of time resolved acoustic measurements. While one scans the lens across a crack, a narrow acoustic pulse (<20ns wide) is sent into the specimen, and the intensities of the signals scattered from the specimen are recorded in a plot of time-of-flight versus lens position, called an s(t,y) plot. Ray theory provides a useful description concerning the significant contributions to the s(t,y) plot from perspex when the lens is scanned across a surface breaking crack. They are (1) specular reflection of incident waves from the specimen surface; (2) diffraction of incident waves at the crack mouth edges; (3) reflection of longitudinal lateral surface waves from the crack mouth; (4) conversion of incident waves into longitudinal lateral surface waves at the crack mouth edges or the other way round; (5) propagation of longitudinal lateral surface waves in the specimen surface; (6) reflection of longitudinal waves from the crack face below the surface, if the crack is oblique; and (7) diffraction of longitudinal waves at the subsurface crack tip. As in the conventional time-of-flight diffraction technique, the crack tip diffracted signals were used to measure the crack depth. In order to enhance the contrast of the crack tip diffracted signals in an s(t,y) plot, the specimens were bent during the acoustic measurements, and a substraction algorithm was used to remove the much stronger specular reflections. The resulting acoustic depth measurements agreed with direct light microscope measurements within 93%, thus demonstrating the ability of the acoustic microscopic to measure the depth of short cracks in perspex. The prospect of using the acoustic microscope to measure the depth of short cracks in opaque materials is apparent.

Depth measurements of short cracks in perspex with the scanning acoustic microscope

By using a scanning acoustic microscope (SAM) combined with the time-of-flight diffraction technique, the depths of short cracks in perspex have been measured. Perspex was chosen for the work because it is a transparent, isotropic, and acoustically slow material; therefore, it enables one to measure the crack geometry in the light microscope, and it eliminates the involvement of the Rayleigh surface waves and the influence of wave speed anisotropy on the acoustic measurements. Short cracks of different geometries (depth to length ratios of 0.72 and 0.25) were initiated in commercial perspex by bending the specimens slightly and adding a little acetone to the surface bearing a tensile stress while at 20°C and 50°C, respectively. The SAM was operated in a short pulse mode capable of time resolved acoustic measurements. While one scans the lens across a crack, a narrow acoustic pulse (<20ns wide) is sent into the specimen, and the intensities of the signals scattered from the specimen are recorded in a plot of time-of-flight versus lens position, called an s(t,y) plot. Ray theory provides a useful description concerning the significant contributions to the s(t,y) plot form perspex when the lens is scanned across a surface breaking crack. They are (1) specular reflection of incident waves from the specimen surface; (2) diffraction of incident waves at the crack mouth edges; (3) reflection of longitudinal lateral surface waves from the crack mouth; (4) conversion of incident waves into longitudinal lateral surface waves at the crack mouth edges or the other way round; (5) propagation of longitudinal lateral surface waves in the specimen surface; (6) reflection of longitudinal waves from the crack face below the surface, if the crack is oblique; and (7) diffraction of longitudinal waves at the subsurface crack tip. As in the conventional time-of-flight diffraction technique, the crack tip diffracted signals were used to measure the crack depth. In order to enhance the contrast of the crack tip diffracted signals in an s(t,y) plot, the specimens were bent during the acoustic measurements, and a subtraction algorithm was used to remove the much stronger specular reflections. The resulting acoustic depth measurements agreed with direct light microscope measurements within 93%, thus demonstrating the ability of the acoustic microscopic to measure the depth of short cracks in perspex. The prospect of using the acoustic microscope to measure the depth of short cracks in opaque materials is apparent.

An ultrasonic interface layer model for bond evaluation

An interface layer model for adhesive bonding weakness evaluation is described to assist in ultrasonic oblique incidence analysis of waves traveling across the interface. This model assumes that the interface between the substrate and adhesive can be treated from a wave propagation point of view as a homogenous isotropic interface layer. The interface bonding quality can then be estimated by predetermined properties of the interface layer. The smooth bond can be formed by a thin nonviscous liquid layer between the two solid media. Numerical results show a frequency dependence of the reflection factors as well as a direct influence of the interface layer properties on reflection. Experiments on bonded structures were conducted to confirm the theoretical prediction. Experiments on smooth bond simulation structures showed the same trends as the theoretical curves of longitudinal wave reflection vs. frequency. Higher sensitivities of shear waves at oblique incidence for bonding weakness detection were found c...

Ultrasonic investigation of contact between solids under high hydrostatic pressure

A model is presented of the reflection and transmission of longitudinal ultrasonic waves through a contact interface of solids. In this model, the contact interface, in the form of a layer of weightless springs, is characterized by three parameters: unit contact stiffness, coefficient of viscous friction and coefficient of reradiation damping. To verify the model experimentally, steel samples with machined surfaces were used. The samples were held together by means of hydrostatic pressure. Using contact pressures up to 1000 MPa, the coefficient of reflection of longitudinal waves incident normally at the contact interface was measured for the frequencies 10, 30, 50, 70 and 90 MHz. Fitting parameters from the theoretical model to the experimental results yielded the relationship between contact pressure and the parameters relating to the contact interface. The relation between contact pressure and unit contact stiffness appeared to be linear. The dependence of vertical displacement of the contacting surfaces upon the contact pressure is in good agreement with theory developed by other authors

Acoustic microscopy of elastic discontinuities

In the reflection-scanning acoustic microscope, interference fringes may be obtained from cracks and grain boundaries running at an angle to the surface. The periodicity of these fringes suggests that while sometimes they are caused by reflection of longitudinal waves within the specimen, when the feature is approximately normal to the surface, Rayleigh waves are responsible, and this confirms the dominant role played by Rayleigh waves in the contrast in acoustic microscopy. The variation of contrast with defocus may be expressed as a Fourier transform of the reflectance function of a specimen; oscillations in V(z) then arise as the transform of the change in phase around the Rayleigh angle. When Rayleigh waves strike a surface-breaking discontinuity, they may be strongly reflected even though the discontinuity is much less than a wavelength thick. This enables fine cracks and other features which would not be resolved according to conventional criteria to be revealed very clearly in acoustic micrographs.

Some laboratory topics in vibrations

Six topics are presented in a laboratory course in vibrations for advanced undergraduate and beginning graduate students. The concepts of moving coil transduction, resonance, damping, and multiple degree of freedom modelling are demonstrated in an experiment employing a mass‐loaded cantilever beam. Clamped circular and rectangular plates are used to illustrate modal patterns, and the jump phenomenon associated with a nonlinear hard‐spring system is observed when the circular plate is strongly excited. Impact and the transmission and reflection of longitudinal waves in rods are the subjects of a spring‐gun and rod experiment. The students conduct a qualification test of the type used to verify that electrical equipment to be installed in nuclear power generating stations can withstand typical earthquakes. Another qualification test employs a drop table and a half‐sine pulse test. Longitudinal vibrations of concrete test specimens are used in a resonance experiment to compare stiffness and damping of differ...