Acoustic Stiffness Research Articles

An Experimentally Validated Micromechanical Model for Elasticity and Strength of Hydroxyapatite Biomaterials

ABSTRACTHydroxyapatite biomaterials production has been a major field in biomaterials science and biomechanical engineering. As concerns prediction of their stiffness and strength, we propose to go beyond statistical correlations with porosity or empirical structure-property relationships, as to resolve the material-immanent microstructures governing the overall mechanical behavior. The macroscopic mechanical properties are estimated from the microstructures of the materials and their composition, in a homogenization process based on continuum micromechanics. Thereby, biomaterials are envisioned as porous polycrystals consisting of hydroxyapatite needles and spherical pores. Validation of respective micromechanical models relies on two independent experimental sets: Biomaterial-specific macroscopic (homogenized) stiffness and uniaxial (tensile and compressive) strength predicted from biomaterial-specific porosities, on the basis of biomaterial-independent (‘universal') elastic and strength properties of hydroxyapatite, are compared to corresponding biomaterial-specific experimentally determined (acoustic and mechanical) stiffness and strength values. The good agreement between model predictions and the corresponding experiments underlines the potential of micromechanical modeling in improving biomaterial design, through optimization of key parameters such as porosities or geometries of microstructures, in order to reach desired values for biomaterial stiffness or strength.

Breeding for improved growth and juvenile corewood stiffness in slash pine

The importance of integrating measures of juvenile corewood mechanical properties, modulus of elasticity in particular, with growth and disease resistance in tree improvement programs has increased. We investigated the utility of in-tree velocity stiffness measurements to estimate the genetic control of corewood stiffness and to select for trees with superior growth and stiffness in a progeny trial of 139 families of slash pine, Pinus elliottii Engelm. grown on six sites. Narrow-sense heritability estimates across all six sites for in-tree acoustic velocity stiffness at 8 years (0.42) were higher than observed for height (0.36) and diameter at breast height (DBH) (0.28) at 5 years. The overall type B genetic correlation across sites for velocity stiffness was 0.68, comparable to those found for DBH and volume growth, indicating that family rankings were moderately repeatable across all sites for these traits. No significant genetic correlations were observed between velocity stiffness, DBH, and volume growth. In contrast, a significant, but small, favorable genetic correlation was found between height and velocity stiffness. Twenty percent of the families had positive breeding values for both velocity stiffness and growth. The low cost, high heritability and nearly independent segregation of the genes involved with in-tree velocity stiffness and growth traits indicate that acoustic methods can be integrated into tree improvement programs to breed for improved corewood stiffness along with growth in slash pine.

Acoustic and stiffness properties of gillnets as they relate to small cetacean bycatch

Abstract Mooney, T. A., Au, W. W. L., Nachtigall, P. E., and Trippel, E. A. 2007. Acoustic and stiffness properties of gillnets as they relate to small cetacean bycatch. – ICES Journal of Marine Science, 64: 1324–1332. Small cetaceans are incidental bycatch in gillnet fisheries. Dolphin and porpoise bycatch has been reduced by the use of barium sulphate-enhanced gillnets. This decreased entanglement is likely the result of either higher acoustic reflectivity or greater stiffness for barium nets. To address these variables, our study quantified the acoustic reflectivity and stiffness of six net types including barium sulphate, iron oxide-enhanced and control demersal gillnets of sizes which typically target cod (Gadus morhua) and monkfish (Lophius americanus). Acoustic reflectivity, or target strength (TS), was assessed using dolphin and porpoise-like sonar signals from 0° to 40°. TS values were used to calculate likely detection ranges. Barium sulphate- and iron oxide-enhanced nets showed increased reflectivity compared with control nets, with the barium sulphate nets generating the highest TS values. Dolphins should detect these nets in time to avoid contact, but porpoises, with typically lower source levels, may not detect nets at a range great enough to avoid entanglement. Barium sulphate line was significantly stiffer than comparable nylon line. All lines lost stiffness when soaked in seawater for 24 h. Barium sulphate nets proved stiffer and more acoustically reflective, and both factors are likely important in reducing harbour porpoise bycatch.

The effect of fruit factors on the bruise susceptibility of apples

Bruise prediction models which are essential for the applicability of the discrete element method (DEM) to simulate bruise damage during fruit transport and handling are discussed. Bruise prediction models relate the contact force during impact, as calculated by DEM through contact force models, with the real bruise damage. Apart from DEM, bruise prediction models can provide useful information about the influence of fruit factors (e.g. ripeness) on bruise susceptibility, leading to recommendations for fruit handling. Regression models were built with impact energy or peak contact force as independent variables. Advantages and disadvantages of both models are discussed. Bruise prediction models were constructed for the apple cultivar ‘Jonagold’, with impacts controlled by a pendulum. Multiple linear and nonlinear regression models were built to link fruit factors such as ripeness, acoustic stiffness, fruit temperature, radius of curvature and harvest date, with bruise damage. Bruise volume was used as a measure for apple bruising. Significant main effects and significant interactions between fruit factors were identified. Interactions between fruit factors (e.g. interaction between harvest date and stiffness), along with interactions between fruit factors and the degree of bruising, were identified. Most of the effects of those fruit factors on bruise damage could be explained by applying theoretical bruise models described in the literature.

Sequential Changes in Implanted Cartilage After Autologous Osteochondral Transplantation: Postoperative Acoustic Properties up to 1 Year in an In Vivo Rabbit Model

For successful autologous osteochondral transplantation, it is important that the cartilage in an implanted plug provide histologic replacement of damaged cartilage with cartilage that is structurally and mechanically normal. The purpose of this study was to investigate whether the press-fit technique reconstructs the normal hyaline cartilage and provides acoustic stiffness equal to that of normal intact cartilage. In 36 rabbits an osteochondral plug, 6 mm in diameter, was removed from the right patellar groove and grafted into a recipient hole, 5 mm in diameter, in the left patellar groove. Specimens at 2, 4, 8, 12, 24, and 52 weeks postoperatively were assessed by macroscopic and histologic observation and by use of an ultrasonic system. The ultrasonic acoustic stiffness, acoustic surface irregularity, and acoustic thickness of the implanted cartilage were examined and compared with normal intact cartilage. The gross appearance of the implanted cartilage was glossy, maintained good surface smoothness, and survived well throughout the observation period. The cartilage recovered histologic features of hyaline cartilage. The acoustic stiffness decreased up to 12 weeks and then increased at 24 and 52 weeks after surgery. The acoustic stiffness at 8 or 12 weeks was significantly lower (acoustically softer) than that of control cartilage (P < .001). The acoustic stiffness at 52 weeks was equal to that of the control. The difference in acoustic surface irregularity was not significant. The acoustic thickness at 8 weeks was higher (acoustically thicker) than that of the control (P < .01). Although the reason acoustically soft cartilage in plugs becomes acoustically stiff and whether the histology of the implanted cartilage had recovered completely remain unclear, the acoustic stiffness recovered to normal control values by 52 weeks postoperatively. Postoperative care for up to 12 weeks should be taken after autologous osteochondral transplantation.

The effect of fruit properties on the bruise susceptibility of tomatoes

Bruise prediction models for tomatoes are discussed. These models can provide useful information about the influence of fruit properties (for example ripeness) on bruise susceptibility, leading to recommendations for fruit handling. Statistical models were constructed with impact energy or peak contact force as the main independent variable. Bruise prediction models were made for tomato cultivar ‘Tradiro’. The impacts were controlled by a pendulum. Multiple linear and nonlinear regression models were made to link fruit properties like ripeness, acoustic stiffness, fruit temperature, radius of curvature and location of impact (partition or compartment of tomato) with bruise damage. Because an objective method to measure the bruise size of tomatoes does not exist, absorbed energy was taken as a measure. Besides significant main effects significant interactions between fruit properties were also identified. Mutual interactions between fruit properties (for example interaction between radius of curvature and temperature) together with significant interactions between some fruit properties and the degree of bruising were noticed. Most of the effects of the fruit properties on bruise damage could be explained.

Postharvest quality of integrated and organically produced apple fruit

Apple cv. ‘Jonagold’ fruit were picked in three different regions of Belgium. In each region one organic and one integrated orchard with identical climatic and soil characteristics was sampled. Fruit were stored in air and under CA conditions (1% O 2, 2.5% CO 2) at 1 °C for 6 months. The acoustic stiffness, firmness, soluble solids contents, acid and sugar contents, and the aroma profile were measured. Quality parameters were analysed right after harvest and storage. At both times an additional shelf-life experiment was carried out to simulate the conditions in the commercial chain. The quality attributes of apples coming from different regions and different production systems did not differ significantly, neither at harvest nor after storage. There was a considerable softening during storage in air and shelf-life, but not under CA conditions. Immediately after harvest, high malic acid, quinic acid and sucrose contents were observed, while glucose and citric acid contents were higher after storage. The aroma profile changed during shelf-life, except for apples stored in air, which even immediately after storage already had an aroma profile comparable to that after shelf-life. The volatile responsible for the typical apple aroma (2-methylbutyl acetate) had the highest relative abundance after CA storage and subsequent shelf-life, followed by apples immediately after CA storage. The effect of storage conditions on the quality of the apples was in general much larger than that of the possible effects of the production system. Aroma profiles of air-stored and CA-apple converge during shelf-life conditions.

Numerical evaluation of the acoustic radiation from planar structures with general baffle conditions using wavelets

A method is presented for computing the acoustic radiation from baffled, unbaffled, or partially baffled planar structures. The surface displacement and the surface pressure are expressed in terms of wavelets, and the acoustic dynamic stiffness (baffled case) or the acoustic receptance (unbaffled case) between any two wavelets is derived in closed form. The wavelets are employed with translation only (i.e., no dilation), and the jinc function is used; the Hankel transform of this function is the Heavyside step function, and this feature greatly simplifies the analysis. There is a trivial mapping between the wavelet amplitudes and the physical motion of the structure, and hence the dynamic stiffness and receptance results can readily be used to derive the acoustic dynamic stiffness matrix (by inverting the receptance matrix in the unbaffled case) in any set of generalized coordinates. Partially baffled systems can then be studied by substructuring the dynamic stiffness matrix. A set of example problems is considered in which the method is used to compute the resistive and reactive radiation efficiency of a range of benchmark systems.

Genetic Parameters and Strategies for Genetic Improvement of Stiffness in Radiata Pine

Abstract The two main objectives of this study were: (1) to determine how early is it possible to undertake selection to improve the stiffness of corewood; (2) to determine if the selection based on corewood stiffness could also improve outerwood stiffness, and vice versa. Breastheight data from two progeny trials of Pinus radiata D. Don were used. In the first trial (age 30 years), data on Silviscan predicted stiffness (MoE) was obtained for each growth ring on each core sample from 50 open-pollinated families. In the second trial (age 14 years), data on static-bending MoE was obtained using clearwood sticks (300 × 20 × 20 mm) cut from each tree from 18 control-pollinated families. MoE varied from 3.5 GPa in rings 1-5 to about 17 GPa in rings 21-25. Coefficients of variation of corewood and outerwood MoE were about 20-30% and 15-20% respectively. Estimates of narrowsense heritability for MoE were generally higher (0.50-0.70) in the corewood compared with the outerwood (0.15-0.30). Early selection for MoE could yield substantial gain in corewood MoE but only small gains, if any, in outerwood MoE (especially for rings 21-30). Estimated genetic correlations between density and stiffness appeared moderate in the corewood zone, but high in the outerwood zone. Selection based on density (using 5-mm cores) and acoustic stiffness (using standing tree tools), assessed at age 6-7 years, appeared to be a good option to improve both corewood and outerwood stiffness.

‘Universal’ microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: Micromechanics-based prediction of anisotropic elasticity

Bone materials are characterized by an astonishing variability and diversity. Still, because of ‘architectural constraints’ due to once chosen material constituents and their physical interaction, the fundamental hierarchical organization or basic building plans of bone materials remain largely unchanged during biological evolution. Such universal patterns of microstructural organization govern the mechanical interaction of the elementary components of bone (hydroxyapatite, collagen, water; with directly measurable tissue-independent elastic properties), which are here quantified through a multiscale homogenization scheme delivering effective elastic properties of bone materials: at a scale of 10 nm, long cylindrical collagen molecules, attached to each other at their ends by ∼ 1.5 nm long crosslinks and hosting intermolecular water inbetween, form a contiguous matrix called wet collagen. At a scale of several hundred nanometers, wet collagen and mineral crystal agglomerations interpenetrate each other, forming the mineralized fibril. At a scale of 5 – 10 μ m , the extracellular solid bone matrix is represented as collagen fibril inclusions embedded in a foam of largely disordered (extrafibrillar) mineral crystals. At a scale above the ultrastructure, where lacunae are embedded in extracellular bone matrix, the extravascular bone material is observed. Model estimates predicted from tissue-specific composition data gained from a multitude of chemical and physical tests agree remarkably well with corresponding acoustic stiffness experiments across a variety of cortical and trabecular, extracellular and extravascular materials. Besides from reconciling the well-documented, seemingly opposed concepts of ‘mineral-reinforced collagen matrix’ and ‘collagen-reinforced mineral matrix’ for bone ultrastructure, this approach opens new possibilities in the exploitation of computer tomographic data for nano-to-macro mechanics of bone organs.

The discrete element method (DEM) to simulate fruit impact damage during transport and handling: Case study of vibration damage during apple bulk transport

Making use of the discrete element method (DEM) a study is presented on the influence of mechanical parameters (vibration frequency and acceleration amplitude, apple size, stack height) and fruit properties (apple harvest date, apple temperature, apple acoustic stiffness) on vibration damage of apples. As acceleration input a sine in the vertical direction was used. Realistic parameters of the Kuwabara and Kono [Kuwabara, G., Kono, K., 1987. Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys. 26, 1230–1233] contact force model for ‘Jonagold’ apples and bruise prediction models were applied. As a general conclusion, major influences of mechanical parameters on the vibration damage were identified, in particular stack height and fruit size, and minor influences of fruit properties. Also a detailed study was performed to investigate the relation between apple positions in the stacking and bruise damage. It was demonstrated that the position–bruise damage relation depends on the acceleration amplitude, vibration frequency and stack height. The existence of damage chains within the centre of the apple stack was also identified, that is in accordance with the well-known force chains in bulk materials.

Maturation-dependent change and regional variations in acoustic stiffness of rabbit articular cartilage: an examination of the superficial collagen-rich zone of cartilage

The purpose of the study was to investigate maturation-dependent changes of acoustic (ultrasound) stiffness and other ultrasound features of articular cartilage in healthy rabbit knees. Five groups of rabbits of various ages (3 weeks, 8 weeks, 6 months, 1 year, 2.5 years) consisting of five rabbits per group were examined. Signal intensity (index of stiffness), signal duration (index of surface irregularity) and interval between signals (index of thickness) of the ultrasound reflection from articular cartilage were examined at four sites: posterior lateral femoral condyle, posterior medial femoral condyle, lateral tibial plateau, and medial tibial plateau. The sites were observed macroscopically and microscopically with a light microscope and a polarized light microscope. At the lateral and medial condyles and the lateral tibial plateau, signal intensity was least in 3-week-old specimens. The intensity increased until 6 months or 1 year of age. At these sites, the signal durations and intervals between signals were least at the ages of 6 months or 1 year. At the medial tibial plateau, the intensity was the least at 2.5 years of age and the interval between signals was least at 3 weeks of age; there was no effect of age on signal duration. Cartilage surfaces of all specimens were smooth and no degenerative changes were macroscopically or microscopically evident. The surface brightness of cartilage under the polarized light microscope was consistent with signal intensity values. The response of articular cartilage to ultrasound was maturation-dependent. Acoustic properties differed from mechanical stiffness properties, which were determined using indentation. Ultrasound may detect properties of the surface collagen of the articular cartilage.

NON-DESTRUCTIVE FIRMNESS MEASUREMENT OF ZESPRI™ GOLD USING THE ACOUSTIC IMPULSE RESPONSE TECHNIQUE AND COMPRESSION TESTS

Quality assurance throughout the value chain can be enhanced by the availability of non-destructive methods that can be repeatedly used to track individual fruit quality and so alleviate some of the challenges arising from the natural variation that occurs between fruit. Penetrometer measurements have been widely used to measure fruit firmness and may be well correlated with consumer perception of texture but are destructive. Compression tests are less destructive and can provide information on other aspects of texture. The acoustic impulse response technique was compared to penetrometer and compression techniques to assess its utility as a measure of firmness for Zespri Gold kiwifruit since it is a truly non-destructive technique. Acoustic stiffness and compression firmness correlated reasonably well at all times and for all harvests. The correlation between penetrometer firmness and acoustic stiffness was lower and dependent on the harvest date, with later harvest showing a better correlation than the earlier harvests. During storage the correlation improved slightly for approximately the first half of the storage period but then declined markedly. The reason for this change in relationship is unknown but did not appear to be due to weight loss.

RELATIONSHIP BETWEEN PHYSICAL AND BIOCHEMICAL PARAMETERS IN APPLE SOFTENING

Postharvest softening of apple is one of the most important problems resulting in quality losses for growers and distributors all over the world. Factors affecting apple softening must be well known to provide a good quality apple to the market all year round. Therefore, our research focuses on the physical and biochemical parameters causing and related to apple softening. Rapid postharvest softening of apple is the result of an undesired, fast ripening process. The two main reasons for apple softening are water loss due to transpiration and cell wall breakdown due to enzymatic activities. The former has a considerable influence on the turgidity of the cells (thus on the stiffness of apple), while the latter affects mainly the firmness of the apple due to reducing the mechanical strength of cell walls. The apple cultivar 'Delbard Estival' was studied during 2 months storage at 18°C, 80-90% relative humidity (shelf life conditions). The acoustic stiffness coefficient, water potential, Brix value, penetrometer firmness, bruise susceptibility and activity of polygalacturonase were investigated. Both the acoustic stiffness coefficient and penetrometer firmness decreased considerably during storage following the characteristic three phase softening curve. Water potential and bruise susceptibility also decreased during storage due to the decrease in turgidity of the apple tissue. The activity of polygalacturonase showed an exponential increase in the first 30 days. The acoustic stiffness coefficient during storage was largely determined by the initial stiffness. The acoustic stiffness coefficient related to penetrometer firmness and water potential. There were also correlations found between water potential and soluble solids content. Bruise susceptibility was affected by both stiffness and the weight of the fruit.

Storability of paprika varieties measured by non-destructive acoustic method

During our experiments, the storability of paprika (Capsicum annuum) samples was measured by a non-destructive acoustic method. The aims of our work were the determination of the applicability and reproducibility of the acoustic stiffness method for paprika, the investigation of the optimum measuring conditions. In order to compare the main paprika varieties regarding shelf-life, our further aim was to follow the softening phenomenon or textural changes (i.e. changes in stiffness) of different paprika varieties measured by the non­destructive acoustic stiffness method. Five different varieties of paprika grown in hydroponics growing system were used for the measurements. All paprika varieties were stored at 20 °C for two weeks. Samples were tested on every 2nd or 3rd day. The acoustic method was found to be suitable to follow the softening of paprika samples. The characteristic frequency of the acoustic signal could be well detected and clearly separated from the other vibration peaks. Tapping the top of the paprika was observed to give a clearer and less noisy signal compared to the signal obtained by tapping the sample's shoulder. The acoustic results showed the same tendencies with regard to softening during storage as the impact method showed in our previous experiments.

A wave model for rigid-frame porous materials using lumped parameter concepts

The work presented in this paper concerns the behaviour of porous media when exposed to a normal incidence sound field. A propagating wave model based on lumped parameter concepts of acoustic mass, stiffness and damping is used to investigate the absorption phenomena due to the wave propagation in the layer(s) and interference effects due to the wave reflection–transmission at the interfaces of the layer(s). Results from the theoretical model have been validated by measurements on samples of consolidated rubber granulate material. Two typical installations where a layer of porous material is placed next to a rigid wall, and where it is placed at a distance from a rigid wall are used as reference cases. The geometrical and physical properties of porous materials can be described by such parameters as the non-dimensional shape factor and the porosity. The propagating model introduced is used to investigate the effect of these two parameters on acoustic absorption and thus relate the physical properties to the acoustic behaviour.

Genetic parameter estimates for wood stiffness, strength, internal checking, and resin bleeding for radiata pine

Data from two separate experiments were used to estimate genetic parameters for different wood properties of Pinus radiata D. Don in New Zealand. In experiment 1, 72 and 60 open-pollinated families were sampled at two sites, Kinleith and Paengaroa, respectively. Fifty-nine such families were common to both sites. In experiment 2, 62 and 29 pollen-parent families were sampled from a female-tester trial at two sites, Kaingaroa and Warrengong (the latter in Australia), respectively. Twenty-nine such families were common to both sites. Clearwood stiffness (MOE) and strength (MOR), wood density (DEN), acoustic stiffness on standing trees (IMLH), acoustic stiffness in 5-m logs (HITMAN), external resin bleeding (ERB), internal checking from discs taken at 1.3-m and 3.0-m height (CHEK_B and CHEK_U), and diameter at breast height (DBH) were assessed. Within-site narrow-sense heritability (h2) estimates of various wood properties were consistent, particularly within New Zealand. Across-sites estimates of h2 of HITMAN, CHEK_B, and DEN were, respectively, 0.24, 0.40, and 0.62 in experiment 1 and 0.21, 0.16, and 0.38 in experiment 2. Estimated type B genetic correlations were generally high for all traits except DBH. DEN showed strong positive genetic correlation with all direct and acoustic measures of stiffness (MOE, HITMAN, and IMLH). DEN and all measures of stiffness showed low to moderate negative genetic correlations with DBH.

Acoustic stiffness and change in plug cartilage over time after autologous osteochondral grafting: correlation between ultrasound signal intensity and histological score in a rabbit model

We investigated quantitative changes over time in ultrasound signal intensity (an index of stiffness), signal duration (an index of surface irregularity), and interval between signals (an index of thickness) of plug cartilage in an animal model of autologous osteochondral grafting. A full-thickness osteochondral plug was surgically removed and replaced in male Japanese white rabbits (n = 22). Specimens obtained at day 0 and weeks 2, 4, 8, 12 and 24 postoperatively were assessed using an ultrasound system and by macroscopic and histological evaluation (modified Mankin's score). Histology revealed that the plug sank until 2 weeks postoperatively, and that newly formed cartilage-like tissue covered the plug, but at 24 weeks the tissue detached. The plug itself survived well throughout the period of observation. Although the signal intensity at the plug site was same as that in the sham operated contralateral knee at day 0, from 2 to 24 weeks postoperatively it was less than that in the sham knee. At 8 weeks, this difference was significant (P < 0.05). Modified Mankin's score revealed early degenerative changes at the site, but macroscopic examination did not. Signal intensity correlated significantly with score (both at day 0 and at the five postoperative time points [P < 0.05, r = -0.91] and as a whole [P < 0.05, r = -0.36]). Signal intensity also significantly correlated with the individual subscores for 'cartilage structure' (P < 0.05, r = -0.32) and 'cartilage cells' (P < 0.05, r = -0.30) from the modified Mankin's score, but not significantly with subscores for 'staining' and 'tidemark'. Signal duration correlated significantly with total score (as a whole [P < 0.05, r = 0.34]), but not significantly with the score for cartilage structure (P = 0.0557, r = 0.29). The interval between signals reflected well the actual thickness of the plug site. The significant relationships between ultrasound signal intensity and scores suggest that early degenerative changes in plug cartilage and cartilage-like tissue, especially in the superficial layer, are detectable by high-frequency ultrasound assessment.

Temperature dependence of the ultrasonic transmission through electrical resistance heated imperfect metal–metal interfaces

Because of surface roughness, the area of contact between real surfaces is less than the geometrical area. For this reason the known rules of acoustic reflection and transmission have to be modified for real interfaces. Ultrasonic transmission through imperfect interfaces is commonly described in terms of the contact stiffness model which assumes distributed springs between the surfaces in contact [Proc. R. Soc. Lond. A 202 244; J. Acoust. Soc. Am. 89 (1991) 503ff; J. Acoust. Soc. Am. 68 1516; J. Nondestr. Eval. 4 177; J. Geophys. Res. 94 (1989) 17681ff]. Several authors [Trans. ASME 123 8ff; J. Acoust. Soc. Am. 103 657ff; Ultrasonics 38 513] theoretically and experimentally show the pressure and frequency dependence of the ultrasonic transmission through such interfaces. Our paper will document, that the temperature of the interface has significant influence on the ultrasonic transmission as well. In the experimental approach, a CuSn8-rod was clamped between the electrodes of a resistance welding unit. Either longitudinally or transversally polarised ultrasonic pulses were generated by a transmitter built in the upper electrode. The transmitted ultrasonic signal was subsequently detected by the receiver integrated in the lower electrode. After the welding current was turned on, a strong decrease in ultrasonic transmission has been observed due to resistance heating of the interfaces between the welding electrodes and the rod. To explain this extraordinary strong temperature effect, a simple quasistatic analytical thermal–electrical model of the contacting area was used to give a rough estimation of the maximum interfacial temperature and the temperature distribution during the flow of the welding current. In a second step, the temperature dependence of the material data in the acoustic contact stiffness model was used to calculate the changes in ultrasonic transmission caused by the welding current. It is shown, that the observed decrease in ultrasonic transmission with increasing temperature is mainly caused by the temperature dependence of the elastic constants of the metals and is much stronger than expected for ideal interfaces. The calculated ultrasonic transmission is in very good agreement with the experimental data and seems to be interpreted correctly by the acoustic contact stiffness model.

Acoustic properties of rigid-frame porous materials — an engineering perspective

Sound propagation in rigid-frame porous materials is governed by the effective density and the effective bulk modulus of the fluid in the pore space. These quantities, for which analytical expressions have already been derived by other researchers, are frequency-dependent, complex and non-linear. However, because of the complexity of these expressions, it is difficult to obtain physical insight into the acoustic behaviour of the porous materials and to determine the dominant mechanism for sound absorption for a given material at a given frequency. Alternatively there are very simple expressions. In this paper the relationships between the complicated and relatively simple models are studied, and simple non-dimensional expressions for the characteristic impedance and wavenumber for sound propagation in rigid-frame porous materials are derived using the concepts of acoustic mass, stiffness and damping. An upper bound for thermal losses in a rigid-frame material is presented, and a simple rule of thumb is given for the required flow resistivity, porosity and tortuosity for a given thickness of porous material.