Makine Mühendisliği Bölümü Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.11779/1944

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Citation - WoS: 1
Citation - Scopus: 1
1441. Quantification of the Flow Noise in Household Refrigerators
(JVE INTERNATIONAL LTD., 2014) Körük, Hasan; Arısoy, Ahmet; Bilgin, Necati
The flow noise in household refrigerators is quantified in this study. First, the sound pressure measurements in a quiet room using typical household refrigerators are conducted and the noise characteristics of the refrigerators are presented. Then, the flow noise in household refrigerators is quantified using the results of the overall analysis and Fourier transform of the measured sound pressure data. After that, the flow noise in household refrigerators is quantified using the sound pressure measurements conducted using a specially designed test rig. The frequency characteristics of the flow noise in household refrigerators are also explored and the contribution of the flow noise is identified.
A Business Model Frame for Innovative Startups - (july 11-15, 2017)
(Global Business & Technology Association, 2017) Dorantes-Gonzalez, Dante Jorge
Current business model frames such as the Business Model Canvas and the Lean Canvas do not address aspects of open innovation, problem statement, innovative problem solving, business metrics and disruptive strategies; therefore, a novel business model frame is introduced to cover these aspects. This new model is based on a combination of key principles of the theory of inventive problem solving applied to business and management, such as multi-screen analysis of value-conflict mapping, trends of ideality of business system evolution positioning, among others; but also, intellectual property, disruptive strategies, and open innovation, as well as startup metrics to describe the business differentiation and attractiveness to potential investors, incubators and accelerators. The entrepreneur designing his/her own startup should be able to justify if not all, most of the items to be able to demonstrate the idea strengths. And regarding both building blocks “Product Formulation and Inventive Problem Solving” and “Disruption Strategy”, certain training should be necessary.
Citation - WoS: 5
Citation - Scopus: 6
A New Approach for Measuring Viscoelastic Properties of Soft Materials Using the Dynamic Response of a Spherical Object Placed at the Sample Interface
(Springer, 2023) Besli, Ayça; Koç,Ömer Hayati; Körük,Hasan; Yurdaer, Berk Salih
Background: There are several techniques to characterize the mechanical properties of soft materials, such as the indentation method and the method based on the application of a spherical object placed inside the sample. The indentation systems usually yield the elastic properties of materials and their mathematical models do not consider the inertia of the sample involved in motion and radiation damping, while placing an object inside the sample is not practical and this procedure can alter the mechanical properties of the sample for the method based on the application of a bubble/sphere placed inside the sample. Objective: A new approach for the identification of the viscoelastic properties of soft materials using the dynamic response of a spherical object placed at the sample interface was proposed. Methods: The spherical object placed at the sample interface was pressed using an electromagnet and the dynamic response of the spherical object was tracked using a high-speed camera, while the dynamic response of the spherical object placed at the sample interface was estimated using a comprehensive analytical model. The effects of the shear modulus, viscosity, Poisson’s ratio and density of the soft sample, the radius and density of the spherical object and the damping due to radiation were considered in this mathematical model. The shear modulus and viscosity of the soft sample were determined by matching the experimentally identified and theoretically estimated responses of the spherical object. Results: The shear moduli and viscosities of the three phantoms with the gelatin mass ratios of 0.20, 0.25 and 0.29 were measured to be 3450, 4300 and 4950 Pa and 12.5, 14.0 and 15.0 Pa⋅s, respectively. The shear modulus and viscosity of the phantom increases as the gelatin mass ratio increases. The frequency of oscillations of the hemisphere placed at the phantom interface increases as the gelatin mass ratio increases due to stiffness increase. Conclusions: After matching the experimental and theoretical steady-state displacements and amplitudes of oscillations of the hemisphere at the sample interface, the comparison of the experimentally identified and theoretically predicted frequency of oscillations further confirmed the identified material properties of the samples. The approach presented here is expected to provide valuable information on material properties in biomedical and industrial applications.
Citation - WoS: 9
Citation - Scopus: 12
A New Triangular Composite Shell Element With Damping Capability
(Elsevier, 2014) Körük, Hasan; Şanlıtürk, Kenan Yüce
This paper presents a new triangular composite shell element with damping capability. Formulation of the composite triangular shell element is based on stacking individual homogeneous triangular shell ele- ments on top of each other. The homogeneous shell element is an assembly of a triangular membrane element with drilling degrees of freedoms and a plate element. Damping capability is provided by means of complex element stiffness matrix of individual flat layers of the composite element. These elements with damping capability allow modelling general structures with damping treatments. A few test cases are modelled using triangular finite element developed here and the results of the complex eigenvalue analyses are compared with those of the quadrilateral shell elements proposed recently. The results obtained using the presented triangular and previous quadrilateral composite elements are also com- pared with those based on modal strain energy method and experimental results. Comparisons of the experimental and the theoretical results confirm that the modal properties including modal damping lev- els of structures with damping treatments can be predicted with high accuracy using the proposed finite element.
A Novel Business Model Frame for Innovative Startups - (may 12-14, 2017)
(World Conference on Technology, Innovation and Entrepreneurship, 2017) Dorantes-Gonzalez, Dante Jorge
The business model canvas has been used in business and entrepreneurship to sketch and frame the key points behind the development of a startup, and it was meant to strategically analyze and develop startups or documenting existing businesses. The business model canvas describes the firm’s value proposition, partners, resources, activities, customer relationships, distribution channels, customers, revenue streams and cost structure. However, when it comes to innovative startups, this template does not explicitly include innovation measures, no problem/opportunity formulation, or even such a basic component of a business model, as the profit formula. The present paper proposes a novel business model frame to visually and concisely sketch, besides accurately state traditional business concepts, key innovation concepts that any startup should integrate to be a game-changer in a competitive market. This new model is based on a combination of key principles of the theory of inventive problem solving (TRIZ) applied to business and management, such as multi-screen analysis of value-conflict mapping, trends of ideality of business system evolution positioning, among others; but also intellectual property, disruptive strategies, and open innovation, as well as startup metrics to describe the business differentiation and attractiveness to potential investors, incubators and accelerators.
A Novel Standard for Graphical Representation of Mental Models and Processes in Cognitive Sciences
(World Congress of Education, 2018) Dorantes-Gonzalez, Dante Jorge; McKeown, John A.G.
Cognitive Science has positioned itself to be a common ground in which models of mental processes from multiple disciplines merge, situating itself as a common field for new learning theories, or for formalizing existing ones. However, the authors have identified a need for updating the existing graphical representations by incorporating more accessible understanding for teachers and researchers in cross- multidisciplinary fields. In this regard, the present investigation attempts to generate a standard graphical language to represent complex mental processes by the introduction of functional principles, schemes and models that have been successfully used in technical areas such as adaptive control systems, algorithm flow charts, and artificial intelligence. This graphical representation, entitled “Cognitive Functional Representation” (CFR), is further shown to be efficacious in incorporating the essence of complex cognitive theories.
Citation - WoS: 1
Citation - Scopus: 1
Acoustic Cavitation Model Based on a Novel Reduced Order Gas Pressure Law
(2021) Pasinlioğlu, Şenay; Delale, Can Fuad
The thermal behavior of a spherical gas bubble in a liquid excited by an acoustic pressure signal is investigated by constructing an iterative solution of the energy balance equations between the gas bubble and the surrounding liquid in the uniform pressure approximation. This iterative solution leads to hierarchy equations for the radial partial derivatives of the temperature at the bubble wall, which control the temporal rate of change of the gas pressure and gas temperature within the bubble. In particular, a closure relation for the hierarchy equations is introduced based on the ansatz that approximates the rapid change of state during the collapse of the bubble from almost isothermal to almost adiabatic behavior by time averaging the complex dynamics of change of state over a relatively short characteristic time. This, in turn, leads to the desired reduced order gas pressure law exhibiting power law dependence on the bubble wall temperature and on the bubble radius, with the polytropic index depending on the isentropic exponent of the gas and on a parameter that is a function of the Péclet number and a characteristic time scale. Results of the linear theory for gas bubbles are recovered by identifying this parameter as a function of the Péclet number based on the Minnaert frequency. The novel gas pressure law is then validated against the near-isothermal solution and against the results of the numerical simulations of the original energy balance equations for large amplitude oscillations using spectral methods. Consequently, an acoustic cavitation model that accounts for phase change but that neglects mass diffusion is constructed by employing the reduced order gas pressure law together with the Plesset–Zwick solution for the bubble wall temperature and the Keller–Miksis equation for spherical bubble dynamics. Results obtained using variable interface properties for acoustically driven cavitation bubbles in water show that the time variations of the bubble radius and the bubble wall temperature lie between those obtained by the isothermal and adiabatic laws depending on the value of the Péclet number and the characteristic time scale.
Citation - WoS: 23
Citation - Scopus: 25
Acoustic Particle Palpation for Measuring Tissue Elasticity
(American Institute of Physics, 2015) El Ghamrawy, Ahmed; Körük, Hasan; Choi, James J; Pouliopoulos, Antonios N
We propose acoustic particle palpation—the use of sound to press a population of acoustic particles against an interface—as a method for measuring the qualitative and quantitative mechanical properties of materials. We tested the feasibility of this method by emitting ultrasound pulses across a tunnel of an elastic material filled with microbubbles. Ultrasound stimulated the microbubble cloud to move in the direction of wave propagation, press against the distal surface, and cause deformations relevant for elasticity measurements. Shear waves propagated away from the palpation site with a velocity that was used to estimate the material’s Young’s modulus.
Citation - WoS: 12
Citation - Scopus: 15
Acoustic Streaming in a Soft Tissue Microenvironment
(Elsevier, 2019) El Ghamrawy, Ahmed; Mohammed, Ali; Jones, Julian R; Körük, Hasan; Choi, James J; de Comtes, Florentina
We demonstrated that sound can push fluid through a tissue-mimicking material. Although acousticstreaming in tissue has been proposed as a mechanism for biomedical ultrasound applications, such as neuromodu-lation and enhanced drug penetration, streaming in tissue or acoustic phantoms has not been directly observed. Wedeveloped a material that mimics the porous structure of tissue and used a dye and a video camera to track fluidmovement. When applied above an acoustic intensity threshold, a continuous focused ultrasound beam (spatialpeak time average intensity: 238 W/cm2, centre frequency: 5 MHz) was found to push the dye axially, that is, in thedirection of wave propagation and in the radial direction. Dye clearance increased with ultrasound intensity andwas modelled using an adapted version of Eckart’s acoustic streaming velocity equation. No microstructuralchanges were observed in the sonicated region when assessed using scanning electron microscopy. Our study indi-cates that acoustic streaming can occur in soft porous materials and provides a mechanistic basis for future use ofstreaming for therapeutic or diagnostic purposes.
Citation - WoS: 54
Citation - Scopus: 63
An Assessment of the Performance of Impedance Tube Method
(Institute of Noise Control Engineering, 2014) Hasan Körük
The impedance tube method is widely used for measuring sound absorption (or reflection) coefficients of acoustic materials as a function of frequency. However, the sound absorption coefficients obtained using the impedance tube method may have some variations due to the dimensions (limits) of an impedance tube, sample preparation and sample mounting. This paper assesses the performance of the two-microphone impedance tube method as a function of frequency for different tube dimensions and materials and presents suggestions for increasing the reliability and repeatability of impedance tube measurements. First, after summarizing a systematic way for measuring acoustic transfer functions, sound absorption coefficients of a variety of materials ranging from conventional absorbing acoustic materials to samples with thin films are measured using two tubes with different tube diameter and microphone spacing. Uncertainty of sound absorption coefficients for various materials is discussed, and the frequency limits of impedance tubes are assessed. Then, a method for minimizing uncertainty due to sample mounting is proposed and the main findings are discussed.
Citation - WoS: 4
Citation - Scopus: 4
Application of Ultrasonic Vibrations for Minimization of the Accumulation of Limescale in Steam Irons
(Elsevier, 2018) Körük, Hasan; Şanlıtürk, Kenan Yüce; Serenli, Muzaffer
The accumulation of limescale in steam irons can significantly reduce the ironing efficiency. It is this problem that inspired us to introduce ultrasonic vibrations to irons in order to minimize limescale accumulation. This study describes a methodology for designing, modelling and optimizing an iron fitted with an ultrasonic exciter in an attempt to minimize limescale accumulation. In our methodology, first, an experimental demonstration of the potential benefits of ultrasonic vibrations in steam irons was conducted, using two existing irons, one of which was equipped with an ultrasonic exciter. Having confirmed the benefits, an experimental iron was designed and then optimized to maximise ultrasonic vibrations using finite element analyses within a predefined frequency range. To validate the results of the finite element analyses, a prototype iron base was built, and forced vibrations of this prototype, at ultrasonic frequencies ranging from 35 to 40 kHz, were measured using a laser vibrometer. The results of the theoretical and experimental vibration analyses as well as the physical experiments on the steam irons indicate that it is possible for ultrasonic vibrations to be utilized in irons to minimize the accumulation of limescale.
Citation - WoS: 2
Citation - Scopus: 2
Approximate Closed-Form Solutions for Vibration of Nano-Beams of Local/Non-local Mixture
(Springer, 2022) Ruta, Giuseppe; Eroğlu, Uğurcan
This paper presents an approach to natural vibration of nano-beams by a linear elastic constitutive law based on a mixture of local and non-local contributions, the latter based on Eringen's model. A perturbation in terms of an evolution parameter lets incremental field equations be derived; another perturbation in terms of the non-local volume fraction yields the variation of the natural angular frequencies and modes with the 'small' amount of non-locality. The latter perturbation does not need to comply with the so-called constitutive boundary conditions, the physical interpretation of which is still debated. The possibility to find closed-form solutions is highlighted following a thorough discussion on the compatibility conditions needed to solve the steps of the perturbation hierarchy; some paradigmatic examples are presented and duly commented.
Citation - WoS: 10
Citation - Scopus: 20
Assessment of the Measurement and Prediction Methods for the Acoustic Properties of Natural Fiber Samples and Evaluation of Their Properties
(Taylor & Francis, 2021) Körük, Hasan
Although some studies have been conducted to show how natural fibers canreplace synthetic materials, the use of many natural fibers is still limited. Onthe other hand, the use of natural fibers can become very common in manyapplications once their performance is fully understood. This paper aims topresent a critical assessment of the acoustic properties of natural fibersamples. First, the methods commonly used for the measurement and prediction of the acoustic properties of natural fiber samples are determined.Second, the common techniques for measuring sound absorption coefficients (SACs) and sound transmission losses (STLs) are presented, and theiradvantages and limitations are evaluated. After that, the models commonlyused for the prediction of acoustic properties are presented. Then, the SACsof many natural fiber samples are presented along with the thickness, bulkdensity and flow resistivity of the samples. Furthermore, the SACs of thesamples are normalized using sample thickness and bulk density, and thesound absorption performance of the fiber samples is evaluated. Based onthe results of many natural fiber samples, an empirical model for estimatingthe SACs of natural fiber samples is presented. Finally, the STLs of someporous natural fiber samples are presented.
Assessment of the Models for Predicting the Responses of Spherical Objects in Viscoelastic Mediums and at Viscoelastic Interfaces
(IOP Publishing Ltd, 2021) Körük, Hasan
Spherical objects, such as bubbles and spheres, embedded in mediums and atviscoelastic interfaces are encountered in many applications, including the determination ofmaterial properties. This paper assesses the models for predicting the responses of sphericalobjects in viscoelastic mediums and at viscoelastic interfaces used in various applications. Themodels are presented very compactly, and evaluations are performed based on the analyses ofthe models for the spherical objects in viscoelastic mediums and at viscoelastic interfaces. First,the models for predicting the static displacements of spherical objects are presented andassessed. After that, the models for predicting the dynamic responses of spherical objects arepresented and their dynamic behaviours are compared. Then, the models for the deformation ofthe medium around spherical objects and stress distribution are presented and evaluated. Themodels and evaluations presented in this study can be exploited in various applications,including biomedical applications.
Biyomalzemelerin Akustik ve Mekanik Özelliklerinin Arastırılması
(2020) Genç, Garip; Körük,Hasan
Bu proje kapsamında, jüt lifleri ve çesitli luffa lifleri kullanılarak, farklı kalınlıklarda reçinesiz (hiçbir reçine kullanılmayan) homojen ve hibrit jüt ve luffa yapılar ve yine farklı kalınlıklarda ve farklı lif/reçine oranlarında reçineli homojen ve hibrit jüt ve luffa yapılar üretilerek, bu yapıların akustik ve mekanik özellikleri ile ilgili kapsamlı bir resmin ortaya konulması hedeflenmistir. Bu kapsamda kullanılan yöntemler/sonuçlar su sekildedir: (i) Akustik testler için farklı kalınlıklarda hem reçinesiz hem de farklı lif/reçine oranlarına sahip reçineli homojen ve hibrit numuneler üretilmistir. Empedans tüp yöntemi kullanılarak bu akustik numunelerin ses yutma ve ses iletim kaybı gibi akustik özellikleri deneysel olarak belirlenmistir. Homojen ve hibrit kompozit yapıların akustik performansları karsılastırılmıstır. Sonuçta, kalınlık ve lif/reçine oranın bu yapıların akustik özellikleri üzerindeki etkisi ortaya konulmustur. (ii) Farklı frekans aralıkları için kalınlıgın ve lif/reçine oranının bir fonksiyonu olarak ölçülen akustik verilere egriler uydurularak, malzemelerin akustik özelliklerini belirlemeye yönelik basit ampirik modeller ortaya konulmustur. Dahası, malzemelerin ses yutma katsayıları Delany-Bazley ve Johnson- Champoux-Allard gibi teorik modeller kullanılarak tahmin edilmis ve sonuçlar deneysel sonuçlarla karsılastırılmıstır. Benzer sekilde, numunelerin ses iletim kayıpları teorik olarak hesaplanmıs ve deneysel sonuçlarla karsılastırılmıstır. Sonuçta, bu yapıların tasarımında akustik amaçla kullanılabilecek ampirik ve teorik modeller ortaya konulmustur. (iii) Titresim testleri için farklı kalınlık ve lif/reçine oranlarına sahip reçineli homojen ve hibrit numuneler üretilmis, üretilen bu yapılar üzerinde akustik ve yapısal frekans tepki fonksiyonları ölçülmüs ve aynı yapıların teorik modellerinden yararlanılarak malzemelerin elastik ve sönüm gibi mekanik özellikleri belirlenmistir. Homojen jüt ve luffa kompozit yapıları hem izotropik varsayılarak hem de bu yapıların yöne baglı elastik özelliklerinin olması durumu dikkate alınarak modellenmislerdir. Sonuçta, kalınlık ve lif/reçine oranın mekanik özellikler üzerindeki etkisi ortaya konulmus ve pratikte bu yapıların tasarımı için kullanılabilecek bazı yaklasımlar ortaya konulmustur.
Citation - WoS: 15
Citation - Scopus: 13
Calibration of the Effective Spring Constant of Ultra-Short Cantilevers for a High-Speed Atomic Force Microscope
(2015) Xu, Lin-Yan; Wu, Sen; Hu, Xiao-Dong; Song, Yun-Peng; Fu, Xing; Zhang, Jun-Ming; Dorantes-Gonzalez, Dante Jorge
Ultra-short cantilevers are a new type of cantilever designed for the next generation of high-speed atomic force microscope (HS-AFM). Ultra-short cantilevers have smaller dimensions and higher resonant frequency than conventional AFM cantilevers. Moreover, their geometry may also be different from the conventional beam-shape or V-shape. These changes increase the difficulty of determining the spring constant for ultra-short cantilevers, and hence limit the accuracy and precision of force measurement based on a HS-AFM. This paper presents an experimental method to calibrate the effective spring constant of ultra-short cantilevers. By using a home-made AFM head, the cantilever is bent against an electromagnetic compensation balance under servo control. Meanwhile the bending force and the cantilever deflection are synchronously measured by the balance and the optical lever in the AFM head, respectively. Then the effective spring constant is simply determined as the ratio of the force to the corresponding deflection. Four ultra-short trapezoid shape cantilevers were calibrated using this method. A quantitative uncertainty analysis showed that the combined relative standard uncertainty of the calibration result is less than 2%, which is better than the uncertainty of any previously reported techniques.
Citation - WoS: 3
Citation - Scopus: 3
Characterization of Viscoelastic Materials Using Free-Layered and Sandwiched Samples: Assessment and Recommendations
(Polish Physical Society, 2015) Özer, Mehmet Sait; Körük, Hasan; Şanlıtürk, Kenan Yüce
Viscoelastic materials are widely used in many applications in practice. However, determination of the elastic and damping properties of these materials is quite difficult in the sense that the identified results may contain high degree of uncertainty. The characterization of viscoelastic materials using the Oberst beam method, based on non-contact excitation and response measurements, is revisited in this paper. The effects of signal processing parameters such as frequency resolution in Frequency Response Function (FRF) measurements, as well as the effects of various single-degree-of-freedom modal analysis methods, including circle-fit, half-power and line-fit are investigated first. Then, the modal loss factors, Young's modulus and shear modulus of some sample viscoelastic materials are identified using both the free-layered and sandwiched samples. The results obtained from different tests are compared, discussed and some recommendations are made so as to identify the damping and elastic properties of typical viscoelastic materials with better accuracy. Analyses of a large number of FRF measurements show that the selection of the appropriate signal processing parameters and the use of appropriate modal analysis method can be very significant during the identification of viscoelastic materials. By following the approach presented in this paper, the damping and elastic properties of viscoelastic materials can be identified with better accuracy using either free-layered or sandwiched samples. The material properties obtained by this approach can be used for developing valid structural models and/or for damping optimization purposes.
Citation - WoS: 6
Citation - Scopus: 10
Detection of Air Leakage Into Vacuum Packages Using Acoustic Measurements and Estimation of Defect Size
(Elsevier, 2019) Körük, Hasan; Şanlıtürk, Kenan Yüce
Air leakages in food and ingredient packages which are sealed in vacuum environments may cause a marked deterioration of the product, leading to a loss of functionality. Manufacturers of such products have very stringent but rather costly quality control procedures and there is a pressing need for developing more economical ways of automated quality control techniques to test the vacuum packages reliably. However, due to the fact that the defect size of a typical package with a leakage problem could be micro- or nano-scale, such faults are not detectable using conventional techniques. In this paper, the performance of a proposed acoustic method is assessed for the detection of air leakage in instant dry yeast packages sealed in a vacuum environment, which are typical of food and ingredients packaged under vacuum conditions. The investigation is carried out in both laboratory and in-situ environments. The acoustic pressure created by leaking air into the faulty packages is measured using a low-noise microphone in an acoustic chamber. Faulty packages are then identified using the changes in measured sound pressure levels within a certain frequency band. A mathematical model is also proposed to predict the pressure inside a yeast package with certain defect size as a function of time. The mathematical model is then used to determine the size of a defect causing the leakage, using the time required for the pressure inside a faulty yeast package to reach to a threshold level. The results of this investigation show that, using the state of the art measurement techniques, it is possible to detect packages with leakage problem if the diameter of the defect is greater than a few tens of micrometres.
Development of a Model for Predicting Dynamic Response of a Sphere at Viscoelastic Interface: a Dynamic Hertz Model
(IOP Publishing Ltd, 2021) Körük, Hasan
A model for predicting the dynamic response of a sphere at viscoelastic interface is presented. The model is based on Hertz contact model and the model for a sphere in a medium.In addition to the elastic properties of medium and the size of sphere, the model considers thedensity of sphere, the density and viscosity of medium, and damping of oscillations of spheredue to radiation of shear waves. The model can predict not only the effects of the mechanicalproperties of medium, the physical properties of sphere, and the amplitude of excitation forceon sphere displacement, but also the effects of these parameters on shift of resonancefrequency. The proposed model can be used to identify the elastic and damping properties ofmaterials, and to understand the dynamic responses of spherical objects at viscoelasticinterfaces in practical applications.
Citation - WoS: 10
Citation - Scopus: 13
Displacement of a Bubble by Acoustic Radiation Force Into a Fluid-Tissue Interface
(2018) Körük, Hasan; Choi, James J
Microbubbles in an ultrasound beam experience a primary Bjerknes force, which pushes the microbubbles against a fluid-tissue interface and deforms the tissue. This interaction has been used to measure tissue elasticity and is a common interaction in many therapeutic and diagnostic applications, but the mechanisms of deformation, and how the deformation dynamic depends on the bubble and ultrasound parameters, remain unknown. In this study, a mathematical model is proposed for the displacement of a bubble onto a fluid-tissue interface and the tissue deformation in response to the primary Bjerknes force. First, a model was derived for static loading and the model's prediction of bubble-mediated tissue displacement and stresses in tissue were explored. Second, the model was updated for dynamic loading. The results showed that the bubble is both displaced by the applied force and changes its shape. The bubble displacement changes nonlinearly with the applied force. The stress values in tissue are quite high for a distance within one radius of the bubble from the bubble surface. The model proposed here is permissible in human tissue and can be used for biomedical ultrasound applications, including material characterization. (C) 2018 Acoustical Society of America.