Thermoacoustic oscillations in an air-filled, looped tube with a stack inserted are simulated numerically by using asymptotic theories for the ratio of a radius of flow passage to a typical thickness of the thermoviscous diffusion layer. The stack is composed of many pores axially and is sandwiched by hot and cold heat exchangers to impose a temperature gradient on the air in each pore. Weakly nonlinear wave equations based on the boundary-layer theory are used for a section in the outside of the stack. In each pore, the diffusion-wave (advection) equation is employed. Matching conditions at both ends of the stack require the conservations of mass, momentum and energy fluxes. An initial-value problem is solved from a disturbance of a pulsed axial velocity along the loop. When the temperature ratio is below a certain value, the initial disturbance is decayed out. However when the ratio exceeds it, it becomes unstable to grow in amplitude. Between the stable and unstable regimes, there exists a marginal sta...
{"title":"Numerical simulations of thermoacoustic oscillations in a looped tube by asymptotic theories for thickness of diffusion layers","authors":"D. Shimizu, T. Iwamatsu, Nobumasa Sugimoto","doi":"10.1121/2.0000888","DOIUrl":"https://doi.org/10.1121/2.0000888","url":null,"abstract":"Thermoacoustic oscillations in an air-filled, looped tube with a stack inserted are simulated numerically by using asymptotic theories for the ratio of a radius of flow passage to a typical thickness of the thermoviscous diffusion layer. The stack is composed of many pores axially and is sandwiched by hot and cold heat exchangers to impose a temperature gradient on the air in each pore. Weakly nonlinear wave equations based on the boundary-layer theory are used for a section in the outside of the stack. In each pore, the diffusion-wave (advection) equation is employed. Matching conditions at both ends of the stack require the conservations of mass, momentum and energy fluxes. An initial-value problem is solved from a disturbance of a pulsed axial velocity along the loop. When the temperature ratio is below a certain value, the initial disturbance is decayed out. However when the ratio exceeds it, it becomes unstable to grow in amplitude. Between the stable and unstable regimes, there exists a marginal sta...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79875916","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Large-scale nonlinear ultrasound simulations using the open-source k-Wave toolbox are now routinely performed using the MPI version of k-Wave running on traditional CPU-based clusters. However, the all-to-all communications required by the 3D fast Fourier transform (FFT) severely impact performance when scaling to large numbers of compute cores. This can be overcome by using a domain decomposition strategy based on a local Fourier basis. In this work, we analyze the performance and accuracy of using local domain decomposition for running a high-intensity focused ultrasound (HIFU) simulation in the kidney on a single server containing eight NVIDIA P40 graphical processing units (GPUs). Different decompositions and overlap sizes are investigated and compared to a global MPI simulation running on a CPU-based supercomputer using 1280 cores. For a grid size of 960 by 960 by 1280 grid points and an overlap size of 4 grid points, the error in the simulation using local domain decomposition is on the order of 0.1$ compared to the global simulation, which is sufficient for most applications. The financial cost for running the simulation is also reduced by more than an order of magnitude.Large-scale nonlinear ultrasound simulations using the open-source k-Wave toolbox are now routinely performed using the MPI version of k-Wave running on traditional CPU-based clusters. However, the all-to-all communications required by the 3D fast Fourier transform (FFT) severely impact performance when scaling to large numbers of compute cores. This can be overcome by using a domain decomposition strategy based on a local Fourier basis. In this work, we analyze the performance and accuracy of using local domain decomposition for running a high-intensity focused ultrasound (HIFU) simulation in the kidney on a single server containing eight NVIDIA P40 graphical processing units (GPUs). Different decompositions and overlap sizes are investigated and compared to a global MPI simulation running on a CPU-based supercomputer using 1280 cores. For a grid size of 960 by 960 by 1280 grid points and an overlap size of 4 grid points, the error in the simulation using local domain decomposition is on the order of 0.1...
{"title":"Performance and accuracy analysis of nonlinear k-Wave simulations using local domain decomposition with an 8-GPU server","authors":"B. Treeby, Filip Vaverka, J. Jaros","doi":"10.1121/2.0000883","DOIUrl":"https://doi.org/10.1121/2.0000883","url":null,"abstract":"Large-scale nonlinear ultrasound simulations using the open-source k-Wave toolbox are now routinely performed using the MPI version of k-Wave running on traditional CPU-based clusters. However, the all-to-all communications required by the 3D fast Fourier transform (FFT) severely impact performance when scaling to large numbers of compute cores. This can be overcome by using a domain decomposition strategy based on a local Fourier basis. In this work, we analyze the performance and accuracy of using local domain decomposition for running a high-intensity focused ultrasound (HIFU) simulation in the kidney on a single server containing eight NVIDIA P40 graphical processing units (GPUs). Different decompositions and overlap sizes are investigated and compared to a global MPI simulation running on a CPU-based supercomputer using 1280 cores. For a grid size of 960 by 960 by 1280 grid points and an overlap size of 4 grid points, the error in the simulation using local domain decomposition is on the order of 0.1$ compared to the global simulation, which is sufficient for most applications. The financial cost for running the simulation is also reduced by more than an order of magnitude.Large-scale nonlinear ultrasound simulations using the open-source k-Wave toolbox are now routinely performed using the MPI version of k-Wave running on traditional CPU-based clusters. However, the all-to-all communications required by the 3D fast Fourier transform (FFT) severely impact performance when scaling to large numbers of compute cores. This can be overcome by using a domain decomposition strategy based on a local Fourier basis. In this work, we analyze the performance and accuracy of using local domain decomposition for running a high-intensity focused ultrasound (HIFU) simulation in the kidney on a single server containing eight NVIDIA P40 graphical processing units (GPUs). Different decompositions and overlap sizes are investigated and compared to a global MPI simulation running on a CPU-based supercomputer using 1280 cores. For a grid size of 960 by 960 by 1280 grid points and an overlap size of 4 grid points, the error in the simulation using local domain decomposition is on the order of 0.1...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85086142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Amplitude death, meaning the stabilization of an unstable equilibrium state, appears in delay coupled oscillators even if the oscillators have the same frequency. In this study, we aim to stop thermoacoustic oscillations by the amplitude death induced by delay. Thermoacoustic oscillations in combustors of gas turbine engines cause serious damage to the engine. Development of the method for suppressing thermoacoustic oscillations is urgent necessity. Recently, the amplitude death in the thermoacoustic oscillators was demonstrated by using delay and diffusive couplings. The delay coupling was introduced by gas-filled tubes. The experimental death regions were compared with the delay-coupled van der Pol systems and qualitative agreement was achieved, but the acoustic feature of the connecting tube was not considered. For a full acoustical modeling of the coupled thermoacoustic oscillator, we modelled two thermoacoustic oscillators coupled by connecting tubes by the linear acoustic theory based on hydrodynami...
振幅死亡，即不稳定平衡状态的稳定化，出现在延迟耦合振荡器中，即使振荡器具有相同的频率。在这项研究中，我们的目标是通过延迟引起的振幅死亡来阻止热声振荡。燃气涡轮发动机燃烧室的热声振荡会对发动机造成严重的损害。开发抑制热声振荡的方法是迫切需要的。近年来，热声振荡器的振幅死亡现象通过延迟和扩散耦合得到了证明。通过充气管引入延迟耦合。在未考虑连接管声学特性的情况下，将实验死亡区与延迟耦合van der Pol系统进行了比较，得到了定性一致的结果。为了对耦合热声振荡器进行完整的声学建模，我们利用基于水动力学的线性声学理论对两个连接管耦合的热声振荡器进行了建模。
{"title":"Derivation of coupling conditions of amplitude death in delay-coupled thermoacoustic oscillators","authors":"H. Hyodo, T. Biwa","doi":"10.1121/2.0000882","DOIUrl":"https://doi.org/10.1121/2.0000882","url":null,"abstract":"Amplitude death, meaning the stabilization of an unstable equilibrium state, appears in delay coupled oscillators even if the oscillators have the same frequency. In this study, we aim to stop thermoacoustic oscillations by the amplitude death induced by delay. Thermoacoustic oscillations in combustors of gas turbine engines cause serious damage to the engine. Development of the method for suppressing thermoacoustic oscillations is urgent necessity. Recently, the amplitude death in the thermoacoustic oscillators was demonstrated by using delay and diffusive couplings. The delay coupling was introduced by gas-filled tubes. The experimental death regions were compared with the delay-coupled van der Pol systems and qualitative agreement was achieved, but the acoustic feature of the connecting tube was not considered. For a full acoustical modeling of the coupled thermoacoustic oscillator, we modelled two thermoacoustic oscillators coupled by connecting tubes by the linear acoustic theory based on hydrodynami...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88766179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thermoacoustic Taconis oscillations of gaseous helium in a closed straight cylindrical tube are numerically studied. The tube is subject to a strong temperature gradient along the tube axis. The ratio of the temperature of the hot end parts to that of the cold center part is 15, and the length ratio of the hot part to that of the cold part is 1.0. The axisymmetric compressible Navier-Stokes equations are solved and fundamental antisymmetric mode of a standing wave is observed. Using the obtained flow field data, we trace fluid particles and their thermodynamic properties are calculated. The fluid particles oscillate and drift in the tube. In order to obtain a general picture of the energy conversion, the evolution of the distribution of the increase rate of heat is examined. It is shown that the rate is large in the region where the temperature gradient is large in the tube.Thermoacoustic Taconis oscillations of gaseous helium in a closed straight cylindrical tube are numerically studied. The tube is subject to a strong temperature gradient along the tube axis. The ratio of the temperature of the hot end parts to that of the cold center part is 15, and the length ratio of the hot part to that of the cold part is 1.0. The axisymmetric compressible Navier-Stokes equations are solved and fundamental antisymmetric mode of a standing wave is observed. Using the obtained flow field data, we trace fluid particles and their thermodynamic properties are calculated. The fluid particles oscillate and drift in the tube. In order to obtain a general picture of the energy conversion, the evolution of the distribution of the increase rate of heat is examined. It is shown that the rate is large in the region where the temperature gradient is large in the tube.
{"title":"Thermodynamic properties of fluid particles and energy fluxes in thermoacoustic oscillations","authors":"S. Adachi","doi":"10.1121/2.0000877","DOIUrl":"https://doi.org/10.1121/2.0000877","url":null,"abstract":"Thermoacoustic Taconis oscillations of gaseous helium in a closed straight cylindrical tube are numerically studied. The tube is subject to a strong temperature gradient along the tube axis. The ratio of the temperature of the hot end parts to that of the cold center part is 15, and the length ratio of the hot part to that of the cold part is 1.0. The axisymmetric compressible Navier-Stokes equations are solved and fundamental antisymmetric mode of a standing wave is observed. Using the obtained flow field data, we trace fluid particles and their thermodynamic properties are calculated. The fluid particles oscillate and drift in the tube. In order to obtain a general picture of the energy conversion, the evolution of the distribution of the increase rate of heat is examined. It is shown that the rate is large in the region where the temperature gradient is large in the tube.Thermoacoustic Taconis oscillations of gaseous helium in a closed straight cylindrical tube are numerically studied. The tube is subject to a strong temperature gradient along the tube axis. The ratio of the temperature of the hot end parts to that of the cold center part is 15, and the length ratio of the hot part to that of the cold part is 1.0. The axisymmetric compressible Navier-Stokes equations are solved and fundamental antisymmetric mode of a standing wave is observed. Using the obtained flow field data, we trace fluid particles and their thermodynamic properties are calculated. The fluid particles oscillate and drift in the tube. In order to obtain a general picture of the energy conversion, the evolution of the distribution of the increase rate of heat is examined. It is shown that the rate is large in the region where the temperature gradient is large in the tube.","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79139078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A bubble in a standing sound wave in water pulsates with such power that, as its minimum radius is approached, the interior undergoes a first order phase transition to a dense plasma. A pulse of blackbody radiation is emitted with temperatures ranging from 6,000K to 20,000K depending on the gas inside the bubble. To date experiments on sonoluminescence inside water, sulfuric acid and phosphoric acid have yielded similar blackbody temperatures. These liquids are hydrogen bonded and so the question arises as to whether their compressibility limits the energy concentration achieved by Sonoluminescence. Liquids where repulsion between nearest neighbor electron shells such as small ion molten slats should be more incompressible. Scaling law estimates of the energy loss due to: acoustic radiation; shear viscosity, and compressibility of the surrounding fluid will be discussed with the goal of predicting a fundamentally new regime of sonoluminescence.
{"title":"Towards higher energy density processes in sonoluminescing bubbles","authors":"S. Putterman, Seth Pree","doi":"10.1121/2.0000869","DOIUrl":"https://doi.org/10.1121/2.0000869","url":null,"abstract":"A bubble in a standing sound wave in water pulsates with such power that, as its minimum radius is approached, the interior undergoes a first order phase transition to a dense plasma. A pulse of blackbody radiation is emitted with temperatures ranging from 6,000K to 20,000K depending on the gas inside the bubble. To date experiments on sonoluminescence inside water, sulfuric acid and phosphoric acid have yielded similar blackbody temperatures. These liquids are hydrogen bonded and so the question arises as to whether their compressibility limits the energy concentration achieved by Sonoluminescence. Liquids where repulsion between nearest neighbor electron shells such as small ion molten slats should be more incompressible. Scaling law estimates of the energy loss due to: acoustic radiation; shear viscosity, and compressibility of the surrounding fluid will be discussed with the goal of predicting a fundamentally new regime of sonoluminescence.","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72682346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lamb waves are attracting significant attention in the nondestructive evaluation for plate structures due to their capability to propagate long distances. In this study, the nonlinear interaction of Lamb waves with an imperfect joint of elastic plates is numerically investigated. In particular, the second harmonic generation behavior from the joint is examined by perturbation analysis. The imperfect joint is modeled as a spring-type interface with quadratic nonlinearity, and the perturbation analysis is carried out using the hybrid finite element method (HFEM). For the incidence of the lowest-order symmetric (S0) Lamb mode below the cut-off frequencies of the higher-order modes, the double-frequency S0 mode is generated from the imperfect joint due to the nonlinear interaction. A nonlinear parameter calculated from the amplitude of the second harmonic S0 mode shows a sharp peak at a certain incident frequency. The peak frequency increases with increasing interfacial stiffness, and the double of the peak frequency corresponds to the resonance frequency of the imperfect joint subjected to the S0 mode incidence. This result shows that the resonance of the imperfect joint leads to the amplification of the second harmonic S0 mode.Lamb waves are attracting significant attention in the nondestructive evaluation for plate structures due to their capability to propagate long distances. In this study, the nonlinear interaction of Lamb waves with an imperfect joint of elastic plates is numerically investigated. In particular, the second harmonic generation behavior from the joint is examined by perturbation analysis. The imperfect joint is modeled as a spring-type interface with quadratic nonlinearity, and the perturbation analysis is carried out using the hybrid finite element method (HFEM). For the incidence of the lowest-order symmetric (S0) Lamb mode below the cut-off frequencies of the higher-order modes, the double-frequency S0 mode is generated from the imperfect joint due to the nonlinear interaction. A nonlinear parameter calculated from the amplitude of the second harmonic S0 mode shows a sharp peak at a certain incident frequency. The peak frequency increases with increasing interfacial stiffness, and the double of the peak f...
{"title":"Numerical study of the second harmonic generation of Lamb waves at an imperfect joint of plates","authors":"Naoki Mori, S. Biwa, T. Kusaka","doi":"10.1121/2.0000868","DOIUrl":"https://doi.org/10.1121/2.0000868","url":null,"abstract":"Lamb waves are attracting significant attention in the nondestructive evaluation for plate structures due to their capability to propagate long distances. In this study, the nonlinear interaction of Lamb waves with an imperfect joint of elastic plates is numerically investigated. In particular, the second harmonic generation behavior from the joint is examined by perturbation analysis. The imperfect joint is modeled as a spring-type interface with quadratic nonlinearity, and the perturbation analysis is carried out using the hybrid finite element method (HFEM). For the incidence of the lowest-order symmetric (S0) Lamb mode below the cut-off frequencies of the higher-order modes, the double-frequency S0 mode is generated from the imperfect joint due to the nonlinear interaction. A nonlinear parameter calculated from the amplitude of the second harmonic S0 mode shows a sharp peak at a certain incident frequency. The peak frequency increases with increasing interfacial stiffness, and the double of the peak frequency corresponds to the resonance frequency of the imperfect joint subjected to the S0 mode incidence. This result shows that the resonance of the imperfect joint leads to the amplification of the second harmonic S0 mode.Lamb waves are attracting significant attention in the nondestructive evaluation for plate structures due to their capability to propagate long distances. In this study, the nonlinear interaction of Lamb waves with an imperfect joint of elastic plates is numerically investigated. In particular, the second harmonic generation behavior from the joint is examined by perturbation analysis. The imperfect joint is modeled as a spring-type interface with quadratic nonlinearity, and the perturbation analysis is carried out using the hybrid finite element method (HFEM). For the incidence of the lowest-order symmetric (S0) Lamb mode below the cut-off frequencies of the higher-order modes, the double-frequency S0 mode is generated from the imperfect joint due to the nonlinear interaction. A nonlinear parameter calculated from the amplitude of the second harmonic S0 mode shows a sharp peak at a certain incident frequency. The peak frequency increases with increasing interfacial stiffness, and the double of the peak f...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82974826","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The acoustic radiation force has been used in many engineering applications and devices. Good performance of these applications require faithful reproduction of the designed wave field in the device. However, mapping out the wave field using current techniques, such as hydrophone measurements, is challenging. This work demonstrates that the trajectories of the transient motion of microspheres moving to their equilibrium positions within a standing wave can be used to calculate the wave amplitude.The acoustic radiation force has been used in many engineering applications and devices. Good performance of these applications require faithful reproduction of the designed wave field in the device. However, mapping out the wave field using current techniques, such as hydrophone measurements, is challenging. This work demonstrates that the trajectories of the transient motion of microspheres moving to their equilibrium positions within a standing wave can be used to calculate the wave amplitude.
{"title":"Characterization of wave fields using transient motion of microspheres under acoustic radiation force","authors":"Y. Wang, B. Anthony","doi":"10.1121/2.0000871","DOIUrl":"https://doi.org/10.1121/2.0000871","url":null,"abstract":"The acoustic radiation force has been used in many engineering applications and devices. Good performance of these applications require faithful reproduction of the designed wave field in the device. However, mapping out the wave field using current techniques, such as hydrophone measurements, is challenging. This work demonstrates that the trajectories of the transient motion of microspheres moving to their equilibrium positions within a standing wave can be used to calculate the wave amplitude.The acoustic radiation force has been used in many engineering applications and devices. Good performance of these applications require faithful reproduction of the designed wave field in the device. However, mapping out the wave field using current techniques, such as hydrophone measurements, is challenging. This work demonstrates that the trajectories of the transient motion of microspheres moving to their equilibrium positions within a standing wave can be used to calculate the wave amplitude.","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78850324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Soft elastic media such as rubber and soft tissue possess small shear moduli, facilitating the generation of large shear deformations. These materials may also exhibit viscoelasticity such as stress relaxation over the frequency range of interest. An augmented form of the Duffing equation was recently developed to model the response near the lowest resonance of a shear wave resonator formed with a nonlinear relaxing material that is shaken at one end and free at the other [J. Acoust. Soc. Am. 143, 1035 (2018)]. The augmented Duffing model was found to accurately describe the response of the resonator when the driving motion is linearly polarized. Here the model is extended to account for elliptical driving motion at frequencies near the lowest resonance. The augmented Duffing model in this case consists of two coupled ordinary differential equations for the two displacement components. Amplitude-dependent phenomena such as amplification of the minor displacement component and an induced phase shift betwee...
{"title":"Nonlinear response of a relaxing shear wave resonator to elliptical driving motion","authors":"J. Cormack, M. Hamilton","doi":"10.1121/2.0000876","DOIUrl":"https://doi.org/10.1121/2.0000876","url":null,"abstract":"Soft elastic media such as rubber and soft tissue possess small shear moduli, facilitating the generation of large shear deformations. These materials may also exhibit viscoelasticity such as stress relaxation over the frequency range of interest. An augmented form of the Duffing equation was recently developed to model the response near the lowest resonance of a shear wave resonator formed with a nonlinear relaxing material that is shaken at one end and free at the other [J. Acoust. Soc. Am. 143, 1035 (2018)]. The augmented Duffing model was found to accurately describe the response of the resonator when the driving motion is linearly polarized. Here the model is extended to account for elliptical driving motion at frequencies near the lowest resonance. The augmented Duffing model in this case consists of two coupled ordinary differential equations for the two displacement components. Amplitude-dependent phenomena such as amplification of the minor displacement component and an induced phase shift betwee...","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78006432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The propagation of an initially antisymmetric disturbance through a relaxing medium in one-dimension is considered. If dissipation and dispersion effects are small compared with the effect of nonlinearity, the disturbance approaches the classic N-wave profile with narrow shocks controlled by relaxation processes. As the N-wave propagates it spreads and decays in amplitude, affecting key balances between competing physical processes. In this paper we analyse the change in the shock structure as the outer solution evolves, using asymptotic analysis supplemented by numerical results. Two numerical schemes are described - an implicit scheme with variable spatial mesh which allows good resolution of the shock structure, and a pseudospectral scheme which is used when multiple relaxation modes are considered. Experimental measurements (Pawlowski et al 2005 and Yuldashev et al 2008) reveal the appearance of a slowly decaying shock tail previously unexplained by analysis of the augmented Burgers equation. In this paper we demonstrate that this phenomenon occurs when one of the relaxation timescales is comparable to the time of pulse duration.
{"title":"Effect of molecular relaxation on nonlinear evolution of N-waves","authors":"P. Hammerton","doi":"10.1121/2.0000881","DOIUrl":"https://doi.org/10.1121/2.0000881","url":null,"abstract":"The propagation of an initially antisymmetric disturbance through a relaxing medium in one-dimension is considered. If dissipation and dispersion effects are small compared with the effect of nonlinearity, the disturbance approaches the classic N-wave profile with narrow shocks controlled by relaxation processes. As the N-wave propagates it spreads and decays in amplitude, affecting key balances between competing physical processes. In this paper we analyse the change in the shock structure as the outer solution evolves, using asymptotic analysis supplemented by numerical results. Two numerical schemes are described - an implicit scheme with variable spatial mesh which allows good resolution of the shock structure, and a pseudospectral scheme which is used when multiple relaxation modes are considered. Experimental measurements (Pawlowski et al 2005 and Yuldashev et al 2008) reveal the appearance of a slowly decaying shock tail previously unexplained by analysis of the augmented Burgers equation. In this paper we demonstrate that this phenomenon occurs when one of the relaxation timescales is comparable to the time of pulse duration.","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82190838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Seth Pree, John P. Koulakis, Alexander L. F. Thornton, S. Putterman
Periodic instability in sulfur plasma bulbs driven at their acoustic resonant frequency leads to behavior similar to a relaxation oscillation. This instability, which develops over the course of more than 500 acoustic periods manifests as both an oscillation in the total luminosity of the lamp and a frequency modulation of the resonator. We present evidence that the cause of this oscillation cycle stems from periodic eruptions of plasma from within a region near the acoustic velocity antinode. We propose that these oscillations and eruptions indicate a coupling between high amplitude acoustic waves and interface waves and consider whether this system might provide a platform with which to study turbulent heat transport.Periodic instability in sulfur plasma bulbs driven at their acoustic resonant frequency leads to behavior similar to a relaxation oscillation. This instability, which develops over the course of more than 500 acoustic periods manifests as both an oscillation in the total luminosity of the lamp and a frequency modulation of the resonator. We present evidence that the cause of this oscillation cycle stems from periodic eruptions of plasma from within a region near the acoustic velocity antinode. We propose that these oscillations and eruptions indicate a coupling between high amplitude acoustic waves and interface waves and consider whether this system might provide a platform with which to study turbulent heat transport.
{"title":"Acousto-convective relaxation oscillation in plasma lamp","authors":"Seth Pree, John P. Koulakis, Alexander L. F. Thornton, S. Putterman","doi":"10.1121/2.0000865","DOIUrl":"https://doi.org/10.1121/2.0000865","url":null,"abstract":"Periodic instability in sulfur plasma bulbs driven at their acoustic resonant frequency leads to behavior similar to a relaxation oscillation. This instability, which develops over the course of more than 500 acoustic periods manifests as both an oscillation in the total luminosity of the lamp and a frequency modulation of the resonator. We present evidence that the cause of this oscillation cycle stems from periodic eruptions of plasma from within a region near the acoustic velocity antinode. We propose that these oscillations and eruptions indicate a coupling between high amplitude acoustic waves and interface waves and consider whether this system might provide a platform with which to study turbulent heat transport.Periodic instability in sulfur plasma bulbs driven at their acoustic resonant frequency leads to behavior similar to a relaxation oscillation. This instability, which develops over the course of more than 500 acoustic periods manifests as both an oscillation in the total luminosity of the lamp and a frequency modulation of the resonator. We present evidence that the cause of this oscillation cycle stems from periodic eruptions of plasma from within a region near the acoustic velocity antinode. We propose that these oscillations and eruptions indicate a coupling between high amplitude acoustic waves and interface waves and consider whether this system might provide a platform with which to study turbulent heat transport.","PeriodicalId":20469,"journal":{"name":"Proc. Meet. Acoust.","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83934103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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