Recently the presence of a Dirac cone within the band structure of graphene has inspired research on phononic crystals with Dirac-like behaviors — including structures mimicking zero refractive index materials. The interesting phenomena produced by these structures occur at fixed frequencies and cannot be adaptive to needs and environmental changes. To address this constraint, researchers have designed tunable phononic structures; however, the tunable frequency ranges from the studies reported to date are limited by geometric constraints. Using a reconfigurable origami structure to modulate between different classes of phononic Bravais lattices, this research numerically investigates the effects of phononic lattice perturbation to produce drastic changes in the frequency of useful accidental degeneracies.
{"title":"On the Modulation of Origami Phononic Structure for Adaptive Wave Transmission in Brillouin Zone","authors":"Megan Hathcock, B. Popa, K. W. Wang","doi":"10.1115/IMECE2020-24498","DOIUrl":"https://doi.org/10.1115/IMECE2020-24498","url":null,"abstract":"\u0000 Recently the presence of a Dirac cone within the band structure of graphene has inspired research on phononic crystals with Dirac-like behaviors — including structures mimicking zero refractive index materials. The interesting phenomena produced by these structures occur at fixed frequencies and cannot be adaptive to needs and environmental changes. To address this constraint, researchers have designed tunable phononic structures; however, the tunable frequency ranges from the studies reported to date are limited by geometric constraints. Using a reconfigurable origami structure to modulate between different classes of phononic Bravais lattices, this research numerically investigates the effects of phononic lattice perturbation to produce drastic changes in the frequency of useful accidental degeneracies.","PeriodicalId":23648,"journal":{"name":"Volume 1: Acoustics, Vibration, and Phononics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90035991","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}
This paper investigates the use of two room acoustics metrics designed to evaluate the degree to which the linearity assumptions of the energy density curves are valid. The study focuses on measured and computer-modeled energy density curves derived from the room impulse response of a space exhibiting a highly non-diffuse sound field due to flutter echo. In conjunction with acoustical remediation, room impulse response measurements were taken before and after the installation of the acoustical panels. A very dramatic decrease in the reverberation time was experienced due to the addition of the acoustical panels. The two non-linearity metrics used in this study are the non-linearity parameter and the curvature. These metrics are calculated from the energy decay curves computed per octave band, based on the definitions presented in ISO 3382-2. The non-linearity parameter quantifies the deviation of the EDC from a straight line fit used to generated T20 and T30 reverberation times. Where the reverberation times are calculated based on a linear regression of the data relating to either −5 to −25 dB for T20 or −5 to −35 dB for T30 reverberation time calculations. This deviation is quantified using the correlation coefficient between the energy decay curve and the linear regression for the specified data. In order to graphically demonstrate these non-linearity metrics, the energy decay curves are plotted along with the linear regression curves for the T20 and T30 reverberation time for both the measured data and two different room acoustics computer-modeling techniques, geometric acoustics modeling and finite-difference wave-based modeling. The intent of plotting these curves together is to demonstrate the relationship between these metrics and the energy decay curve, and to evaluate their use for quantifying degree of non-linearity in non-diffuse sound fields. Observations of these graphical representations are used to evaluate the accuracy of reverberation time estimations in non-diffuse environments, and to evaluate the use of these non-linearity parameters for comparison of different computer-modeling techniques or room configurations. Using these techniques, the non-linearity parameter based on both T20 and T30 linear regression curves and the curvature parameter were calculated over 250–4000 Hz octave bands for the measured and computer-modeled room impulse response curves at two different locations and two different room configurations. Observations of these calculated results are used to evaluate the consistency of these metrics, and the application of these metrics to quantifying the degree of non-linearity of the energy decay curve derived from a non-diffuse sound field. These calculated values are also used to evaluate the differences in the degree of diffusivity between the measured and computer-modeled room impulse response. Acoustical computer modeling is often based on geometrical acoustics using ray-tracing and image-source algorith
{"title":"Quantifying Non-Linearity in Early Decay Curves of Measured and Computer-Modeled Room Impulse Responses of a Highly Non-Diffuse Room Exhibiting Flutter Echo","authors":"Heather Lai, B. Hamilton","doi":"10.1115/IMECE2020-24348","DOIUrl":"https://doi.org/10.1115/IMECE2020-24348","url":null,"abstract":"\u0000 This paper investigates the use of two room acoustics metrics designed to evaluate the degree to which the linearity assumptions of the energy density curves are valid. The study focuses on measured and computer-modeled energy density curves derived from the room impulse response of a space exhibiting a highly non-diffuse sound field due to flutter echo. In conjunction with acoustical remediation, room impulse response measurements were taken before and after the installation of the acoustical panels. A very dramatic decrease in the reverberation time was experienced due to the addition of the acoustical panels. The two non-linearity metrics used in this study are the non-linearity parameter and the curvature. These metrics are calculated from the energy decay curves computed per octave band, based on the definitions presented in ISO 3382-2. The non-linearity parameter quantifies the deviation of the EDC from a straight line fit used to generated T20 and T30 reverberation times. Where the reverberation times are calculated based on a linear regression of the data relating to either −5 to −25 dB for T20 or −5 to −35 dB for T30 reverberation time calculations. This deviation is quantified using the correlation coefficient between the energy decay curve and the linear regression for the specified data.\u0000 In order to graphically demonstrate these non-linearity metrics, the energy decay curves are plotted along with the linear regression curves for the T20 and T30 reverberation time for both the measured data and two different room acoustics computer-modeling techniques, geometric acoustics modeling and finite-difference wave-based modeling. The intent of plotting these curves together is to demonstrate the relationship between these metrics and the energy decay curve, and to evaluate their use for quantifying degree of non-linearity in non-diffuse sound fields. Observations of these graphical representations are used to evaluate the accuracy of reverberation time estimations in non-diffuse environments, and to evaluate the use of these non-linearity parameters for comparison of different computer-modeling techniques or room configurations. Using these techniques, the non-linearity parameter based on both T20 and T30 linear regression curves and the curvature parameter were calculated over 250–4000 Hz octave bands for the measured and computer-modeled room impulse response curves at two different locations and two different room configurations.\u0000 Observations of these calculated results are used to evaluate the consistency of these metrics, and the application of these metrics to quantifying the degree of non-linearity of the energy decay curve derived from a non-diffuse sound field. These calculated values are also used to evaluate the differences in the degree of diffusivity between the measured and computer-modeled room impulse response. Acoustical computer modeling is often based on geometrical acoustics using ray-tracing and image-source algorith","PeriodicalId":23648,"journal":{"name":"Volume 1: Acoustics, Vibration, and Phononics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83081736","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}
R. Adlakha, M. Moghaddaszadeh, M. Attarzadeh, Abdollah Doosti Aref, M. Nouh
Acoustic phased arrays are capable of steering and focusing a beam of sound via selective coordination of the spatial distribution of phase angles between multiple sound emitters. Here, we propose a controllable acoustic phased array with space-time modulation that breaks time-reversal symmetry, and enables phononic transition in both momentum and energy spaces. By leveraging the dynamic phase modulation, the proposed linear phased array is no longer bound by the reciprocity principle, and supports asymmetric transmission and reception patterns that can be tuned independently. Through theoretical and numerical investigations, we develop and verify a mathematical framework to characterize the nonreciprocal phenomena, and analyze the frequency conversion between the wave fields. The space-time acoustic phased array facilitates unprecedented control over sound waves in a variety of applications including underwater telecommunication.
{"title":"A Linear Acoustic Phased Array for Nonreciprocal Transmission and Reception","authors":"R. Adlakha, M. Moghaddaszadeh, M. Attarzadeh, Abdollah Doosti Aref, M. Nouh","doi":"10.1115/IMECE2020-24237","DOIUrl":"https://doi.org/10.1115/IMECE2020-24237","url":null,"abstract":"\u0000 Acoustic phased arrays are capable of steering and focusing a beam of sound via selective coordination of the spatial distribution of phase angles between multiple sound emitters. Here, we propose a controllable acoustic phased array with space-time modulation that breaks time-reversal symmetry, and enables phononic transition in both momentum and energy spaces. By leveraging the dynamic phase modulation, the proposed linear phased array is no longer bound by the reciprocity principle, and supports asymmetric transmission and reception patterns that can be tuned independently. Through theoretical and numerical investigations, we develop and verify a mathematical framework to characterize the nonreciprocal phenomena, and analyze the frequency conversion between the wave fields. The space-time acoustic phased array facilitates unprecedented control over sound waves in a variety of applications including underwater telecommunication.","PeriodicalId":23648,"journal":{"name":"Volume 1: Acoustics, Vibration, and Phononics","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76996783","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}
In a recent investigation of external fuel leaks from an aerospace pressure control valve, cavitation damages were discovered in a small deadheaded cavity, which was created by the axial clearance between the mating subcomponents. Experiments using high bandwidth pressure sensors showed that there were severe pressure fluctuations in the cavity and that the pressure repeatedly fell below the local vapor pressure of the fuel, which would cause cavitation. Spectral analyses showed resonance-like amplification of flow ripple in the valve surrounding inside the valve cavity. The apparent resonance frequency matched the computed fundamental Helmholtz resonance frequency of the cavity. These findings led to a venting solution of the deadheaded cavity by placing an appropriately sized through hole. Back-to-back testing with unvented valves showed stark improvements of the vented solution. This paper presents test and analytical data on the formation of a Helmholtz resonator in the small deadhead cavity of a gas turbine fuel delivery system component. This paper also demonstrates the validity of simple engineering formulas widely available in acoustics literature for predicting the Helmholtz resonance frequencies as a function of neck geometry, neck arrangement, and fuel properties.
{"title":"Acoustic Amplification of Flow Ripple and Cavitation Damage in an Aerospace Fuel System Component","authors":"A. Lee, Mihir Desai","doi":"10.1115/IMECE2020-23568","DOIUrl":"https://doi.org/10.1115/IMECE2020-23568","url":null,"abstract":"\u0000 In a recent investigation of external fuel leaks from an aerospace pressure control valve, cavitation damages were discovered in a small deadheaded cavity, which was created by the axial clearance between the mating subcomponents. Experiments using high bandwidth pressure sensors showed that there were severe pressure fluctuations in the cavity and that the pressure repeatedly fell below the local vapor pressure of the fuel, which would cause cavitation. Spectral analyses showed resonance-like amplification of flow ripple in the valve surrounding inside the valve cavity. The apparent resonance frequency matched the computed fundamental Helmholtz resonance frequency of the cavity. These findings led to a venting solution of the deadheaded cavity by placing an appropriately sized through hole. Back-to-back testing with unvented valves showed stark improvements of the vented solution. This paper presents test and analytical data on the formation of a Helmholtz resonator in the small deadhead cavity of a gas turbine fuel delivery system component. This paper also demonstrates the validity of simple engineering formulas widely available in acoustics literature for predicting the Helmholtz resonance frequencies as a function of neck geometry, neck arrangement, and fuel properties.","PeriodicalId":23648,"journal":{"name":"Volume 1: Acoustics, Vibration, and Phononics","volume":"14 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75161660","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}
Dynamometers are used to measure integrated fluid dynamic loads such as thrust, torque or side forces. To resolve all of three force and three moment components, multiple embedded force gages are often used. Due to arrangement, static loads, and redundancy, the number of sensor channels can exceed the six degrees of freedom needed to resolve the generalized rigid body forces. This paper considers modeling of the force gages as simple springs to develop an elastic model of the dynamometer. The method was applied to a dynamometer consisting of six three-component force gages arranged in an axisymmetric ring. A calibration matrix based on the elastic model with individual force gage sensitivities was shown to match a full calibration matrix where properly summed force gage voltages were obtained under global load application. The elastic model was then extended to consider calibration matrices where sensors were assumed to fail. In this scenario, several virtual loads were applied to the dynamometer and the calibration matrix was obtained by minimizing the least square error. It was found that nearly half of the sensors could be lost and still a virtual calibration could be applied to the measurements. Extending the least square idea, an actual in-situ calibration matrix was formed by striking the dynamometer with a diverse set of instrumented hammer strikes. This calibration matrix also agreed with the other calibrations at frequencies below where system dynamics become important.
{"title":"Effect of Sensor Failure on Dynamometry Calibration","authors":"N. Vlajic, Michael L. Jonson, M. Guers","doi":"10.1115/IMECE2020-24264","DOIUrl":"https://doi.org/10.1115/IMECE2020-24264","url":null,"abstract":"\u0000 Dynamometers are used to measure integrated fluid dynamic loads such as thrust, torque or side forces. To resolve all of three force and three moment components, multiple embedded force gages are often used. Due to arrangement, static loads, and redundancy, the number of sensor channels can exceed the six degrees of freedom needed to resolve the generalized rigid body forces. This paper considers modeling of the force gages as simple springs to develop an elastic model of the dynamometer. The method was applied to a dynamometer consisting of six three-component force gages arranged in an axisymmetric ring. A calibration matrix based on the elastic model with individual force gage sensitivities was shown to match a full calibration matrix where properly summed force gage voltages were obtained under global load application. The elastic model was then extended to consider calibration matrices where sensors were assumed to fail. In this scenario, several virtual loads were applied to the dynamometer and the calibration matrix was obtained by minimizing the least square error. It was found that nearly half of the sensors could be lost and still a virtual calibration could be applied to the measurements. Extending the least square idea, an actual in-situ calibration matrix was formed by striking the dynamometer with a diverse set of instrumented hammer strikes. This calibration matrix also agreed with the other calibrations at frequencies below where system dynamics become important.","PeriodicalId":23648,"journal":{"name":"Volume 1: Acoustics, Vibration, and Phononics","volume":"55 9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83458234","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}
Qian Dong, Xiaolei Song, Subhrodeep Ray, Haijun Liu
Membrane-based acoustic metamaterials have been reported to achieve 100% absorption, the acoustic analogue of photonic black-hole. However, the bandwidth is usually very narrow around some local resonance frequency, which limits its practical use. To address this limitation and achieve a broadband absorption, this paper first establishes a theoretical framework for unit cells of air-backed diaphragms, modeled as an equivalent mass-spring-dashpot system. Based on the impedance match principle, three different approaches are numerically investigated by tuning the cavity length, the static pressure in the cavity, and the effective damping of perforated plates. A prototype with polyimide diaphragm and 3D printed substrate is then fabricated and characterized using an acoustic impedance tube. Preliminary experiments show the feasibility to achieve an absorption bandwidth of ∼200 Hz at center frequency of 1.45 kHz. This work pays the way for developing a sub-wavelength light weight broadband acoustic absorber for a variety of applications in noise control.
{"title":"Acoustic Metamaterial With Air-Backed Diaphragm for Broadband Absorption: A Preliminary Study","authors":"Qian Dong, Xiaolei Song, Subhrodeep Ray, Haijun Liu","doi":"10.1115/IMECE2020-23928","DOIUrl":"https://doi.org/10.1115/IMECE2020-23928","url":null,"abstract":"\u0000 Membrane-based acoustic metamaterials have been reported to achieve 100% absorption, the acoustic analogue of photonic black-hole. However, the bandwidth is usually very narrow around some local resonance frequency, which limits its practical use. To address this limitation and achieve a broadband absorption, this paper first establishes a theoretical framework for unit cells of air-backed diaphragms, modeled as an equivalent mass-spring-dashpot system. Based on the impedance match principle, three different approaches are numerically investigated by tuning the cavity length, the static pressure in the cavity, and the effective damping of perforated plates. A prototype with polyimide diaphragm and 3D printed substrate is then fabricated and characterized using an acoustic impedance tube. Preliminary experiments show the feasibility to achieve an absorption bandwidth of ∼200 Hz at center frequency of 1.45 kHz. This work pays the way for developing a sub-wavelength light weight broadband acoustic absorber for a variety of applications in noise control.","PeriodicalId":23648,"journal":{"name":"Volume 1: Acoustics, Vibration, and Phononics","volume":"600 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77257124","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}
Vibration attenuation is an important factor while designing rotating machinery since frequency lying in the range corresponding to natural modes of structures can result in resonance and ultimately failure. Damping dissipates energy in the system, which reduces the vibration level. The mitigation of vibrations can be achieved by designing the base frame with periodic air holes. The periodicity in air holes result in vibration attenuation by providing a stop band. A finite element-based approach is developed to predict the modal and frequency response. The analysis is carried out with different shapes of periodic cavities in order to study the effectiveness of periodic stop bands in attenuating vibrations. The amount of mass removed due to the periodic cavities is kept constant. It is seen that better attenuation is obtained in case of periodic cavities compared to a uniform base frame. Among the different geometries tested, rectangular cavities showed better results than circular and square cavities. As a result, it is seen that waves propagate along periodic cells only within specific frequency bands called the “Pass bands”, while these waves are completely blocked within other frequency bands called the “Stopbands”. The air cavities filter structural vibrations in certain frequency bands resulting in effective attenuation.
{"title":"Effect of Geometric Shape of Periodic Cavities in Attenuating Baseframe Vibration","authors":"S. Das, K. Kohli, Ayush Kumar, G. Sabareesh","doi":"10.1115/IMECE2020-23585","DOIUrl":"https://doi.org/10.1115/IMECE2020-23585","url":null,"abstract":"\u0000 Vibration attenuation is an important factor while designing rotating machinery since frequency lying in the range corresponding to natural modes of structures can result in resonance and ultimately failure. Damping dissipates energy in the system, which reduces the vibration level. The mitigation of vibrations can be achieved by designing the base frame with periodic air holes. The periodicity in air holes result in vibration attenuation by providing a stop band. A finite element-based approach is developed to predict the modal and frequency response. The analysis is carried out with different shapes of periodic cavities in order to study the effectiveness of periodic stop bands in attenuating vibrations. The amount of mass removed due to the periodic cavities is kept constant. It is seen that better attenuation is obtained in case of periodic cavities compared to a uniform base frame. Among the different geometries tested, rectangular cavities showed better results than circular and square cavities. As a result, it is seen that waves propagate along periodic cells only within specific frequency bands called the “Pass bands”, while these waves are completely blocked within other frequency bands called the “Stopbands”. The air cavities filter structural vibrations in certain frequency bands resulting in effective attenuation.","PeriodicalId":23648,"journal":{"name":"Volume 1: Acoustics, Vibration, and Phononics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85891760","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}
An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed based on the fast Fourier transform (FFT) and tensor contraction to increase efficiency and robustness of the IHB method when calculating periodic responses of complex nonlinear systems with non-polynomial nonlinearities. As a semi-analytical method, derivation of formulae and programming are significantly simplified in the EGA-IHB method. The residual vector and Jacobian matrix corresponding to nonlinear terms in the EGA-IHB method are expressed using truncated Fourier series. After calculating Fourier coefficient vectors using the FFT, tensor contraction is used to calculate the Jacobian matrix, which can significantly improve numerical efficiency. Since inaccurate results may be obtained from discrete Fourier transform-based methods when aliasing occurs, the minimal non-aliasing sampling rate is determined for the EGA-IHB method. Performances of the EGA-IHB method are analyzed using several benchmark examples; its accuracy, efficiency, convergence, and robustness are analyzed and compared with several widely used semi-analytical methods. The EGA-IHB method has high efficiency and good robustness for both polynomial and nonpolynomial nonlinearities, and it has considerable advantages over the other methods.
{"title":"An Efficient Galerkin Averaging-Incremental Harmonic Balance Method Based on the Fast Fourier Transform and Tensor Contraction","authors":"Ren Ju, W. Fan, Wei-dong Zhu","doi":"10.1115/1.4047235","DOIUrl":"https://doi.org/10.1115/1.4047235","url":null,"abstract":"\u0000 An efficient Galerkin averaging-incremental harmonic balance (EGA-IHB) method is developed based on the fast Fourier transform (FFT) and tensor contraction to increase efficiency and robustness of the IHB method when calculating periodic responses of complex nonlinear systems with non-polynomial nonlinearities. As a semi-analytical method, derivation of formulae and programming are significantly simplified in the EGA-IHB method. The residual vector and Jacobian matrix corresponding to nonlinear terms in the EGA-IHB method are expressed using truncated Fourier series. After calculating Fourier coefficient vectors using the FFT, tensor contraction is used to calculate the Jacobian matrix, which can significantly improve numerical efficiency. Since inaccurate results may be obtained from discrete Fourier transform-based methods when aliasing occurs, the minimal non-aliasing sampling rate is determined for the EGA-IHB method. Performances of the EGA-IHB method are analyzed using several benchmark examples; its accuracy, efficiency, convergence, and robustness are analyzed and compared with several widely used semi-analytical methods. The EGA-IHB method has high efficiency and good robustness for both polynomial and nonpolynomial nonlinearities, and it has considerable advantages over the other methods.","PeriodicalId":23648,"journal":{"name":"Volume 1: Acoustics, Vibration, and Phononics","volume":"310 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88162120","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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