A superposing principle, by suitably adding the strain waves from a number of concentrated explosive charges to approximate the waves generated by a cylindrical charge based on the strain wave of a point or small sphe...A superposing principle, by suitably adding the strain waves from a number of concentrated explosive charges to approximate the waves generated by a cylindrical charge based on the strain wave of a point or small spherical explosive charge generated in rock, is used to further study the triggering time of strain gauges installed in radial direction at same distances but different positions surrounding a cylindrical explosive charge in rock. The duration of the first compression phase and peak value of strain wave, and furthermore, their differences are analyzed and some explanations are given. Besides that, the gauge orientation in which the maximum peak value occurs is also discussed. At last, the effect of velocity of detonation(V.O.D.) of a cylindrical explosive charge on the strain waves generated in the surrounding rock is taken as key research and the pattern of peak amplitude of a strain wave varies with the V.O.D. is likely to have been found.展开更多
In this paper,we mainly study the time-space fractional strain wave equation in microstructured solids.He’s variational method,combined with the two-scale transform are implemented to seek the solitary and periodic w...In this paper,we mainly study the time-space fractional strain wave equation in microstructured solids.He’s variational method,combined with the two-scale transform are implemented to seek the solitary and periodic wave solutions of the time-space strain wave equation.The main advantage of the variational method is that it can reduce the order of the differential equation,thus simplifying the equation,making the solving process more intuitive and avoiding the tedious solving process.Finally,the numerical results are shown in the form of 3D and 2D graphs to prove the applicability and effectiveness of the method.The obtained results in this work are expected to shed a bright light on the study of fractional nonlinear partial differential equations in physics.展开更多
In the materials of micro-structured, the propagation of wave modeling should take into account the scale of various microstructures. The different kinds solitary wave solutions of strain wave dynamical model are deri...In the materials of micro-structured, the propagation of wave modeling should take into account the scale of various microstructures. The different kinds solitary wave solutions of strain wave dynamical model are derived via utilizing exp(-φ(ξ))-expansion and extended simple equation methods. This dynamical equation plays a key role in engineering and mathematical physics. Solutions obtained in this work include periodic solitary waves, Kink and antiKink solitary waves, bell-shaped solutions, solitons, and rational solutions. These exact solutions help researchers for knowing the physical phenomena of this wave equation. The stability of this dynamical model is examined via standard linear stability analysis, which authenticate that the model is stable and their solutions are exact. Graphs are depicted for knowing the movements of some solutions. The results show that the current methods, by the assist of symbolic calculation, give an effectual and direct mathematical tools for resolving the nonlinear problems in applied sciences.展开更多
The theoretical discovery of slow strain (tectonic) waves, the so-called strain waves in the Earth, served as a motivation to develop physical backgrounds of the mathematical theory of propagation of these waves and t...The theoretical discovery of slow strain (tectonic) waves, the so-called strain waves in the Earth, served as a motivation to develop physical backgrounds of the mathematical theory of propagation of these waves and to search for methods of their experimental detection. For fifty years, scientists from different countries in different regions of the Earth, using direct and indirect methods, discovered the migration of crustal deformation and revealed its wave nature, and, therefore, proved the reality of the existence of strain waves of the Earth. This overview briefly describes the history of the development of the concept of strain waves on the Earth, the observation methods and properties of strain waves, and the main types of geological structures generating these waves. The most prominent results of the theoretical, laboratory, and in-situ observations of slow strain migration, including slow earthquakes and periodic Episodic Tremor and Slow (ETS) slip effects, are presented. In the near future, studies of slow strain waves may lead to a fundamental revision of the current concepts about the physics of the seismic process.展开更多
The torsional low strain integrity test(TLSIT),known for its advantages such as a smaller detection blind zone,improved identification of shallowly buried defects,stable phase velocity for signal interpretation,and be...The torsional low strain integrity test(TLSIT),known for its advantages such as a smaller detection blind zone,improved identification of shallowly buried defects,stable phase velocity for signal interpretation,and better adaptability for existing pile testing.However,it lacks a comprehensive understanding of the authentic three-dimensional(3D)strain wave propagation mechanism,particularly wave reflection and transmission at defects.To address this gap,a novel 3D theoretical framework is introduced in this context to model the authentic 3D wave propagation during the TLSIT.The proposed approach is validated by comparing its results with those obtained from 3D finite element method(FEM)simulations and simplified 1D(one-dimensional)and 3D analytical solutions.Additionally,a parametric study is conducted to enhance insights into the formation mechanism of high-frequency interference observed during the TLSIT.Finally,a defect identification study is performed to provide guidance for interpreting the wave spectrum in terms of defect characteristics.展开更多
The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external...The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions are derived and global attractors in E-1 space is obtained.展开更多
When strain wave passes through rock, a changing magnetic field due to piezomagnetic effect will propagate at the velocity of sound. The changing magnetic field will stimulate electromagnetic ef fect in the surroundin...When strain wave passes through rock, a changing magnetic field due to piezomagnetic effect will propagate at the velocity of sound. The changing magnetic field will stimulate electromagnetic ef fect in the surrounding area. This paper reports the experimental results which proves the existence of such phenomena. And the synthetic piezomagnetic coefficients of rock are measured from experimental results. The piezomagnetic effect can be used to explain some electromagnetic phenomena produced in the process of earthquakes.展开更多
In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and the finiteness of the Hausdorff a...In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and the finiteness of the Hausdorff and the fractal dimensions of the attractors.展开更多
This paper is concerned with the wave propagation behavior of rotating functionally graded（FG）temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform...This paper is concerned with the wave propagation behavior of rotating functionally graded（FG）temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform,linear and nonlinear temperature distributions across the thickness are investigated.Thermo-elastic properties of FG beam change gradually according to the Mori–Tanaka distribution model in the spatial coordinate.The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function.The governing equations are derived by Hamilton’s principle as a function of axial force due to centrifugal stiffening and displacement.The solution of these equations is provided employing a Galerkin-based approach which has the potential to capture various boundary conditions.By applying an analytical solution and solving an eigenvalue problem,the dispersion relations of rotating FG nanobeam are obtained.Numerical results illustrate that various parameters including temperature change,angular velocity,nonlocality parameter,wave number and gradient index have significant effects on the wave dispersion characteristics of the nanobeam under study.The outcome of this study can provide beneficial information for the next-generation research and the exact design of nano-machines including nanoscale molecular bearings,nanogears,etc.展开更多
At a sampling rate of 100 samples per second,the YRY-4 four-gauge borehole strainmeters（FGBS） are capable of recording transient strains caused by seismic waves such as P and S waves or strain seismograms. At such a...At a sampling rate of 100 samples per second,the YRY-4 four-gauge borehole strainmeters（FGBS） are capable of recording transient strains caused by seismic waves such as P and S waves or strain seismograms. At such a high sampling rate, data from the YRY-4 strainmeters demonstrate fairly satisfactory self-consistency. The strain tensor seismograms demonstrate the senses of motion of P waves, that is, the type of seismic wave travels in the direction of the maximum normal strain change. The observed strain patterns of S waves significantly differ from those of P waves and should contain information about the source mechanism. Spectrum analysis shows that the strain seismograms are consistent with conventional broadband seismograms from the same site.展开更多
How the wave propagation analysis plays a key role in the studies of dynamic response of materials at high strain rates is analyzed. For the wave propagation technique, the followings are important: the loading and un...How the wave propagation analysis plays a key role in the studies of dynamic response of materials at high strain rates is analyzed. For the wave propagation technique, the followings are important: the loading and unloading constitutive relation presumed, the positions of the sensors embedded, the interactions between loading waves and unloading waves. For the split Hopkinson pressure bar (SHPB) technique, the assumption of one-dimensional stress wave propagation and the assumption of stress uniformity along the specimen should be satisfied. When the larger diameter bars are employed, the wave dispersion effects should be considered, including the high frequency oscillations, non-uniform stress distribution across the bar section, increase of rise time, and amplitude attenuation. The stress uniformity along the specimen is influenced by the reflection times in specimen, the wave impedance ratio of the specimen and the bar, and the waveform.展开更多
Based on the body strain record of Tiantanghe station from 2008 to 2014,we make a statistical analysis of the relationship between the maximum amplitude of the body strain record and the surface-wave magnitude,epicent...Based on the body strain record of Tiantanghe station from 2008 to 2014,we make a statistical analysis of the relationship between the maximum amplitude of the body strain record and the surface-wave magnitude,epicenter distance of the earthquakes,which occurred in the Chinese mainland and its surrounding areas with MS≥6. 0 and the rest of the world with MS≥7. 0. According to statistical results,we propose a statistical formula between the surface-wave magnitude of earthquake and the maximum amplitude of the body strain record,the epicenter distance: M_S~*= 0. 37 ln A_max+ 0. 57 ln D + 0. 07. We can also derive a theoretical estimation formula for the maximum amplitude: A_max=e^(2. 7(M_S^*-0. 07))D^(-1. 54). This demonstrates that the maximum amplitude of the body strain record increases exponentially with the increase of the surface-wave magnitude, and decreases with the increase of the epicenter distance,and shows a negative correlation with their product. We further discuss the necessity of adding instruments with high frequency sampling to earthquake monitoring, and dicuss the prospects for precise earthquake prediction in future.展开更多
A shear-lag theory was developed to investigate the strain transfer from the metal substrate to the surface acoustic wave （SAW） resonator through a bonding layer. A three-layer model of host structure-adhesive layer...A shear-lag theory was developed to investigate the strain transfer from the metal substrate to the surface acoustic wave （SAW） resonator through a bonding layer. A three-layer model of host structure-adhesive layer-resonator layer was established. The strain transfer was theoretically analyzed, and the main factors impacting the SAW sensor measurement were studied. The relationship between the sensor response and the individual effect of all these factors under static loads was discussed. Results showed that better accuracy could be achieved with increase in the adhesive stiffness or resonator length, or decrease in the adhesive thickness. The values of the strain transfer rate calculated from the analytical model agreed well with that from the available experiment data.展开更多
In this research, vibration and wave propagation analysis of a twisted micro- beam on Pasternak foundation is investigated. The strain-displacement relations （kine-matic equations） are calculated by the displacement...In this research, vibration and wave propagation analysis of a twisted micro- beam on Pasternak foundation is investigated. The strain-displacement relations （kine-matic equations） are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory （SGT） is used to implement the size dependent effect at micro-scale. Finally, using an energy method and Hamilton＇s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave prop- agation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is in- versely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.展开更多
A dynamic Timoshenko beam model is established based on the new nonlocal strain gradient theory and slip boundary theory to study the wave propagation behaviors of fluid-filled carbon nanotubes （CNTs） at nanoscale. ...A dynamic Timoshenko beam model is established based on the new nonlocal strain gradient theory and slip boundary theory to study the wave propagation behaviors of fluid-filled carbon nanotubes （CNTs） at nanoscale. The nanoscale effects caused by the CNTs and the inner fluid are simulated by the nonlocal strain gradient effect and the slip boundary effect, respectively. The governing equations of motion are derived and resolved to investigate the wave characteristics in detail. The numerical solution shows that the strain gradient effect leads to the stiffness enhancement of CNTs when the nonlocal stress effect causes the decrease in stiffness. The dynamic properties of CNTs are affected by the coupling of these two scale effects. The flow velocity of fluid inside the CNT is increased due to the slip boundary effect, resulting in the promotion of wave propagation in the dynamic system.展开更多
In the present communication, the hydrodynamic model is used to investigate the amplitude modulation as well as demodulation of an electromagnetic wave of high power helicon pump wave into another helicon wave in stra...In the present communication, the hydrodynamic model is used to investigate the amplitude modulation as well as demodulation of an electromagnetic wave of high power helicon pump wave into another helicon wave in strain dependent dielectric material incorporating carrier heating (CH) effects. The consideration of CH in modulation and demodulation is prime importance for the adding of new dimension in analysis of amplification of acoustic helicon wave. By using the dispersion relation, threshold pump electric filed and growth rate of unstable mode from the modulation and demodulation of the high power helicon wave well above from the threshold value will be discussed in the present analysis. The numerical analysis is applied to a strain dependent dielectric material, BaTiO3 at room temperature and irradiated with high power helicon wave of frequency 1.78 × 1014 Hz. This material is very sensitive to the pump intensities, therefore during studies, Gaussian shape of the helicon pump wave is considered during the propagation in stain dependent dielectric material and opto-acoustic wave in the form of Gaussian profile (ω0,κ0) is induced longitudinally along the crystallographic plane of BaTiO3. Its variation is caused by the available magnetic field (ωc), interaction length (z) and pulsed duration of interaction (τ). From the analysis of numerical results, the incorporation of CH effect can effectively modify the magnitude of modulation or demodulation of the amplitude of high power helicon laser wave through diffusion process. Not only the amplitude modulation and demodulation of the wave, the diffusion of the CH effectively modifies the growth rate of unstable mode of frequency in BaTiO3. The propagation of the threshold electric field shows the sinusoidal or complete Gaussian profile, whereas this profile is found to be completely lost in growth of unstable mode. It has also been seen that the growth rate is observed to be of the order of 108 - 1010 s-1 but from diffusion of carrier heating, and that its order is enhanced from 1010 - 1012 s-1 with the variation of the magnetized frequency from 1 to 2.5 × 1014 Hz.展开更多
基金Projects(51304239,51374243)supported by the National Natural Science Foundation of China
文摘A superposing principle, by suitably adding the strain waves from a number of concentrated explosive charges to approximate the waves generated by a cylindrical charge based on the strain wave of a point or small spherical explosive charge generated in rock, is used to further study the triggering time of strain gauges installed in radial direction at same distances but different positions surrounding a cylindrical explosive charge in rock. The duration of the first compression phase and peak value of strain wave, and furthermore, their differences are analyzed and some explanations are given. Besides that, the gauge orientation in which the maximum peak value occurs is also discussed. At last, the effect of velocity of detonation(V.O.D.) of a cylindrical explosive charge on the strain waves generated in the surrounding rock is taken as key research and the pattern of peak amplitude of a strain wave varies with the V.O.D. is likely to have been found.
基金supported by Program of Henan Polytechnic University(No.B2018-40)Innovative Scientists and Technicians Team of Henan Provincial High Education(21IRTSTHN016)the Fundamental Research Funds for the Universities of Henan Province。
文摘In this paper,we mainly study the time-space fractional strain wave equation in microstructured solids.He’s variational method,combined with the two-scale transform are implemented to seek the solitary and periodic wave solutions of the time-space strain wave equation.The main advantage of the variational method is that it can reduce the order of the differential equation,thus simplifying the equation,making the solving process more intuitive and avoiding the tedious solving process.Finally,the numerical results are shown in the form of 3D and 2D graphs to prove the applicability and effectiveness of the method.The obtained results in this work are expected to shed a bright light on the study of fractional nonlinear partial differential equations in physics.
文摘In the materials of micro-structured, the propagation of wave modeling should take into account the scale of various microstructures. The different kinds solitary wave solutions of strain wave dynamical model are derived via utilizing exp(-φ(ξ))-expansion and extended simple equation methods. This dynamical equation plays a key role in engineering and mathematical physics. Solutions obtained in this work include periodic solitary waves, Kink and antiKink solitary waves, bell-shaped solutions, solitons, and rational solutions. These exact solutions help researchers for knowing the physical phenomena of this wave equation. The stability of this dynamical model is examined via standard linear stability analysis, which authenticate that the model is stable and their solutions are exact. Graphs are depicted for knowing the movements of some solutions. The results show that the current methods, by the assist of symbolic calculation, give an effectual and direct mathematical tools for resolving the nonlinear problems in applied sciences.
文摘The theoretical discovery of slow strain (tectonic) waves, the so-called strain waves in the Earth, served as a motivation to develop physical backgrounds of the mathematical theory of propagation of these waves and to search for methods of their experimental detection. For fifty years, scientists from different countries in different regions of the Earth, using direct and indirect methods, discovered the migration of crustal deformation and revealed its wave nature, and, therefore, proved the reality of the existence of strain waves of the Earth. This overview briefly describes the history of the development of the concept of strain waves on the Earth, the observation methods and properties of strain waves, and the main types of geological structures generating these waves. The most prominent results of the theoretical, laboratory, and in-situ observations of slow strain migration, including slow earthquakes and periodic Episodic Tremor and Slow (ETS) slip effects, are presented. In the near future, studies of slow strain waves may lead to a fundamental revision of the current concepts about the physics of the seismic process.
基金supported by the National Natural Science Foundation of China(Grant Nos.52408407 and 52478373)the‘CUG Scholar’Scientific Research Funds at China University of Geosciences(Grant No.2023082).
文摘The torsional low strain integrity test(TLSIT),known for its advantages such as a smaller detection blind zone,improved identification of shallowly buried defects,stable phase velocity for signal interpretation,and better adaptability for existing pile testing.However,it lacks a comprehensive understanding of the authentic three-dimensional(3D)strain wave propagation mechanism,particularly wave reflection and transmission at defects.To address this gap,a novel 3D theoretical framework is introduced in this context to model the authentic 3D wave propagation during the TLSIT.The proposed approach is validated by comparing its results with those obtained from 3D finite element method(FEM)simulations and simplified 1D(one-dimensional)and 3D analytical solutions.Additionally,a parametric study is conducted to enhance insights into the formation mechanism of high-frequency interference observed during the TLSIT.Finally,a defect identification study is performed to provide guidance for interpreting the wave spectrum in terms of defect characteristics.
基金National Natural Science Foundation of China!(No:19861004)
文摘The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions are derived and global attractors in E-1 space is obtained.
文摘When strain wave passes through rock, a changing magnetic field due to piezomagnetic effect will propagate at the velocity of sound. The changing magnetic field will stimulate electromagnetic ef fect in the surrounding area. This paper reports the experimental results which proves the existence of such phenomena. And the synthetic piezomagnetic coefficients of rock are measured from experimental results. The piezomagnetic effect can be used to explain some electromagnetic phenomena produced in the process of earthquakes.
基金the National Natural Science Foundation of China (No. 19861004).
文摘In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and the finiteness of the Hausdorff and the fractal dimensions of the attractors.
文摘This paper is concerned with the wave propagation behavior of rotating functionally graded（FG）temperature-dependent nanoscale beams subjected to thermal loading based on nonlocal strain gradient stress field.Uniform,linear and nonlinear temperature distributions across the thickness are investigated.Thermo-elastic properties of FG beam change gradually according to the Mori–Tanaka distribution model in the spatial coordinate.The nanobeam is modeled via a higher-order shear deformable refined beam theory which has a trigonometric shear stress function.The governing equations are derived by Hamilton’s principle as a function of axial force due to centrifugal stiffening and displacement.The solution of these equations is provided employing a Galerkin-based approach which has the potential to capture various boundary conditions.By applying an analytical solution and solving an eigenvalue problem,the dispersion relations of rotating FG nanobeam are obtained.Numerical results illustrate that various parameters including temperature change,angular velocity,nonlocality parameter,wave number and gradient index have significant effects on the wave dispersion characteristics of the nanobeam under study.The outcome of this study can provide beneficial information for the next-generation research and the exact design of nano-machines including nanoscale molecular bearings,nanogears,etc.
基金supported by the Special Fund for Earthquake Research in the Public Interest(No.201108009)
文摘At a sampling rate of 100 samples per second,the YRY-4 four-gauge borehole strainmeters（FGBS） are capable of recording transient strains caused by seismic waves such as P and S waves or strain seismograms. At such a high sampling rate, data from the YRY-4 strainmeters demonstrate fairly satisfactory self-consistency. The strain tensor seismograms demonstrate the senses of motion of P waves, that is, the type of seismic wave travels in the direction of the maximum normal strain change. The observed strain patterns of S waves significantly differ from those of P waves and should contain information about the source mechanism. Spectrum analysis shows that the strain seismograms are consistent with conventional broadband seismograms from the same site.
文摘How the wave propagation analysis plays a key role in the studies of dynamic response of materials at high strain rates is analyzed. For the wave propagation technique, the followings are important: the loading and unloading constitutive relation presumed, the positions of the sensors embedded, the interactions between loading waves and unloading waves. For the split Hopkinson pressure bar (SHPB) technique, the assumption of one-dimensional stress wave propagation and the assumption of stress uniformity along the specimen should be satisfied. When the larger diameter bars are employed, the wave dispersion effects should be considered, including the high frequency oscillations, non-uniform stress distribution across the bar section, increase of rise time, and amplitude attenuation. The stress uniformity along the specimen is influenced by the reflection times in specimen, the wave impedance ratio of the specimen and the bar, and the waveform.
基金founded by the Combined Project of Monitoring,Prediction and Research of China Earthquake Administration entitled "Statistical Study on the Earthquake Cases of Imminent Anomaly in Sacks Volume Strain Measurements (154201)"the Operation Maintenance of Shisanling Seismic Station,Institute of Earthquake Science,CEA(40417600105)
文摘Based on the body strain record of Tiantanghe station from 2008 to 2014,we make a statistical analysis of the relationship between the maximum amplitude of the body strain record and the surface-wave magnitude,epicenter distance of the earthquakes,which occurred in the Chinese mainland and its surrounding areas with MS≥6. 0 and the rest of the world with MS≥7. 0. According to statistical results,we propose a statistical formula between the surface-wave magnitude of earthquake and the maximum amplitude of the body strain record,the epicenter distance: M_S~*= 0. 37 ln A_max+ 0. 57 ln D + 0. 07. We can also derive a theoretical estimation formula for the maximum amplitude: A_max=e^(2. 7(M_S^*-0. 07))D^(-1. 54). This demonstrates that the maximum amplitude of the body strain record increases exponentially with the increase of the surface-wave magnitude, and decreases with the increase of the epicenter distance,and shows a negative correlation with their product. We further discuss the necessity of adding instruments with high frequency sampling to earthquake monitoring, and dicuss the prospects for precise earthquake prediction in future.
文摘A shear-lag theory was developed to investigate the strain transfer from the metal substrate to the surface acoustic wave （SAW） resonator through a bonding layer. A three-layer model of host structure-adhesive layer-resonator layer was established. The strain transfer was theoretically analyzed, and the main factors impacting the SAW sensor measurement were studied. The relationship between the sensor response and the individual effect of all these factors under static loads was discussed. Results showed that better accuracy could be achieved with increase in the adhesive stiffness or resonator length, or decrease in the adhesive thickness. The values of the strain transfer rate calculated from the analytical model agreed well with that from the available experiment data.
基金Project supported by the Iranian Nanotechnology Development Committee and the University of Kashan(No.463855/11)
文摘In this research, vibration and wave propagation analysis of a twisted micro- beam on Pasternak foundation is investigated. The strain-displacement relations （kine-matic equations） are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory （SGT） is used to implement the size dependent effect at micro-scale. Finally, using an energy method and Hamilton＇s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave prop- agation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is in- versely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.
基金This project is supported by the National Natural Science Foundation of China （Grant No. 11462010）.
文摘A dynamic Timoshenko beam model is established based on the new nonlocal strain gradient theory and slip boundary theory to study the wave propagation behaviors of fluid-filled carbon nanotubes （CNTs） at nanoscale. The nanoscale effects caused by the CNTs and the inner fluid are simulated by the nonlocal strain gradient effect and the slip boundary effect, respectively. The governing equations of motion are derived and resolved to investigate the wave characteristics in detail. The numerical solution shows that the strain gradient effect leads to the stiffness enhancement of CNTs when the nonlocal stress effect causes the decrease in stiffness. The dynamic properties of CNTs are affected by the coupling of these two scale effects. The flow velocity of fluid inside the CNT is increased due to the slip boundary effect, resulting in the promotion of wave propagation in the dynamic system.
文摘In the present communication, the hydrodynamic model is used to investigate the amplitude modulation as well as demodulation of an electromagnetic wave of high power helicon pump wave into another helicon wave in strain dependent dielectric material incorporating carrier heating (CH) effects. The consideration of CH in modulation and demodulation is prime importance for the adding of new dimension in analysis of amplification of acoustic helicon wave. By using the dispersion relation, threshold pump electric filed and growth rate of unstable mode from the modulation and demodulation of the high power helicon wave well above from the threshold value will be discussed in the present analysis. The numerical analysis is applied to a strain dependent dielectric material, BaTiO3 at room temperature and irradiated with high power helicon wave of frequency 1.78 × 1014 Hz. This material is very sensitive to the pump intensities, therefore during studies, Gaussian shape of the helicon pump wave is considered during the propagation in stain dependent dielectric material and opto-acoustic wave in the form of Gaussian profile (ω0,κ0) is induced longitudinally along the crystallographic plane of BaTiO3. Its variation is caused by the available magnetic field (ωc), interaction length (z) and pulsed duration of interaction (τ). From the analysis of numerical results, the incorporation of CH effect can effectively modify the magnitude of modulation or demodulation of the amplitude of high power helicon laser wave through diffusion process. Not only the amplitude modulation and demodulation of the wave, the diffusion of the CH effectively modifies the growth rate of unstable mode of frequency in BaTiO3. The propagation of the threshold electric field shows the sinusoidal or complete Gaussian profile, whereas this profile is found to be completely lost in growth of unstable mode. It has also been seen that the growth rate is observed to be of the order of 108 - 1010 s-1 but from diffusion of carrier heating, and that its order is enhanced from 1010 - 1012 s-1 with the variation of the magnetized frequency from 1 to 2.5 × 1014 Hz.
