A new method to detect the magnetic field direction by using a silicon structure is presented in this paper. The structure includes a micro beam and an in-plane coil electrode. When the electrode under a magnetic fiel...A new method to detect the magnetic field direction by using a silicon structure is presented in this paper. The structure includes a micro beam and an in-plane coil electrode. When the electrode under a magnetic field is applied with an alternating current, the micro beam is actuated under the effect of the Lorentz forces. Magnetic fields of different directions cause different vibration profiles. The direction of the magnetic field is obtained by measuring the vibration amplitudes of the micro beam, which is driven to work at first- and second-order resonant modes. A micro structure has been fabricated using the bulk microma^hined silicon process. A laser Doppler vibrometer system is implemented to measure the vibration amplitudes. The experimental results show that the amplitude of the structure, which depends on the different modes, is a sine or cosine function of the angle of the magnetic field. It agrees well with the simulation result. Currently a resolution of 10~ for the magnetic field direction measurement can be obtained using the detecting principle.展开更多
The dynamic characteristics of a quartz crystal resonator(QCR) in thicknessshear modes(TSM) with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inv...The dynamic characteristics of a quartz crystal resonator(QCR) in thicknessshear modes(TSM) with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction(surface shear force), thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.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
With introduction of the first-order strain-gradient of surface micro-beams into the energy density function,we developed a two-dimensional dynamic model for a compound quartz crystal resonator(QCR) system,consistin...With introduction of the first-order strain-gradient of surface micro-beams into the energy density function,we developed a two-dimensional dynamic model for a compound quartz crystal resonator(QCR) system,consisting of a QCR and surface micro-beam arrays.The frequency shift that was induced by micro-beams with consideration of strain-gradients is discussed in detail and some useful results are obtained,which have important significance in resonator design and applications.展开更多
This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded (FG) beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-...This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded (FG) beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-mechanical systems (MEMS/NEMS) with a wide range of aspect ratios. Based on the modified couple stress theory and the principle of minimum potential energy, the governing equations and boundary conditions for a micro-structure-dependent beam theory are derived. The present beam theory incorporates different kinds of higher-order shear assumptions as well as the two familiar beam theories, namely, the Euler-Bernoulli and Timoshenko beam theories. A numerical solu- tion procedure, based on a generalized differential quadrature method (GDQM), is used to calculate the results of the bi-directional FG beams. The effects of the two exponential FG indexes, the higher-order shear deformations, the length scale parameter, the geomet- ric dimensions, and the different boundary conditions on the critical buckling loads are studied in detail, by assuming that Young's modulus obeys an exponential distribution function in both length and thickness directions. To reach the desired critical buckling load, the appropriate exponential FG indexes and geometric shape of micro-beams can be designed according to the proposed theory.展开更多
We study the dynamic behavior of a quartz crystal resonator (QCR) in thickness-shear vibrations with the upper surface covered by an array of micro-beams (MBs) under large deflection. Through taking into account t...We study the dynamic behavior of a quartz crystal resonator (QCR) in thickness-shear vibrations with the upper surface covered by an array of micro-beams (MBs) under large deflection. Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator, dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations. It is found that the frequency shift produces a little right (left) translation for increasing elastic modulus (length/radius ratio) of MBs. Moreover, the frequency right (left) translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one,展开更多
In this study, compounded surface modification technology-high current pulsed electron beam (HCPEB) + micro-plasma oxidation (MPO) was applied to treat ZK60 Mg alloys. The characteristics of the microstructure of...In this study, compounded surface modification technology-high current pulsed electron beam (HCPEB) + micro-plasma oxidation (MPO) was applied to treat ZK60 Mg alloys. The characteristics of the microstructure of ZK60 Mg alloy after single MPO and HCPEB+MPO compounded treatment were investigated by SEM. The results showed that the density of the ceramic layer of HCPEB+MPO-treated ZK60 Mg alloy was improved and defects were reduced compared to that under MPO treatment alone. Surface modified layer of ZK60 Mg alloys treated by HCPEB+MPO was divided into three zones, namely the top loose ceramic zone, middle compact zone and inside HCPEB-induced melted zone. Corrosion resistance of ZK60 Mg alloy before and after the compounded surface modification was measured in a solution of 3.5% NaCl by potentiodynamic polarization curves. It was found that the corrosion current density of ZK60 Mg alloys could be reduced by about three orders of magnitude, from 311μA/cm^2 of the original sample to 0.2μA/cm^2 of the HCPEB+MPO-treated sample. This indicates the great application potential of the HCPEB+MPO compounded surface modification technology in improving the corrosion resistance of ZK60 Mg alloys in the future.展开更多
A new method for micro-beam XRF localiztion is presented.A laser beam along with an incident X-ray hits on the surface of a sample.The micro region on the sample that reached by X-ray beam can be localized by means of...A new method for micro-beam XRF localiztion is presented.A laser beam along with an incident X-ray hits on the surface of a sample.The micro region on the sample that reached by X-ray beam can be localized by means of the visible spot of the laser beam.This method is suitable for X-ray microprobes using an X-ray tube or synchrotron radiation as excitation sources.展开更多
The Ni microcantilevers were fabricated by femtosecond laser. The corrosion behavior of the micro-sized Ni cantilever beams was studied by electrochemical noise and a newly developed fatigue testing method. The result...The Ni microcantilevers were fabricated by femtosecond laser. The corrosion behavior of the micro-sized Ni cantilever beams was studied by electrochemical noise and a newly developed fatigue testing method. The results show that the micro-sized specimens exhibit general corrosion behavior under the studied corrosion condition,whereas the ordinary-sized plates exhibit the localized corrosion behavior. The critical load amplitude of the micro-sized Ni specimens under corrosion fatigue status was determined to be 15 mN. The maximum bending loads,which were measured by fatigue tests,decrease gradually prior to final fracture. Corrosion fracture first occurs in the range of notch with a higher tensile bending stress,and exhibits clear evidence of trans-columnar fracture. The variation of maximum bending loads with time agrees with that creep deformation of the micro-sized Ni specimens can easily occur at room temperature,which implies that the micro-sized Ni specimens appear to have an improved resistance towards total crack as compared with the ordinary-sized Ni specimens.展开更多
The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is...The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beam solutions of the loads with di?erent distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation o?ers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length o?ers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The e?ects of dielectric layer thickness and electrostatic voltage on the cantilever beam stiction are studied. The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.展开更多
Cu bump was transferred using a focused laser pulse for microelectronic packaging.An Nd:YAG laser pulse (maximum energy of 500 mJ;wavelength of 1064 nm;fluences of 0.4-2.1 kJ/cm2) was irradiated on a sacrificial absor...Cu bump was transferred using a focused laser pulse for microelectronic packaging.An Nd:YAG laser pulse (maximum energy of 500 mJ;wavelength of 1064 nm;fluences of 0.4-2.1 kJ/cm2) was irradiated on a sacrificial absorption layer with copper coating.The focused laser beam induced plasma between the semi-transparent donor slide and the sacrificial layer,causing a shock wave.The shock wave pressure pushed the Cu layer and transferred material to deposit a bump on substrate.A beam-shaper was used to produce uniform pressure at the interface to reduce fragmentation of the transferred material on the substrate.The calculated shock wave pressure with respect to laser fluence was 1-3 GPa.A Cu bump of diameter of 200 μm was successfully deposited at laser fluence of 0.6 kJ/cm 2.The pressure control at the sacrificial layer using a laser pulse was critical to produce a bump with less fragmentation.The technique can be applied to forming Cu bump for an interconnecting process in electronics.展开更多
CVD diamond microdosimeter is an ideal substitute of common Si.GaAs detector for extremely strong radiation experimental environment due to its high band gap energy, fast charge collection, low dielectric constant and...CVD diamond microdosimeter is an ideal substitute of common Si.GaAs detector for extremely strong radiation experimental environment due to its high band gap energy, fast charge collection, low dielectric constant and hardness. In order to improve its character, a CVD diamond microdosimeter was irradiated by a proton dose of 46 Gy, and a lateral micro-ion beam induced charge (IBIC) technique was utilized to characterize it in low beam current (~fA). It was clearly shown that charge collection efficiency and energy resolution were greatly improved after proton irradiation of that dose. Moreover, the homogeneities of both its counting performance and collection efficiency were enhanced. Proton irradiation of 46 Gy has been proved to be an effective way to prime a CVD diamond.展开更多
Magneto-rheological elastomers (MILEs) are used to construct composite structures for micro-vibration control of equipment under stochastic support-motion excitations. The dynamic behavior of MREs as a smart viscoel...Magneto-rheological elastomers (MILEs) are used to construct composite structures for micro-vibration control of equipment under stochastic support-motion excitations. The dynamic behavior of MREs as a smart viscoelastic material is characterized by a complex modulus dependent on vibration frequency and controllable by external magnetic fields. Frequency-domain solution methods for stochastic micro-vibration response analysis of the MRE-based structural systems are developed to derive the system frequency-response function matrices and the expressions of the velocity response spectrum. With these equations, the root-mean-square (RMS) velocity responses in terms of the one-third octave frequency band spectrum can be calculated. Further, the optimization problem of the complex moduli of the MRE cores is defined by minimizing the velocity response spectra and the RMS velocity responses through altering the applied magnetic fields. Simulation results illustrate the influences of MRE parameters on the RMS velocity responses and the high response reduction capacities of the MRE-based structures. In addition, the developed frequency-domain analysis methods are applicable to sandwich beam structures with arbitrary cores characterized by complex shear moduli under stochastic excitations described by power spectral density functions, and are valid for a wide frequency range.展开更多
A combined beam model representing the periodicity of the microstructure and micro deformation of 3D woven composites is developed for predicting mechanical properties. The model considers the effects of off axial ten...A combined beam model representing the periodicity of the microstructure and micro deformation of 3D woven composites is developed for predicting mechanical properties. The model considers the effects of off axial tension/compression and bending/shearing couplings as well as the mutual reactions of fiber yarns. The method determining microstructure by using woven parameters is described for a typical 3D woven composite material. An analytical cell, constructed by a minimum periodic section of yarn and interlayer matrix, is adopted. Micro stresses in the cell under in-plane tensile loading are obtained by using the proposed beam model and macro modulus is then obtained by the averaging method. Material tests and a 2D micro FEM analysis are made to evaluate this model. Analyses reveal that micro stress caused by tensile/bending coupling effect is not negligible in the stress analysis.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.61076071)
文摘A new method to detect the magnetic field direction by using a silicon structure is presented in this paper. The structure includes a micro beam and an in-plane coil electrode. When the electrode under a magnetic field is applied with an alternating current, the micro beam is actuated under the effect of the Lorentz forces. Magnetic fields of different directions cause different vibration profiles. The direction of the magnetic field is obtained by measuring the vibration amplitudes of the micro beam, which is driven to work at first- and second-order resonant modes. A micro structure has been fabricated using the bulk microma^hined silicon process. A laser Doppler vibrometer system is implemented to measure the vibration amplitudes. The experimental results show that the amplitude of the structure, which depends on the different modes, is a sine or cosine function of the angle of the magnetic field. It agrees well with the simulation result. Currently a resolution of 10~ for the magnetic field direction measurement can be obtained using the detecting principle.
基金Project supported by the National Natural Science Foundation of China(Nos.11272127 and51425006)the Research Fund for the Doctoral Program of Higher Education of China(No.20130142110022)the Grant from the Impact and Safety of Coastal Engineering Initiative Program of Zhejiang Provincial Government at Ningbo University(No.zj1213)
文摘The dynamic characteristics of a quartz crystal resonator(QCR) in thicknessshear modes(TSM) with the upper surface covered by an array of micro-beams immersed in liquid are studied. The liquid is assumed to be inviscid and incompressible for simplicity. Dynamic equations of the coupled system are established. The added mass effect of liquid on micro-beams is discussed in detail. Characteristics of frequency shift are clarified for different liquid depths. Modal analysis shows that a drag effect of liquid has resulted in the change of phase of interaction(surface shear force), thus changing the system resonant frequency. The obtained results are useful in resonator design and applications.
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supported by the National Science Foundation of China(Grants 11272127 and 51435006)Research Fund for the Doctoral Program of Higher Education of China(Grant 20130142110022)the Grant from the Impact and Safety of Coastal Engineering Initiative Program of Zhejiang Provincial Government at Ningbo University(Grant zj1213)
文摘With introduction of the first-order strain-gradient of surface micro-beams into the energy density function,we developed a two-dimensional dynamic model for a compound quartz crystal resonator(QCR) system,consisting of a QCR and surface micro-beam arrays.The frequency shift that was induced by micro-beams with consideration of strain-gradients is discussed in detail and some useful results are obtained,which have important significance in resonator design and applications.
基金supported by the National Natural Science Foundation of China(Nos.51375184 and 51605172)the Fundamental Research Funds for the Central Universities(No.2015MS014)
文摘This paper focuses on the buckling behaviors of a micro-scaled bi-directional functionally graded (FG) beam with a rectangular cross-section, which is now widely used in fabricating components of micro-nano-electro-mechanical systems (MEMS/NEMS) with a wide range of aspect ratios. Based on the modified couple stress theory and the principle of minimum potential energy, the governing equations and boundary conditions for a micro-structure-dependent beam theory are derived. The present beam theory incorporates different kinds of higher-order shear assumptions as well as the two familiar beam theories, namely, the Euler-Bernoulli and Timoshenko beam theories. A numerical solu- tion procedure, based on a generalized differential quadrature method (GDQM), is used to calculate the results of the bi-directional FG beams. The effects of the two exponential FG indexes, the higher-order shear deformations, the length scale parameter, the geomet- ric dimensions, and the different boundary conditions on the critical buckling loads are studied in detail, by assuming that Young's modulus obeys an exponential distribution function in both length and thickness directions. To reach the desired critical buckling load, the appropriate exponential FG indexes and geometric shape of micro-beams can be designed according to the proposed theory.
基金supported by the National Natural Science Foundation of China(11272127 and 51435006)the Research Fund for the Doctoral Program of Higher Education of China(20130142110022)
文摘We study the dynamic behavior of a quartz crystal resonator (QCR) in thickness-shear vibrations with the upper surface covered by an array of micro-beams (MBs) under large deflection. Through taking into account the continuous conditions of shear force and bending moment at the interface of MBs/resonator, dependences of frequency shift of the compound QCR system versus material parameter and geometrical parameter are illustrated in detail for nonlinear and linear vibrations. It is found that the frequency shift produces a little right (left) translation for increasing elastic modulus (length/radius ratio) of MBs. Moreover, the frequency right (left) translation distance caused by nonlinear deformation becomes more serious in the second-order mode than in the first-order one,
基金supported by Liaoning BaiQianWan Talents Program of China (No. 2008921028)Doctoral Fund of Ministry of Education of China (No. 200801451082)
文摘In this study, compounded surface modification technology-high current pulsed electron beam (HCPEB) + micro-plasma oxidation (MPO) was applied to treat ZK60 Mg alloys. The characteristics of the microstructure of ZK60 Mg alloy after single MPO and HCPEB+MPO compounded treatment were investigated by SEM. The results showed that the density of the ceramic layer of HCPEB+MPO-treated ZK60 Mg alloy was improved and defects were reduced compared to that under MPO treatment alone. Surface modified layer of ZK60 Mg alloys treated by HCPEB+MPO was divided into three zones, namely the top loose ceramic zone, middle compact zone and inside HCPEB-induced melted zone. Corrosion resistance of ZK60 Mg alloy before and after the compounded surface modification was measured in a solution of 3.5% NaCl by potentiodynamic polarization curves. It was found that the corrosion current density of ZK60 Mg alloys could be reduced by about three orders of magnitude, from 311μA/cm^2 of the original sample to 0.2μA/cm^2 of the HCPEB+MPO-treated sample. This indicates the great application potential of the HCPEB+MPO compounded surface modification technology in improving the corrosion resistance of ZK60 Mg alloys in the future.
文摘A new method for micro-beam XRF localiztion is presented.A laser beam along with an incident X-ray hits on the surface of a sample.The micro region on the sample that reached by X-ray beam can be localized by means of the visible spot of the laser beam.This method is suitable for X-ray microprobes using an X-ray tube or synchrotron radiation as excitation sources.
基金Project(50671040) supported by the National Natural Science Foundation of ChinaProject(2006CB806006) supported by the National Basic Research Program of China
文摘The Ni microcantilevers were fabricated by femtosecond laser. The corrosion behavior of the micro-sized Ni cantilever beams was studied by electrochemical noise and a newly developed fatigue testing method. The results show that the micro-sized specimens exhibit general corrosion behavior under the studied corrosion condition,whereas the ordinary-sized plates exhibit the localized corrosion behavior. The critical load amplitude of the micro-sized Ni specimens under corrosion fatigue status was determined to be 15 mN. The maximum bending loads,which were measured by fatigue tests,decrease gradually prior to final fracture. Corrosion fracture first occurs in the range of notch with a higher tensile bending stress,and exhibits clear evidence of trans-columnar fracture. The variation of maximum bending loads with time agrees with that creep deformation of the micro-sized Ni specimens can easily occur at room temperature,which implies that the micro-sized Ni specimens appear to have an improved resistance towards total crack as compared with the ordinary-sized Ni specimens.
文摘The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beam solutions of the loads with di?erent distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation o?ers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length o?ers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The e?ects of dielectric layer thickness and electrostatic voltage on the cantilever beam stiction are studied. The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.
基金Project(2012-0001900)supported by the National Research Foundation of Korea
文摘Cu bump was transferred using a focused laser pulse for microelectronic packaging.An Nd:YAG laser pulse (maximum energy of 500 mJ;wavelength of 1064 nm;fluences of 0.4-2.1 kJ/cm2) was irradiated on a sacrificial absorption layer with copper coating.The focused laser beam induced plasma between the semi-transparent donor slide and the sacrificial layer,causing a shock wave.The shock wave pressure pushed the Cu layer and transferred material to deposit a bump on substrate.A beam-shaper was used to produce uniform pressure at the interface to reduce fragmentation of the transferred material on the substrate.The calculated shock wave pressure with respect to laser fluence was 1-3 GPa.A Cu bump of diameter of 200 μm was successfully deposited at laser fluence of 0.6 kJ/cm 2.The pressure control at the sacrificial layer using a laser pulse was critical to produce a bump with less fragmentation.The technique can be applied to forming Cu bump for an interconnecting process in electronics.
文摘CVD diamond microdosimeter is an ideal substitute of common Si.GaAs detector for extremely strong radiation experimental environment due to its high band gap energy, fast charge collection, low dielectric constant and hardness. In order to improve its character, a CVD diamond microdosimeter was irradiated by a proton dose of 46 Gy, and a lateral micro-ion beam induced charge (IBIC) technique was utilized to characterize it in low beam current (~fA). It was clearly shown that charge collection efficiency and energy resolution were greatly improved after proton irradiation of that dose. Moreover, the homogeneities of both its counting performance and collection efficiency were enhanced. Proton irradiation of 46 Gy has been proved to be an effective way to prime a CVD diamond.
基金Research Grants Council of the Hong Kong Special Administrative Region,China Under Grant No.PolyU 5252/07EThe Hong Kong Polytechnic University through the Development of Niche Areas Programme Under Grant No.1-BB95Zhejiang Provincial Natural Science Foundation of China Under Grant No.Y607087)
文摘Magneto-rheological elastomers (MILEs) are used to construct composite structures for micro-vibration control of equipment under stochastic support-motion excitations. The dynamic behavior of MREs as a smart viscoelastic material is characterized by a complex modulus dependent on vibration frequency and controllable by external magnetic fields. Frequency-domain solution methods for stochastic micro-vibration response analysis of the MRE-based structural systems are developed to derive the system frequency-response function matrices and the expressions of the velocity response spectrum. With these equations, the root-mean-square (RMS) velocity responses in terms of the one-third octave frequency band spectrum can be calculated. Further, the optimization problem of the complex moduli of the MRE cores is defined by minimizing the velocity response spectra and the RMS velocity responses through altering the applied magnetic fields. Simulation results illustrate the influences of MRE parameters on the RMS velocity responses and the high response reduction capacities of the MRE-based structures. In addition, the developed frequency-domain analysis methods are applicable to sandwich beam structures with arbitrary cores characterized by complex shear moduli under stochastic excitations described by power spectral density functions, and are valid for a wide frequency range.
文摘A combined beam model representing the periodicity of the microstructure and micro deformation of 3D woven composites is developed for predicting mechanical properties. The model considers the effects of off axial tension/compression and bending/shearing couplings as well as the mutual reactions of fiber yarns. The method determining microstructure by using woven parameters is described for a typical 3D woven composite material. An analytical cell, constructed by a minimum periodic section of yarn and interlayer matrix, is adopted. Micro stresses in the cell under in-plane tensile loading are obtained by using the proposed beam model and macro modulus is then obtained by the averaging method. Material tests and a 2D micro FEM analysis are made to evaluate this model. Analyses reveal that micro stress caused by tensile/bending coupling effect is not negligible in the stress analysis.