Significant temperature difference(300-77 K or even 4 K) can cause large deformations and displacements of the beam position monitors(BPMs),which affect BPMs measurement resolution or even cause their malfunction in c...Significant temperature difference(300-77 K or even 4 K) can cause large deformations and displacements of the beam position monitors(BPMs),which affect BPMs measurement resolution or even cause their malfunction in cryogenic situations.In this paper,to check the offset from the mechanical to electrical center in low temperature(77 K),Fourier's law and finite element method are used to simulate cryo-deformation.Laser tracker and micro-alignment telescope are employed in combined BPM calibration,installation and monitoring.The calibration error is<0.02 mm,and the installation and monitoring precision are 0.06 mm and 0.01 mm,respectively.The monitored cryo-deformation agrees well with the simulation results.These indicate that the combined alignment can improve performance of the BPM system.All these guaranteed the success of running the 9.55 MeV@2.14 mA cw protons.展开更多
The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton's principle. The viscoelastic ma...The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton's principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscos- ity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method (DQM) is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.展开更多
Vibration mode of the constrained damping cantilever is built up according to the mode superposition of the elastic cantilever beam. The control equation of the constrained damping cantilever beam is then derived usin...Vibration mode of the constrained damping cantilever is built up according to the mode superposition of the elastic cantilever beam. The control equation of the constrained damping cantilever beam is then derived using Lagrange's equation. Dynamic response of the constrained damping cantilever beam is obtained according to the principle of virtual work, when the concentrated force is suddenly unloaded. Frequencies and transient response of a series of constrained damping cantilever beams are calculated and tested. Influence of parameters of the damping layer on the response time is analyzed. Analyitcal and experimental approaches are used for verification. The results show that the method is reliable.展开更多
The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented.The constant gain distributed controller of the velo...The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented.The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping.The formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory(ECBT),Timoshenko’s first-order beam theory(TFBT),Reddy’s third-order shear deformation beam theory,and the simple sinusoidal shear deformation beam theory.Hamilton’s principle is utilized to give the equations of motion and then to describe the vibration of the current beam.Based on Navier’s approach,the solution of the dynamic system is obtained.The effects of the material properties,the modes,the thickness ratios,the lamination schemes,the magnitudes of the feedback coefficient,the position of magnetostrictive layers at the structure,and the foundation modules are extensively studied and discussed.展开更多
In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by ...In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji's method (AGM). AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method (Runk45) and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration (A), the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure Therefore, AGM can be considered as a significant progress in nonlinear sciences.展开更多
A dual S shaped micro strip antenna with a realistic feed is proposed for generation of tilted beam radiation pattern pertaining for beam steering applications. To achieve this, four feeding points are located at a di...A dual S shaped micro strip antenna with a realistic feed is proposed for generation of tilted beam radiation pattern pertaining for beam steering applications. To achieve this, four feeding points are located at a distance of 5.6 mm from the antenna centre. These feeding points when excited one by one generate four tilted beams in four different space quadrants, thus yielding a beam steerable antenna, Importantly, since the proposed antenna is symmetrical in the structure, all the four tilted beams have the same radiation pattern characteristics. A further enhancement of the antenna bandwidth is also achieved using 100-μn capacitive coupling between the feed and the antenna strip.展开更多
This study investigates seismic interferometry in which the Green's function is estimated between two receiv- ers by cross-correlation and integration over sources. For smoothly varying source strengths, the dominant...This study investigates seismic interferometry in which the Green's function is estimated between two receiv- ers by cross-correlation and integration over sources. For smoothly varying source strengths, the dominant contributions of the correlation integral come from the stationary phase directions in the forward and backward directions from the alignment of the two receivers. Gaussian beams can be used to evaluate the correlation integral and concentrate the amplitudes in a vicinity of the stationary phase regions instead of completely relying on phase interference. Several numerical examples are shown to illustrate how this process works. The use of Gaussian beams for the evaluation of the correlation integral results in stable estimates, and also provides physical insight into the estimation of the Green's function based on seismic interferometry.展开更多
The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the secon...The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical light beams exceeds the classical limit. The visibility of the second-order interference pattern of photons emitted by two independent single-photon sources is independent of the ratio between the intensities. These conclusions are important for the researches and applications in quantum optics and quantum information when an asymmetrical beam splitter is employed.展开更多
Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak's foundation is studied in this paper. Timoshenko's beam model and nonlocal elasticity theory ar...Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak's foundation is studied in this paper. Timoshenko's beam model and nonlocal elasticity theory are employed for formulation of the problem. The equations of motion are derived using Hamilton's principals by calculating kinetic energy, strain energy and work due to viscoelastic foundation. The effects of various parameters such as wavenumber, non-homogeneous index, nonlocal parameter and three parameters of foundation are performed on the phase velocity of the nanobeam. The obtained results indicate that some parameters such as non-homogeneous index, nonlocal parameter and wavenumber have significant effect on the response of the system.展开更多
Cu x S thin films are implanted by low energy N + ion beam. The influences of the energy and dose of N + ion implantation on Cu x S films are investigated. The results show that the ratio of copper to sulfur is increa...Cu x S thin films are implanted by low energy N + ion beam. The influences of the energy and dose of N + ion implantation on Cu x S films are investigated. The results show that the ratio of copper to sulfur is increased to some extent, the constituents of the film are turned to rich copper phase from rich sulfurous phase after ion beam irradiation. X-ray diffraction spectrum and optical transmission spectra of sample have confirmed the results.展开更多
Air or inert atmosphere irradiation of liquid normal alkanes C5-C8 and benzene by electron beam was carried out. Oxidation (in the air) or isomerization (in the inert gases) of liquid normal alkanes under electron...Air or inert atmosphere irradiation of liquid normal alkanes C5-C8 and benzene by electron beam was carried out. Oxidation (in the air) or isomerization (in the inert gases) of liquid normal alkanes under electron beam was shown. Action of electron beam on benzene molecules in the air or in the inert atmosphere leads to biphenyl, terphenyl and polymers. Irradiation by the bunch of electrons of mixture hexane with 10% benzene reduced to firm fractions (fullerene's similar structures) in a deposit.展开更多
A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite...A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation. Results of numerically simulating the injected field at z =0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides (with linear and/or nonlinear refractive index) , which are similar to those in the related publications. Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator. The iterative process needs fewer steps to be stable. Also, when the light wave meets the changes of mediums, the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.展开更多
Thin films of ZnxCd1-xS have been prepared by electron beam evaporation of a mixture of ZnS & CdS powders. The films are deposited onto sodalime glass slides under similar conditions.The composition of the films i...Thin films of ZnxCd1-xS have been prepared by electron beam evaporation of a mixture of ZnS & CdS powders. The films are deposited onto sodalime glass slides under similar conditions.The composition of the films is varied from CdS to ZnS (x=0 to 1). The films show a regular change in color from toner red to orange yellow as Zn concentration increases to maximum.These films are characterized for their optical, electricaI and structural properties. The bandgap value of ZnxCd1-xS films is found to vary linearIy from 2.20 eV to 3.44 eV with change in the x value from 0 to 1. The resistivity of these films is in the range of 171.0 Ωcm to 5.5× 106Ωcm for x=0~0.6. All the samples show cubic structure after annealing in air at 250℃ for 40 min.The lattice constant ao varies from 0.5884 nm to 0.54109 nm linearly.展开更多
Utilizing the Young’s double slits and Mach-Zehnder interferometer, we proposed an experimental method to measure the generalized Stokes parameters of a radially polarized random electromagnetic beam. After the parti...Utilizing the Young’s double slits and Mach-Zehnder interferometer, we proposed an experimental method to measure the generalized Stokes parameters of a radially polarized random electromagnetic beam. After the partially coherent beam propagating through the Young’s double slits, the interference fringe is obtained by the help of a Mach-Zehnder interferometer consisting of apertures, quarter-wave plates and polarizers. The electric cross-spectral density matrix is detected by the coherence degree of interference fringe and the density of each single slit. The generalized Stokes parameters can be obtained from the electric cross-spectral density matrix. This experiment measures the generalized Stokes parameters of the random electromagnetic beam successfully. The results show that the spectral degree of coherence for copolarized cases (xx and yy) is similar with that for cross-polaried cases (xy and yx) for the radially polarized random electromagnetic beam. This method will help us determine the change of the polarization and coherence of the light in propagation by detecting the change of the generalized Stokes parameters.展开更多
A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the founda...A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.展开更多
The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active be...The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.展开更多
基金supported by the National Natural Science Foundation of China(No.11605262)
文摘Significant temperature difference(300-77 K or even 4 K) can cause large deformations and displacements of the beam position monitors(BPMs),which affect BPMs measurement resolution or even cause their malfunction in cryogenic situations.In this paper,to check the offset from the mechanical to electrical center in low temperature(77 K),Fourier's law and finite element method are used to simulate cryo-deformation.Laser tracker and micro-alignment telescope are employed in combined BPM calibration,installation and monitoring.The calibration error is<0.02 mm,and the installation and monitoring precision are 0.06 mm and 0.01 mm,respectively.The monitored cryo-deformation agrees well with the simulation results.These indicate that the combined alignment can improve performance of the BPM system.All these guaranteed the success of running the 9.55 MeV@2.14 mA cw protons.
基金Project supported by the National Natural Science Foundation of China(Nos.11202136,11372195,11502147,and 11602146)
文摘The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton's principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscos- ity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method (DQM) is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.
基金Project supported by the National Natural Science Foundation of China (No. 10572150)the Natural Science Foundation of Naval University of Engineering (No. HGDQNJJ008)
文摘Vibration mode of the constrained damping cantilever is built up according to the mode superposition of the elastic cantilever beam. The control equation of the constrained damping cantilever beam is then derived using Lagrange's equation. Dynamic response of the constrained damping cantilever beam is obtained according to the principle of virtual work, when the concentrated force is suddenly unloaded. Frequencies and transient response of a series of constrained damping cantilever beams are calculated and tested. Influence of parameters of the damping layer on the response time is analyzed. Analyitcal and experimental approaches are used for verification. The results show that the method is reliable.
文摘The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented.The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping.The formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory(ECBT),Timoshenko’s first-order beam theory(TFBT),Reddy’s third-order shear deformation beam theory,and the simple sinusoidal shear deformation beam theory.Hamilton’s principle is utilized to give the equations of motion and then to describe the vibration of the current beam.Based on Navier’s approach,the solution of the dynamic system is obtained.The effects of the material properties,the modes,the thickness ratios,the lamination schemes,the magnitudes of the feedback coefficient,the position of magnetostrictive layers at the structure,and the foundation modules are extensively studied and discussed.
文摘In the present paper a vibrational differential equation governing on a rigid beam on viscoelastic foundation has been investigated. The nonlinear differential equation governing on this vibrating system is solved by a simple and innovative approach, which has been called Akbari-Ganji's method (AGM). AGM is a very suitable computational process and is usable for solving various nonlinear differential equations. Moreover, using AGM which solving a set of algebraic equations, complicated nonlinear equations can easily be solved without any mathematical operations. Also, the damping ratio and energy lost per cycle for three cycles have been investigated. Furthermore, comparisons have been made between the obtained results by numerical method (Runk45) and AGM. Results showed the high accuracy of AGM. The results also showed that by increasing the amount of initial amplitude of vibration (A), the value of damping ratio will be increased, and the energy lost per cycle decreases by increasing the number of cycle. It is concluded that AGM is a reliable and precise approach for solving differential equations. On the other hand, it is better to say that AGM is able to solve linear and nonlinear differential equations directly in most of the situations. This means that the final solution can be obtained without any dimensionless procedure Therefore, AGM can be considered as a significant progress in nonlinear sciences.
基金the European Union through the Welsh As-sembly Government
文摘A dual S shaped micro strip antenna with a realistic feed is proposed for generation of tilted beam radiation pattern pertaining for beam steering applications. To achieve this, four feeding points are located at a distance of 5.6 mm from the antenna centre. These feeding points when excited one by one generate four tilted beams in four different space quadrants, thus yielding a beam steerable antenna, Importantly, since the proposed antenna is symmetrical in the structure, all the four tilted beams have the same radiation pattern characteristics. A further enhancement of the antenna bandwidth is also achieved using 100-μn capacitive coupling between the feed and the antenna strip.
基金supported by U.S. National Science Foundation EAR06-35611U.S. Air Force contract FA8718-08-C-002the members of the Geo-Mathematical Imaging Group (GMIG) at Purdue University
文摘This study investigates seismic interferometry in which the Green's function is estimated between two receiv- ers by cross-correlation and integration over sources. For smoothly varying source strengths, the dominant contributions of the correlation integral come from the stationary phase directions in the forward and backward directions from the alignment of the two receivers. Gaussian beams can be used to evaluate the correlation integral and concentrate the amplitudes in a vicinity of the stationary phase regions instead of completely relying on phase interference. Several numerical examples are shown to illustrate how this process works. The use of Gaussian beams for the evaluation of the correlation integral results in stable estimates, and also provides physical insight into the estimation of the Green's function based on seismic interferometry.
基金supported by the National Natural Science Foundation of China(Grant No.11404255)the Doctor Foundation of Education Ministry of China(Grant No.20130201120013)+1 种基金the Programme of Introducing Talents of Discipline to Universities,China(Grant No.B14040)the Fundamental Research Funds for the Central Universities,China
文摘The second-order temporal interference of classical and nonclassical light at an asymmetrical beam splitter is discussed based on two-photon interference in Feynman's path integral theory. The visibility of the second-order interference pattern is determined by the properties of the superposed light beams, the ratio between the intensities of these two light beams, and the reflectivity of the asymmetrical beam splitter. Some requirements about the asymmetrical beam splitter have to be satisfied in order to ensure that the visibility of the second-order interference pattern of nonclassical light beams exceeds the classical limit. The visibility of the second-order interference pattern of photons emitted by two independent single-photon sources is independent of the ratio between the intensities. These conclusions are important for the researches and applications in quantum optics and quantum information when an asymmetrical beam splitter is employed.
基金financially supported by the University of Kashan(Grant Number:363460/5)Iranian Nanotechnology Development Committee(Grant Number:1396/17)
文摘Wave propagation analysis for a functionally graded nanobeam with rectangular cross-section resting on visco-Pasternak's foundation is studied in this paper. Timoshenko's beam model and nonlocal elasticity theory are employed for formulation of the problem. The equations of motion are derived using Hamilton's principals by calculating kinetic energy, strain energy and work due to viscoelastic foundation. The effects of various parameters such as wavenumber, non-homogeneous index, nonlocal parameter and three parameters of foundation are performed on the phase velocity of the nanobeam. The obtained results indicate that some parameters such as non-homogeneous index, nonlocal parameter and wavenumber have significant effect on the response of the system.
文摘Cu x S thin films are implanted by low energy N + ion beam. The influences of the energy and dose of N + ion implantation on Cu x S films are investigated. The results show that the ratio of copper to sulfur is increased to some extent, the constituents of the film are turned to rich copper phase from rich sulfurous phase after ion beam irradiation. X-ray diffraction spectrum and optical transmission spectra of sample have confirmed the results.
文摘Air or inert atmosphere irradiation of liquid normal alkanes C5-C8 and benzene by electron beam was carried out. Oxidation (in the air) or isomerization (in the inert gases) of liquid normal alkanes under electron beam was shown. Action of electron beam on benzene molecules in the air or in the inert atmosphere leads to biphenyl, terphenyl and polymers. Irradiation by the bunch of electrons of mixture hexane with 10% benzene reduced to firm fractions (fullerene's similar structures) in a deposit.
文摘A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation. Results of numerically simulating the injected field at z =0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides (with linear and/or nonlinear refractive index) , which are similar to those in the related publications. Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator. The iterative process needs fewer steps to be stable. Also, when the light wave meets the changes of mediums, the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.
文摘Thin films of ZnxCd1-xS have been prepared by electron beam evaporation of a mixture of ZnS & CdS powders. The films are deposited onto sodalime glass slides under similar conditions.The composition of the films is varied from CdS to ZnS (x=0 to 1). The films show a regular change in color from toner red to orange yellow as Zn concentration increases to maximum.These films are characterized for their optical, electricaI and structural properties. The bandgap value of ZnxCd1-xS films is found to vary linearIy from 2.20 eV to 3.44 eV with change in the x value from 0 to 1. The resistivity of these films is in the range of 171.0 Ωcm to 5.5× 106Ωcm for x=0~0.6. All the samples show cubic structure after annealing in air at 250℃ for 40 min.The lattice constant ao varies from 0.5884 nm to 0.54109 nm linearly.
文摘Utilizing the Young’s double slits and Mach-Zehnder interferometer, we proposed an experimental method to measure the generalized Stokes parameters of a radially polarized random electromagnetic beam. After the partially coherent beam propagating through the Young’s double slits, the interference fringe is obtained by the help of a Mach-Zehnder interferometer consisting of apertures, quarter-wave plates and polarizers. The electric cross-spectral density matrix is detected by the coherence degree of interference fringe and the density of each single slit. The generalized Stokes parameters can be obtained from the electric cross-spectral density matrix. This experiment measures the generalized Stokes parameters of the random electromagnetic beam successfully. The results show that the spectral degree of coherence for copolarized cases (xx and yy) is similar with that for cross-polaried cases (xy and yx) for the radially polarized random electromagnetic beam. This method will help us determine the change of the polarization and coherence of the light in propagation by detecting the change of the generalized Stokes parameters.
文摘A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while under the force P exists the modulus of the subgrade reaction k, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.
文摘The basic concepts about the active structures and some attributes of the modes were presented in paper “Liner Active Structures and Modes]( I) ". The characteristics of the active discrete systems and active beams were discussed, especially, the stability of the active structures and the orthogonality of the eigenvectors. The notes about modes were portrayed by a model of a seven-storeyed building with sensors and actuators. The concept of the adjoint active structure was extended from the discrete systems to the beams that were the representations of the continuous structures. Two types of beams with different placements of the measuring and actuating systems were discussed in detail. One is the beam with the discrete sensors and actuators, and the other is the beam with distributed sensor and actuator function. The orthogonality conditions were derived with the modal shapes of the active beam and its adjoint active beam. An example shows that the variation of eigenvalues with feedback amplitude for the homo-configuration and non-homo-configuration active structures.