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
A mechanical model is proposed for the system of elastic beam and strain-softening pillar where strain localization is initiated at peak shear stress. To obtain the plastic deformation of the pillar due to the shear s...A mechanical model is proposed for the system of elastic beam and strain-softening pillar where strain localization is initiated at peak shear stress. To obtain the plastic deformation of the pillar due to the shear slips of multiple shear bands, the pillar is divided into several narrow slices where compressive deformation is treated as uniformity. In the light of the compatibility condition of deformation, the total compressive displacement of the pillar is equal to the displacement of the beam in the middle span. An instability criterion is derived analytically based on the energy principle using a known size of localization band according to gradient dependent plasticity. The main advantage of the present model is that the effects of the constitutive parameters of rock and the geometrical size of structure are reflected in the criterion. The condition that the derivative of distributed load with respect to the deflection of the beam in the middle span is less than zero is not only equivalent to, but also even more concise in form than the instability criterion. To study the influences of constitutive parameters and geometrical size on stability, some examples are presented.展开更多
Based on the theory of concrete structure, a new expression was derived for lagged strain of fiber-reinforced polymer （FLIP） laminates in reinforced concrete （RC） beams strengthened with FRP. The influence of diff...Based on the theory of concrete structure, a new expression was derived for lagged strain of fiber-reinforced polymer （FLIP） laminates in reinforced concrete （RC） beams strengthened with FRP. The influence of different preloaded states and nonlinear stress-strain relationship of compressed concrete were both taken into account in this approach. Then a simplified expression was given by ignoring tensile resistance of concrete. Comparison of analytical predictions with experimental results indicates satisfactory accuracy of the procedures. The errors are less than 8% and 10% respectively when the tensile resistance of concrete is or not considered. While the maximum error of existing procedures is up to 60%.展开更多
提出了缺陷桩-梁系统的理论模型。桩周土采用了三维连续介质模型,桩身则采用Rayleigh-love杆件,以考虑大直径桩的横向惯性效应。为了模拟桩身的缺陷段,采用了不同于正常桩身半径的桩段。通过结合阻抗函数递推法、虚土环法(ring soil pil...提出了缺陷桩-梁系统的理论模型。桩周土采用了三维连续介质模型,桩身则采用Rayleigh-love杆件,以考虑大直径桩的横向惯性效应。为了模拟桩身的缺陷段,采用了不同于正常桩身半径的桩段。通过结合阻抗函数递推法、虚土环法(ring soil pile theory,简称RSPT)和修正的阻抗函数递推法(amended impedance function transfer method,简称AIFTM),得到了桩-土系统的桩顶阻抗。桩顶梁采用了Timoshenko杆件进行模拟,同时在桩-梁连接处施加瞬态激振。成功求得了桩-梁系统动力响应在频域内的解析解,并利用离散傅里叶变换获得了时域内的半解析解。为了验证模型的合理性,将获得的半解析解与试验数据和有限元法结果进行了对比。研究结果显示,桩-梁系统较为适合的激振拾取点通常为桩梁连接处,同时需要综合考虑桩梁参数的影响。最后,通过参数分析方法探讨了在桩-梁系统上使用低应变测试的注意事项。展开更多
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.
文摘A mechanical model is proposed for the system of elastic beam and strain-softening pillar where strain localization is initiated at peak shear stress. To obtain the plastic deformation of the pillar due to the shear slips of multiple shear bands, the pillar is divided into several narrow slices where compressive deformation is treated as uniformity. In the light of the compatibility condition of deformation, the total compressive displacement of the pillar is equal to the displacement of the beam in the middle span. An instability criterion is derived analytically based on the energy principle using a known size of localization band according to gradient dependent plasticity. The main advantage of the present model is that the effects of the constitutive parameters of rock and the geometrical size of structure are reflected in the criterion. The condition that the derivative of distributed load with respect to the deflection of the beam in the middle span is less than zero is not only equivalent to, but also even more concise in form than the instability criterion. To study the influences of constitutive parameters and geometrical size on stability, some examples are presented.
基金Project(2002G043) supported by the Science & Technology Research Program of Chinese Railway MinistryProject (05JJ30101)supported by the Natural Science Foundation of Hunan Province, China
文摘Based on the theory of concrete structure, a new expression was derived for lagged strain of fiber-reinforced polymer （FLIP） laminates in reinforced concrete （RC） beams strengthened with FRP. The influence of different preloaded states and nonlinear stress-strain relationship of compressed concrete were both taken into account in this approach. Then a simplified expression was given by ignoring tensile resistance of concrete. Comparison of analytical predictions with experimental results indicates satisfactory accuracy of the procedures. The errors are less than 8% and 10% respectively when the tensile resistance of concrete is or not considered. While the maximum error of existing procedures is up to 60%.
文摘提出了缺陷桩-梁系统的理论模型。桩周土采用了三维连续介质模型,桩身则采用Rayleigh-love杆件,以考虑大直径桩的横向惯性效应。为了模拟桩身的缺陷段,采用了不同于正常桩身半径的桩段。通过结合阻抗函数递推法、虚土环法(ring soil pile theory,简称RSPT)和修正的阻抗函数递推法(amended impedance function transfer method,简称AIFTM),得到了桩-土系统的桩顶阻抗。桩顶梁采用了Timoshenko杆件进行模拟,同时在桩-梁连接处施加瞬态激振。成功求得了桩-梁系统动力响应在频域内的解析解,并利用离散傅里叶变换获得了时域内的半解析解。为了验证模型的合理性,将获得的半解析解与试验数据和有限元法结果进行了对比。研究结果显示,桩-梁系统较为适合的激振拾取点通常为桩梁连接处,同时需要综合考虑桩梁参数的影响。最后,通过参数分析方法探讨了在桩-梁系统上使用低应变测试的注意事项。
