In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even ap...In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even approximately is difficult. However, rather than solving the system of 4 first-order equations governing the dynamics of each cable, the governing equations are instead converted to a set of equations that the exterior matrix satisfies. Therefore, the exterior matrix method （EMM） is used without solving the original governing equations. Even though this produces a system of 6 first-order equations, the simple asymptotic techniques to find the first three terms of the perturbative solution can be used. The solutions can then be assembled to produce a 6 x 6 exterior matrix for a cable section. The matrices for each cable in the structure are multiplied together, along with the exterior matrices for each joint. The roots of the product give us the eigenfrequencies of the system.展开更多
In-plane auto-parametric stochastic vibration of inclined cables subjected to Gaussian white noise in transverse bridge orientation is investigated. Based on Newton＇s laws of motion and Galerkin＇s modal truncation p...In-plane auto-parametric stochastic vibration of inclined cables subjected to Gaussian white noise in transverse bridge orientation is investigated. Based on Newton＇s laws of motion and Galerkin＇s modal truncation principle, the influences of geometry nonlinearity induced by sag and large displacement of cables and the initial equilibrium state are taken into account. Meanwhile, the three-dimensional non-linear differential equations of inclined cables for coupling vibration are deduced, equivalent stochastic linearization method is applied to derive the 14-dimensional first-order nonlinear differential equations of state vectors, and the Runge-Kutta integration method is utilized to obtain the root mean square （RMS） response. Results show that when the transverse random excitation imposed on the stayed cable exceeds a critical value, the in-plane transverse vibration of the cable are excited due to tim auto-parametric nonlinear coupling, and the critical value of random excitation increases with the damping ratio. In this motion, the cable response possesses non-stationary characteristics, even though the loading keeps stationary.展开更多
A dynamic model for an inclined carbon ?ber reinforced polymer(CFRP)cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-p...A dynamic model for an inclined carbon ?ber reinforced polymer(CFRP)cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-plane and out-of-plane dynamics of the inclined CFRP cable are obtained by Hamilton's principle. The linear eigenvalues are explored theoretically. Then, the ordinary differential equations for analyzing the dynamic behaviors are obtained by the Galerkin integral and dimensionless treatments.The steady-state solutions of the nonlinear equations are obtained by the multiple scale method(MSM) and the Newton-Raphson method. The frequency-and force-response curves are used to investigate the dynamic behaviors of the inclined CFRP cable under simultaneous internal(between the lowest in-plane and out-of-plane modes) and external resonances, i.e., the primary resonances induced by the excitations of the in-plane mode,the out-of-plane mode, and both the in-plane mode and the out-of-plane mode, respectively. The effects of the key parameters, e.g., Young's modulus, the excitation amplitude,and the frequency on the dynamic behaviors, are discussed in detail. Some interesting phenomena and results are observed and concluded.展开更多
In order to solve the surrounding rock control problem of large section gangue replacement roadway under complicated conditions, this paper analyzed the impact to the roadway controlling produced by the geological con...In order to solve the surrounding rock control problem of large section gangue replacement roadway under complicated conditions, this paper analyzed the impact to the roadway controlling produced by the geological conditions such as high ground stress, folded structure tilted roof asymmetry and soft wall rock, and built the tilt layered roof structural mechanics model to clarify the increase span mechanism of the weak coal instability. Then, we proposed the combined control system including roof inclined truss cable, coal-side cable-channel steel and intensive bolt support. And then by building the structural mechanics model of roof inclined truss cable system, the support principle was described. Besides, according to this model, we deduced the calculation formula of cable anchoring force and its tensile stress. Finally surrounding rock control technology of large section roadway in fold coal pillar area was formed. Field practice shows that the greatest roof convergence of gangue replacement roadway is 158 mm and coal-side deformation is 243 mm. Roadway deformation is controlled effectively and technical support is provided for replacement mining.展开更多
Combining lubrication theory and CFD technology, a finite element model is established to simulate the rain-wind-induced vibration(RWIV). Based on Spalart-Allmaras(S-A)turbulence type, COMSOL software is adopted to ca...Combining lubrication theory and CFD technology, a finite element model is established to simulate the rain-wind-induced vibration(RWIV). Based on Spalart-Allmaras(S-A)turbulence type, COMSOL software is adopted to calculate the wind pressure coefficient and wind friction coefficient that vary with the location and time. To verify the veracity and rationality of this method, the formation and evolution of rivulets at different wind speeds are studied and compared with the existing experimental results. Furthermore, the time, location, height and width of the initial formation of rivulets are analyzed at different wind speeds, cable inclination angles and wind yaw angles. The results show that the three influencing factors mentioned above have great effect on the formation of rivulet, and the influencing tendency, range and degree are different from each other.展开更多
文摘In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even approximately is difficult. However, rather than solving the system of 4 first-order equations governing the dynamics of each cable, the governing equations are instead converted to a set of equations that the exterior matrix satisfies. Therefore, the exterior matrix method （EMM） is used without solving the original governing equations. Even though this produces a system of 6 first-order equations, the simple asymptotic techniques to find the first three terms of the perturbative solution can be used. The solutions can then be assembled to produce a 6 x 6 exterior matrix for a cable section. The matrices for each cable in the structure are multiplied together, along with the exterior matrices for each joint. The roots of the product give us the eigenfrequencies of the system.
基金Soft Science Foundation of Ministry of Construction of China (No.06-k3-14)
文摘In-plane auto-parametric stochastic vibration of inclined cables subjected to Gaussian white noise in transverse bridge orientation is investigated. Based on Newton＇s laws of motion and Galerkin＇s modal truncation principle, the influences of geometry nonlinearity induced by sag and large displacement of cables and the initial equilibrium state are taken into account. Meanwhile, the three-dimensional non-linear differential equations of inclined cables for coupling vibration are deduced, equivalent stochastic linearization method is applied to derive the 14-dimensional first-order nonlinear differential equations of state vectors, and the Runge-Kutta integration method is utilized to obtain the root mean square （RMS） response. Results show that when the transverse random excitation imposed on the stayed cable exceeds a critical value, the in-plane transverse vibration of the cable are excited due to tim auto-parametric nonlinear coupling, and the critical value of random excitation increases with the damping ratio. In this motion, the cable response possesses non-stationary characteristics, even though the loading keeps stationary.
基金Project supported by the National Natural Science Foundation of China(Nos.11572117 and 11502076)
文摘A dynamic model for an inclined carbon ?ber reinforced polymer(CFRP)cable is established, and the linear and nonlinear dynamic behaviors are investigated in detail. The partial differential equations for both the in-plane and out-of-plane dynamics of the inclined CFRP cable are obtained by Hamilton's principle. The linear eigenvalues are explored theoretically. Then, the ordinary differential equations for analyzing the dynamic behaviors are obtained by the Galerkin integral and dimensionless treatments.The steady-state solutions of the nonlinear equations are obtained by the multiple scale method(MSM) and the Newton-Raphson method. The frequency-and force-response curves are used to investigate the dynamic behaviors of the inclined CFRP cable under simultaneous internal(between the lowest in-plane and out-of-plane modes) and external resonances, i.e., the primary resonances induced by the excitations of the in-plane mode,the out-of-plane mode, and both the in-plane mode and the out-of-plane mode, respectively. The effects of the key parameters, e.g., Young's modulus, the excitation amplitude,and the frequency on the dynamic behaviors, are discussed in detail. Some interesting phenomena and results are observed and concluded.
文摘In order to solve the surrounding rock control problem of large section gangue replacement roadway under complicated conditions, this paper analyzed the impact to the roadway controlling produced by the geological conditions such as high ground stress, folded structure tilted roof asymmetry and soft wall rock, and built the tilt layered roof structural mechanics model to clarify the increase span mechanism of the weak coal instability. Then, we proposed the combined control system including roof inclined truss cable, coal-side cable-channel steel and intensive bolt support. And then by building the structural mechanics model of roof inclined truss cable system, the support principle was described. Besides, according to this model, we deduced the calculation formula of cable anchoring force and its tensile stress. Finally surrounding rock control technology of large section roadway in fold coal pillar area was formed. Field practice shows that the greatest roof convergence of gangue replacement roadway is 158 mm and coal-side deformation is 243 mm. Roadway deformation is controlled effectively and technical support is provided for replacement mining.
基金Supported by the National Natural Science Foundation of China(No.51408399)
文摘Combining lubrication theory and CFD technology, a finite element model is established to simulate the rain-wind-induced vibration(RWIV). Based on Spalart-Allmaras(S-A)turbulence type, COMSOL software is adopted to calculate the wind pressure coefficient and wind friction coefficient that vary with the location and time. To verify the veracity and rationality of this method, the formation and evolution of rivulets at different wind speeds are studied and compared with the existing experimental results. Furthermore, the time, location, height and width of the initial formation of rivulets are analyzed at different wind speeds, cable inclination angles and wind yaw angles. The results show that the three influencing factors mentioned above have great effect on the formation of rivulet, and the influencing tendency, range and degree are different from each other.
