A frequency and amplitude dependent model is used to describe the complex behavior of rail pads. ... more A frequency and amplitude dependent model is used to describe the complex behavior of rail pads. It is implemented into the dynamic analysis of three dimensional coupled vehicle-slab track (3D-CVST) systems. The vehicle is treated as a 35-degreeof-freedom multi-body system, and the slab track is represented by two continuous Bernoulli-Euler beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The rail pad model takes into account the influences of the excitation frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, respectively. The Grünwald representation of the fractional derivatives is employed to numerically solve the fractional and nonlinear equations of motion of the 3D-CVST system by means of an explicit integration algorithm. A dynamic analysis of the 3D-CVST system exposed to excitations of rail harmonic irregularities is primarily carried out, which reveals the dependence of stiffness and damping on excitation frequency and displacement amplitude. Subsequently, sensitive analyses of the model parameters are investigated by conducting the dynamic analysis of the 3D-CVST system subjected to excitations of welded rail joint irregularities. Following this, parameters of the rail pad model are optimized with respect to experimental values. For elucidation, the 3D-CVST dynamic model incorporated with the rail pads model is used to calculate the wheel/rail forces induced by excitations of measured random track irregularities. Further, the numerical results are compared with experimental data, demonstrating the reliability of the proposed model. rail pads, vehicle-track coupled dynamics, frequency dependent, amplitude dependent Citation: Zhu S Y, Cai C B, Luo Z, et al. A frequency and amplitude dependent model of rail pads for the dynamic analysis of train-track interaction.
This study aims to effectively and robustly suppress the low-frequency vibrations of floating sla... more This study aims to effectively and robustly suppress the low-frequency vibrations of floating slab tracks (FSTs) using dynamic vibration absorbers (DVAs). First, the optimal locations where the DVAs are attached are determined by modal analysis with a finite element model of the FST. Further, by identifying the equivalent mass of the concerned modes, the optimal stiffness and damping coefficient of each DVA are obtained to minimise the resonant vibration amplitudes based on fixed-point theory. Finally, a three-dimensional coupled dynamic model of a metro vehicle and the FST with the DVAs is developed based on the nonlinear Hertzian contact theory and the modified Kalker linear creep theory. The track irregularities are included and generated by means of a time-frequency transformation technique. The effect of the DVAs on the vibration absorption of the FST subjected to the vehicle dynamic loads is evaluated with the help of the insertion loss in one-third octave frequency bands. The sensitivities of the mass ratio of DVAs and the damping ratio of steel-springs under the floating slab are discussed as well, which provided engineers with the DVA's adjustable room for vibration mitigation. The numerical results show that the proposed DVAs could effectively suppress low-frequency vibrations of the FST when tuned correctly and attached properly. The insertion loss due to the attachment of DVAs increases as the mass ratio increases, whereas it decreases with the increase in the damping ratio of steel-springs.
A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the
complex be... more A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the
complex behavior of rail pads. It is implemented into the dynamic analysis of coupled
vehicle–slab track (CVST) systems. The vehicle is treated as a multi-body system with 10
degrees of freedom, and the slab track is represented by a three layer Bernoulli–Euler
beam model. The model for the rail pads is one dimensional, and the force–displacement
relation is based on a superposition of elastic, friction, and FDV forces. This model takes
into account the influences of the excitation frequency and of the displacement amplitude
through a fractional derivative element, and a nonlinear friction element, respectively. The
Grünwald representation of the fractional derivatives is employed to numerically solve the
fractional and nonlinear equations of motion of the CVST system by means of an explicit
integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail
harmonic irregularities is carried out, pointing out the stiffness and damping dependence
on the excitation frequency and the displacement amplitude. The analysis indicates that
the dynamic stiffness and damping of the rail pads increase with the excitation frequency
while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under
excitations of welded rail joint irregularities and of random track irregularities, are
conducted in the time domain as well as in the frequency domain. The proposed model is
shown to possess several modeling advantages over the ordinary Kelvin element which
overestimates both the stiffness and damping features at high frequencies
The damage evolution and dynamic performance of a cement asphalt (CA) mortar layer of slab track ... more The damage evolution and dynamic performance of a cement asphalt (CA) mortar layer of slab track subjected to vehicle dynamic load is investigated in this paper. Initially, a statistical damage constitutive model for the CA mortar layer is developed using continuous damage mechanics and probability theory. In this model, the strength of the CA mortar elements is treated as a random variable, which follows the Weibull distribution. The inclusion of strain rate dependence affords considering its influence on the damage development and the transition between viscosity and elasticity. Comparisons with experimental data support the reliability of the model. A three-dimensional finite element (FE) model of a slab track is then created with the commercial software ABAQUS, where the devised model for the CA mortar is implemented as a user-defined material subroutine. Finally, a vertical vehicle model is coupled with the FE model of the slab track, through the wheel-rail contact forces, based on the nonlinear Hertzian contact theory. The evolution of the damage and of the dynamic performance of the CA mortar layer with various initial damage is investigated under the train and track interaction. The analysis indicates that the proposed model is capable of predicting the damage evolution of the CA mortar layer exposed to vehicle dynamic load. The dynamic compressive strain, the strain rate, and the induced damage increase significantly with an increase in the initial damage, whereas the dynamic compressive stress exhibits a sharp decrease with the increasing initial damage. Also, it is found that the strain rate dependence significantly influences the damage evolution and the dynamic behavior of the CA mortar layer. cement asphalt mortar, slab track, statistical damage constitutive model, vehicle-track coupled dynamics, damage evolution Citation: Zhu S Y, Fu Q, Cai C B, et al. Damage evolution and dynamic response of cement asphalt mortar layer of slab track under vehicle dynamic load. Sci
Extended finite element method Vehicle-track coupled dynamics Stress intensity factors a b s t r ... more Extended finite element method Vehicle-track coupled dynamics Stress intensity factors a b s t r a c t
This paper presents a three-dimensional finite element model to investigate the interface damage ... more This paper presents a three-dimensional finite element model to investigate the interface damage occurred between prefabricated slab and CA (cement asphalt) mortar layer in the China Railway Track System (CRTS-II) slab track system. In the finite element model, a cohesive zone model with a non-linear constitutive law is introduced and utilized to model the damage, cracking and delamination at the interface. Combining with the temperature field database obtained from the three-dimensional transient heat transfer analysis, the interface damage evolution as a result of temperature change is analyzed. A three-dimensional coupled dynamic model of a vehicle and the slab track is then established to calculate the varying rail-supporting forces which are utilized as the inputs to the finite element model. The non-linearities of the wheel-rail contact geometry, the wheel-rail normal contact force and the wheel-rail tangential creep force are taken into account in the model. Setting the maximum interface damaged state calculated under temperature change as the initial condition, the interface damage evolution and its influence on the dynamic response of the slab track are investigated under the joint action of the temperature change and vehicle dynamic load. The analysis indicates that the proposed model is capable of predicting the initiation and propagation of cracks at the interface. The prefabricated slab presents lateral warping, resulting in severe interface damage on both the sides of the slab track along the longitudinal direction during temperature drop process, while the interface damage level does not change significantly under vehicle dynamic loads. The interface damage has great effects on the dynamic responses of the slab track.
A frequency and amplitude dependent model is used to describe the complex behavior of rail pads. ... more A frequency and amplitude dependent model is used to describe the complex behavior of rail pads. It is implemented into the dynamic analysis of three dimensional coupled vehicle-slab track (3D-CVST) systems. The vehicle is treated as a 35-degreeof-freedom multi-body system, and the slab track is represented by two continuous Bernoulli-Euler beams supported by a series of elastic rectangle plates on a viscoelastic foundation. The rail pad model takes into account the influences of the excitation frequency and of the displacement amplitude through a fractional derivative element, and a nonlinear friction element, respectively. The Grünwald representation of the fractional derivatives is employed to numerically solve the fractional and nonlinear equations of motion of the 3D-CVST system by means of an explicit integration algorithm. A dynamic analysis of the 3D-CVST system exposed to excitations of rail harmonic irregularities is primarily carried out, which reveals the dependence of stiffness and damping on excitation frequency and displacement amplitude. Subsequently, sensitive analyses of the model parameters are investigated by conducting the dynamic analysis of the 3D-CVST system subjected to excitations of welded rail joint irregularities. Following this, parameters of the rail pad model are optimized with respect to experimental values. For elucidation, the 3D-CVST dynamic model incorporated with the rail pads model is used to calculate the wheel/rail forces induced by excitations of measured random track irregularities. Further, the numerical results are compared with experimental data, demonstrating the reliability of the proposed model. rail pads, vehicle-track coupled dynamics, frequency dependent, amplitude dependent Citation: Zhu S Y, Cai C B, Luo Z, et al. A frequency and amplitude dependent model of rail pads for the dynamic analysis of train-track interaction.
This study aims to effectively and robustly suppress the low-frequency vibrations of floating sla... more This study aims to effectively and robustly suppress the low-frequency vibrations of floating slab tracks (FSTs) using dynamic vibration absorbers (DVAs). First, the optimal locations where the DVAs are attached are determined by modal analysis with a finite element model of the FST. Further, by identifying the equivalent mass of the concerned modes, the optimal stiffness and damping coefficient of each DVA are obtained to minimise the resonant vibration amplitudes based on fixed-point theory. Finally, a three-dimensional coupled dynamic model of a metro vehicle and the FST with the DVAs is developed based on the nonlinear Hertzian contact theory and the modified Kalker linear creep theory. The track irregularities are included and generated by means of a time-frequency transformation technique. The effect of the DVAs on the vibration absorption of the FST subjected to the vehicle dynamic loads is evaluated with the help of the insertion loss in one-third octave frequency bands. The sensitivities of the mass ratio of DVAs and the damping ratio of steel-springs under the floating slab are discussed as well, which provided engineers with the DVA's adjustable room for vibration mitigation. The numerical results show that the proposed DVAs could effectively suppress low-frequency vibrations of the FST when tuned correctly and attached properly. The insertion loss due to the attachment of DVAs increases as the mass ratio increases, whereas it decreases with the increase in the damping ratio of steel-springs.
A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the
complex be... more A nonlinear and fractional derivative viscoelastic (FDV) model is used to capture the
complex behavior of rail pads. It is implemented into the dynamic analysis of coupled
vehicle–slab track (CVST) systems. The vehicle is treated as a multi-body system with 10
degrees of freedom, and the slab track is represented by a three layer Bernoulli–Euler
beam model. The model for the rail pads is one dimensional, and the force–displacement
relation is based on a superposition of elastic, friction, and FDV forces. This model takes
into account the influences of the excitation frequency and of the displacement amplitude
through a fractional derivative element, and a nonlinear friction element, respectively. The
Grünwald representation of the fractional derivatives is employed to numerically solve the
fractional and nonlinear equations of motion of the CVST system by means of an explicit
integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail
harmonic irregularities is carried out, pointing out the stiffness and damping dependence
on the excitation frequency and the displacement amplitude. The analysis indicates that
the dynamic stiffness and damping of the rail pads increase with the excitation frequency
while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under
excitations of welded rail joint irregularities and of random track irregularities, are
conducted in the time domain as well as in the frequency domain. The proposed model is
shown to possess several modeling advantages over the ordinary Kelvin element which
overestimates both the stiffness and damping features at high frequencies
The damage evolution and dynamic performance of a cement asphalt (CA) mortar layer of slab track ... more The damage evolution and dynamic performance of a cement asphalt (CA) mortar layer of slab track subjected to vehicle dynamic load is investigated in this paper. Initially, a statistical damage constitutive model for the CA mortar layer is developed using continuous damage mechanics and probability theory. In this model, the strength of the CA mortar elements is treated as a random variable, which follows the Weibull distribution. The inclusion of strain rate dependence affords considering its influence on the damage development and the transition between viscosity and elasticity. Comparisons with experimental data support the reliability of the model. A three-dimensional finite element (FE) model of a slab track is then created with the commercial software ABAQUS, where the devised model for the CA mortar is implemented as a user-defined material subroutine. Finally, a vertical vehicle model is coupled with the FE model of the slab track, through the wheel-rail contact forces, based on the nonlinear Hertzian contact theory. The evolution of the damage and of the dynamic performance of the CA mortar layer with various initial damage is investigated under the train and track interaction. The analysis indicates that the proposed model is capable of predicting the damage evolution of the CA mortar layer exposed to vehicle dynamic load. The dynamic compressive strain, the strain rate, and the induced damage increase significantly with an increase in the initial damage, whereas the dynamic compressive stress exhibits a sharp decrease with the increasing initial damage. Also, it is found that the strain rate dependence significantly influences the damage evolution and the dynamic behavior of the CA mortar layer. cement asphalt mortar, slab track, statistical damage constitutive model, vehicle-track coupled dynamics, damage evolution Citation: Zhu S Y, Fu Q, Cai C B, et al. Damage evolution and dynamic response of cement asphalt mortar layer of slab track under vehicle dynamic load. Sci
Extended finite element method Vehicle-track coupled dynamics Stress intensity factors a b s t r ... more Extended finite element method Vehicle-track coupled dynamics Stress intensity factors a b s t r a c t
This paper presents a three-dimensional finite element model to investigate the interface damage ... more This paper presents a three-dimensional finite element model to investigate the interface damage occurred between prefabricated slab and CA (cement asphalt) mortar layer in the China Railway Track System (CRTS-II) slab track system. In the finite element model, a cohesive zone model with a non-linear constitutive law is introduced and utilized to model the damage, cracking and delamination at the interface. Combining with the temperature field database obtained from the three-dimensional transient heat transfer analysis, the interface damage evolution as a result of temperature change is analyzed. A three-dimensional coupled dynamic model of a vehicle and the slab track is then established to calculate the varying rail-supporting forces which are utilized as the inputs to the finite element model. The non-linearities of the wheel-rail contact geometry, the wheel-rail normal contact force and the wheel-rail tangential creep force are taken into account in the model. Setting the maximum interface damaged state calculated under temperature change as the initial condition, the interface damage evolution and its influence on the dynamic response of the slab track are investigated under the joint action of the temperature change and vehicle dynamic load. The analysis indicates that the proposed model is capable of predicting the initiation and propagation of cracks at the interface. The prefabricated slab presents lateral warping, resulting in severe interface damage on both the sides of the slab track along the longitudinal direction during temperature drop process, while the interface damage level does not change significantly under vehicle dynamic loads. The interface damage has great effects on the dynamic responses of the slab track.
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Papers by Shengyang Zhu
complex behavior of rail pads. It is implemented into the dynamic analysis of coupled
vehicle–slab track (CVST) systems. The vehicle is treated as a multi-body system with 10
degrees of freedom, and the slab track is represented by a three layer Bernoulli–Euler
beam model. The model for the rail pads is one dimensional, and the force–displacement
relation is based on a superposition of elastic, friction, and FDV forces. This model takes
into account the influences of the excitation frequency and of the displacement amplitude
through a fractional derivative element, and a nonlinear friction element, respectively. The
Grünwald representation of the fractional derivatives is employed to numerically solve the
fractional and nonlinear equations of motion of the CVST system by means of an explicit
integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail
harmonic irregularities is carried out, pointing out the stiffness and damping dependence
on the excitation frequency and the displacement amplitude. The analysis indicates that
the dynamic stiffness and damping of the rail pads increase with the excitation frequency
while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under
excitations of welded rail joint irregularities and of random track irregularities, are
conducted in the time domain as well as in the frequency domain. The proposed model is
shown to possess several modeling advantages over the ordinary Kelvin element which
overestimates both the stiffness and damping features at high frequencies
complex behavior of rail pads. It is implemented into the dynamic analysis of coupled
vehicle–slab track (CVST) systems. The vehicle is treated as a multi-body system with 10
degrees of freedom, and the slab track is represented by a three layer Bernoulli–Euler
beam model. The model for the rail pads is one dimensional, and the force–displacement
relation is based on a superposition of elastic, friction, and FDV forces. This model takes
into account the influences of the excitation frequency and of the displacement amplitude
through a fractional derivative element, and a nonlinear friction element, respectively. The
Grünwald representation of the fractional derivatives is employed to numerically solve the
fractional and nonlinear equations of motion of the CVST system by means of an explicit
integration algorithm. A dynamic analysis of the CVST system exposed to excitations of rail
harmonic irregularities is carried out, pointing out the stiffness and damping dependence
on the excitation frequency and the displacement amplitude. The analysis indicates that
the dynamic stiffness and damping of the rail pads increase with the excitation frequency
while they decrease with the displacement amplitude. Furthermore, comparisons between the proposed model and ordinary Kelvin model adopted for the CVST system, under
excitations of welded rail joint irregularities and of random track irregularities, are
conducted in the time domain as well as in the frequency domain. The proposed model is
shown to possess several modeling advantages over the ordinary Kelvin element which
overestimates both the stiffness and damping features at high frequencies