This study examines the nonlinear behaviors of a clamped-clamped porous pipe made of a functionally graded material(FGM)that conveys fluids and is equipped with a retaining clip,focusing on primary resonance and subcr...This study examines the nonlinear behaviors of a clamped-clamped porous pipe made of a functionally graded material(FGM)that conveys fluids and is equipped with a retaining clip,focusing on primary resonance and subcritical dynamics.The nonlinear governing equations for the FGM pipe are derived by the extended Hamilton's principle,and subsequently discretized through the application of the Galerkin method.The direct method of multi-scales is then used to solve the derived equations.A thorough analysis of various parameters,including the clip stiffness,the power-law index,the porosity,and the clip location,is conducted to gain a comprehensive understanding of the system's nonlinear dynamics.Through the analysis of the first natural frequency,the study highlights the influence of the flow velocity and the clip stiffness,while the comparisons with metallic pipes emphasize the role of FGM composition.The examination of the forced response curves reveals saddle-node bifurcations and their dependence on parameters such as the detuning parameter and the power-law index,offering valuable insights into the system's nonlinear resonant behavior.Furthermore,the frequency-response curves illustrate the hardening nonlinearities influenced by factors such as the porosity and the clip stiffness,revealing nuanced effects on the system response and resonance characteristics.This comprehensive analysis enhances the understanding of nonlinear behaviors in FGM porous pipes with a retaining clip,providing key insights for practical engineering applications in system design and optimization.展开更多
The hollow centre cracked disc(HCCD) specimen is one of the suggested alternative methods for determining the fracture toughness of rock. This work aims to investigate the fracture mechanism in HCCD in macro- and micr...The hollow centre cracked disc(HCCD) specimen is one of the suggested alternative methods for determining the fracture toughness of rock. This work aims to investigate the fracture mechanism in HCCD in macro- and micro-scales using numerical methods, extended finite element method(X-FEM) and particle flow code(PFC) modeling, respectively. In the X-FEM, heaviside and near-tip enrichment functions are employed to consider the presence of the crack in the model. In PFC modeling the movement and interaction of stressed assemblies of rigid spherical particles are modeled using the distinct element method(DEM). A numerical code called MEX-FEM based on XFEM has been developed to simulate the problems involving crack. The models of pure modes I and Ⅱ in macro-scale are simulated in micro-scale. The results show that dimensionless stress intensity factors(YI, YⅡ) for pure modes I and Ⅱ increase by increasing the crack length ratio. The angle at which the pure mode Ⅱ occurs decreases by increasing the crack length ratio. In mixed mode I-Ⅱ, The value of YI decreases by increasing the crack angle, while the value of YⅡ increases to a given crack angle and then it decreases. Moreover, the fracture in micro-scale, unlike the macro-scale, includes a combination of different modes of fracturing.展开更多
The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the ro...The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonlinearity in the inertia, the curvature, and the electromagnetic load. After discretization of the governing partial differential equations by the Galerkin method, the multiple-scale perturbation method is used to derive the approximate solutions to the equations. In the numerical results, the effects of the electromagnetic parameter load, the damping coefficient, the amplitude of the initial displacement, the mass moment of inertia, and the rotation speed on the linear and nonlinear backward and forward frequencies are investigated. The results show that the magnetic field has significant effects on the nonlinear frequency of oscillation.展开更多
文摘This study examines the nonlinear behaviors of a clamped-clamped porous pipe made of a functionally graded material(FGM)that conveys fluids and is equipped with a retaining clip,focusing on primary resonance and subcritical dynamics.The nonlinear governing equations for the FGM pipe are derived by the extended Hamilton's principle,and subsequently discretized through the application of the Galerkin method.The direct method of multi-scales is then used to solve the derived equations.A thorough analysis of various parameters,including the clip stiffness,the power-law index,the porosity,and the clip location,is conducted to gain a comprehensive understanding of the system's nonlinear dynamics.Through the analysis of the first natural frequency,the study highlights the influence of the flow velocity and the clip stiffness,while the comparisons with metallic pipes emphasize the role of FGM composition.The examination of the forced response curves reveals saddle-node bifurcations and their dependence on parameters such as the detuning parameter and the power-law index,offering valuable insights into the system's nonlinear resonant behavior.Furthermore,the frequency-response curves illustrate the hardening nonlinearities influenced by factors such as the porosity and the clip stiffness,revealing nuanced effects on the system response and resonance characteristics.This comprehensive analysis enhances the understanding of nonlinear behaviors in FGM porous pipes with a retaining clip,providing key insights for practical engineering applications in system design and optimization.
文摘The hollow centre cracked disc(HCCD) specimen is one of the suggested alternative methods for determining the fracture toughness of rock. This work aims to investigate the fracture mechanism in HCCD in macro- and micro-scales using numerical methods, extended finite element method(X-FEM) and particle flow code(PFC) modeling, respectively. In the X-FEM, heaviside and near-tip enrichment functions are employed to consider the presence of the crack in the model. In PFC modeling the movement and interaction of stressed assemblies of rigid spherical particles are modeled using the distinct element method(DEM). A numerical code called MEX-FEM based on XFEM has been developed to simulate the problems involving crack. The models of pure modes I and Ⅱ in macro-scale are simulated in micro-scale. The results show that dimensionless stress intensity factors(YI, YⅡ) for pure modes I and Ⅱ increase by increasing the crack length ratio. The angle at which the pure mode Ⅱ occurs decreases by increasing the crack length ratio. In mixed mode I-Ⅱ, The value of YI decreases by increasing the crack angle, while the value of YⅡ increases to a given crack angle and then it decreases. Moreover, the fracture in micro-scale, unlike the macro-scale, includes a combination of different modes of fracturing.
文摘The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonlinearity in the inertia, the curvature, and the electromagnetic load. After discretization of the governing partial differential equations by the Galerkin method, the multiple-scale perturbation method is used to derive the approximate solutions to the equations. In the numerical results, the effects of the electromagnetic parameter load, the damping coefficient, the amplitude of the initial displacement, the mass moment of inertia, and the rotation speed on the linear and nonlinear backward and forward frequencies are investigated. The results show that the magnetic field has significant effects on the nonlinear frequency of oscillation.
