A damage detection method for complicated beam-like structures is proposed based on the subsection strain energy method （SSEM）, and its applicability condition is introduced. For a beam with the continuously varying...A damage detection method for complicated beam-like structures is proposed based on the subsection strain energy method （SSEM）, and its applicability condition is introduced. For a beam with the continuously varying fiexural stiffness and an edge crack, the SSEM is used to detect the crack location effectively by numerical modal shapes. As a complicated beam, the glass fiber-reinforced composite model of a wind turbine blade is studied based on an experimental modal analysis. The SSEM is used to calculate the damage index from the measured modal parameters and locate the damage position in the blade model successfully. The results indicate that the SSEM based on the modal shapes can be used to detect the damages in complicated beams or beam-like structures for engineering applications.展开更多
The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation metho...The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.展开更多
Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of con...Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh’s quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh’s quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.展开更多
In the longitudinal seismic deformation method for shield tunnels,one of the most commonly used is the longitudinal equivalent stiffness beam model(LES)for simulating the mechanical behavior of the lining.In this mode...In the longitudinal seismic deformation method for shield tunnels,one of the most commonly used is the longitudinal equivalent stiffness beam model(LES)for simulating the mechanical behavior of the lining.In this model,axial deformation and bending deformation are independent,so the equivalent stiffness is a constant value.However,the actual situation is that axial deformation and bending deformation occur simultaneously,which is not considered in LES.At present,we are not clear about the effect on the calculation results when axial deformation and bending deformation occur simultaneously.Therefore,in this paper,we improve the traditional LES by taking the relative deformation as a load and considering the coordinated deformation of axial and bending degrees of freedom.This improved model is called DNLES,and its neutral axis equations are an explicit expression.Then,we propose an iterative algorithm to solve the calculation model of the DNLES-based longitudinal seismic deformation method.Through a calculation example,we find that the internal forces based on LES are notably underestimated than those of DNLES in the compression bending zone,while are overestimated in the tension bending zone.When considering the combined effect,the maximum bending moment reached 13.7 times that of the LES model,and the axial pressure and tension were about 1.14 and 0.96 times,respectively.Further analysis reveals the coordinated deformation process in the axial and bending directions of the shield tunnel,which leads to a consequent change in equivalent stiffness.This explains why,in the longitudinal seismic deformation method,the traditional LES may result in unreasonable calculation results.展开更多
基金supported by the National Basic Research Program of China (973 Program)(No. 2007CB714603)
文摘A damage detection method for complicated beam-like structures is proposed based on the subsection strain energy method （SSEM）, and its applicability condition is introduced. For a beam with the continuously varying fiexural stiffness and an edge crack, the SSEM is used to detect the crack location effectively by numerical modal shapes. As a complicated beam, the glass fiber-reinforced composite model of a wind turbine blade is studied based on an experimental modal analysis. The SSEM is used to calculate the damage index from the measured modal parameters and locate the damage position in the blade model successfully. The results indicate that the SSEM based on the modal shapes can be used to detect the damages in complicated beams or beam-like structures for engineering applications.
文摘The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.
基金supported by the Portuguese Foundation for Science and Tech-nology(FCT),under the project POCI 2010 and the PhD grant SFRH/BD/44696/2008
文摘Facing the lateral vibration problem of a machine rotor as a beam on elastic supports in bending,the authors deal with the free vibration of elastically restrained Bernoulli-Euler beams carrying a finite number of concentrated elements along their length.Based on Rayleigh’s quotient,an iterative strategy is developed to find the approximated torsional stiffness coefficients,which allows the reconciliation between the theoretical model results and the experimental ones,obtained through impact tests.The mentioned algorithm treats the vibration of continuous beams under a determined set of boundary and continuity conditions, including different torsional stiffness coefficients and the effect of attached concentrated masses and rotational inertias, not only in the energetic terms of the Rayleigh’s quotient but also on the mode shapes,considering the shape functions defined in branches.Several loading cases are examined and examples are given to illustrate the validity of the model and accuracy of the obtained natural frequencies.
基金the National Natural Science Foundation of China(Grant Nos.52130808 and 51878566)National Key R&D Program of China(Key Projects for International Science and Technology Innovation Cooperation between Governments,Grant No.2022YFE0104300).
文摘In the longitudinal seismic deformation method for shield tunnels,one of the most commonly used is the longitudinal equivalent stiffness beam model(LES)for simulating the mechanical behavior of the lining.In this model,axial deformation and bending deformation are independent,so the equivalent stiffness is a constant value.However,the actual situation is that axial deformation and bending deformation occur simultaneously,which is not considered in LES.At present,we are not clear about the effect on the calculation results when axial deformation and bending deformation occur simultaneously.Therefore,in this paper,we improve the traditional LES by taking the relative deformation as a load and considering the coordinated deformation of axial and bending degrees of freedom.This improved model is called DNLES,and its neutral axis equations are an explicit expression.Then,we propose an iterative algorithm to solve the calculation model of the DNLES-based longitudinal seismic deformation method.Through a calculation example,we find that the internal forces based on LES are notably underestimated than those of DNLES in the compression bending zone,while are overestimated in the tension bending zone.When considering the combined effect,the maximum bending moment reached 13.7 times that of the LES model,and the axial pressure and tension were about 1.14 and 0.96 times,respectively.Further analysis reveals the coordinated deformation process in the axial and bending directions of the shield tunnel,which leads to a consequent change in equivalent stiffness.This explains why,in the longitudinal seismic deformation method,the traditional LES may result in unreasonable calculation results.
