In this paper,we investigate the existence of strange nonchaotic attractors(SNAs)in a slender rigid rocking block under quasi-periodic forcing with two frequencies.We find that an SNA can exist between a quasi-periodi...In this paper,we investigate the existence of strange nonchaotic attractors(SNAs)in a slender rigid rocking block under quasi-periodic forcing with two frequencies.We find that an SNA can exist between a quasi-periodic attractor and a chaotic attractor,or between two chaotic attractors.In particular,we demonstrate that a torus doubling bifurcation of a quasi-periodic attractor can result in SNAs via the fractal route before transforming into chaotic attractors.This phenomenon is rarely reported in quasiperiodically forced discontinuous differential equations and vibro-impact systems.The properties of SNAs are verified by the Lyapunov exponent,rational approximation,phase sensitivity,power spectrum,and separation of nearby trajectories.展开更多
A three-dimensional rigid body on the shape of a parallelepiped is modelled in order to rock on a side or a vertex of the base,in order to evaluate the seismic response of rigid blocks lying on a horizontal support.Th...A three-dimensional rigid body on the shape of a parallelepiped is modelled in order to rock on a side or a vertex of the base,in order to evaluate the seismic response of rigid blocks lying on a horizontal support.The center of mass of the body is considered as eccentric with respect to its geometric center.As seismic input,three Italian recorded accelerograms,with different spectral content,are used.The study is mainly conducted to highlight the differences between the seismic response of 2D and 3D models of rigid blocks,with the aim to understand if,in some cases,the use of the 3D model of rigid block is required to obtain safer results.In fact,the outcomes show that in some ranges of the geometrical and mechanical parameters that characterize the excitation and the body,a two-dimensional model,which is not able to consider the 3D rocking on a vertex,can provide unsafe results.In particular,it is found that the overturning process of the three-dimensional block can occur under excitations which are lower than those which overturn a corresponding two-dimensional block.展开更多
Rigid Finite Element Method (RFEM) was proposed to simulate the mechanical behavior of discontinuous structures such as rock and soil structures. The authors' work on the theory and applications of RFEM is summari...Rigid Finite Element Method (RFEM) was proposed to simulate the mechanical behavior of discontinuous structures such as rock and soil structures. The authors' work on the theory and applications of RFEM is summarized in this paper. Based on the theory of RFEM, the Elastic Body-Seams Model (EBSM) is proposed to take the deformation and damage of rock masses into account.展开更多
The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are propose...The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.展开更多
Using normal and shear rigid coefficients of intact rock and fracture plane, rigidly normal, shear equivalent rigid coefficients of fissure rock mass are conducted. On the basis of hypotheses of small displacement of ...Using normal and shear rigid coefficients of intact rock and fracture plane, rigidly normal, shear equivalent rigid coefficients of fissure rock mass are conducted. On the basis of hypotheses of small displacement of rock mass, principle of superposition, irrelevance of strength parameters C and T and Coulomb theory, formulas to calculate equivalent strength parameters C and phi of equivalent continuous mass from fissured rock mass with anchor piles are given. The achievement is extremely valuable in integral stability analysis of the rock mass slope and important in promoting the research of the rock mass's constitutive relation.展开更多
基金supported by the National Natural Science Foundation of China under grant number 11971019.
文摘In this paper,we investigate the existence of strange nonchaotic attractors(SNAs)in a slender rigid rocking block under quasi-periodic forcing with two frequencies.We find that an SNA can exist between a quasi-periodic attractor and a chaotic attractor,or between two chaotic attractors.In particular,we demonstrate that a torus doubling bifurcation of a quasi-periodic attractor can result in SNAs via the fractal route before transforming into chaotic attractors.This phenomenon is rarely reported in quasiperiodically forced discontinuous differential equations and vibro-impact systems.The properties of SNAs are verified by the Lyapunov exponent,rational approximation,phase sensitivity,power spectrum,and separation of nearby trajectories.
基金partially funded by FY 2009-2010 PRIN–Italian Ministry for Research
文摘A three-dimensional rigid body on the shape of a parallelepiped is modelled in order to rock on a side or a vertex of the base,in order to evaluate the seismic response of rigid blocks lying on a horizontal support.The center of mass of the body is considered as eccentric with respect to its geometric center.As seismic input,three Italian recorded accelerograms,with different spectral content,are used.The study is mainly conducted to highlight the differences between the seismic response of 2D and 3D models of rigid blocks,with the aim to understand if,in some cases,the use of the 3D model of rigid block is required to obtain safer results.In fact,the outcomes show that in some ranges of the geometrical and mechanical parameters that characterize the excitation and the body,a two-dimensional model,which is not able to consider the 3D rocking on a vertex,can provide unsafe results.In particular,it is found that the overturning process of the three-dimensional block can occur under excitations which are lower than those which overturn a corresponding two-dimensional block.
文摘Rigid Finite Element Method (RFEM) was proposed to simulate the mechanical behavior of discontinuous structures such as rock and soil structures. The authors' work on the theory and applications of RFEM is summarized in this paper. Based on the theory of RFEM, the Elastic Body-Seams Model (EBSM) is proposed to take the deformation and damage of rock masses into account.
文摘The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.
文摘Using normal and shear rigid coefficients of intact rock and fracture plane, rigidly normal, shear equivalent rigid coefficients of fissure rock mass are conducted. On the basis of hypotheses of small displacement of rock mass, principle of superposition, irrelevance of strength parameters C and T and Coulomb theory, formulas to calculate equivalent strength parameters C and phi of equivalent continuous mass from fissured rock mass with anchor piles are given. The achievement is extremely valuable in integral stability analysis of the rock mass slope and important in promoting the research of the rock mass's constitutive relation.
