The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical ...The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.展开更多
Structural deterioration in the roof in an underground mine can easily cause roof fall,and deterioration is difficult to detect.When drilling holes for roof bolts,there is a relationship between the vibration of the d...Structural deterioration in the roof in an underground mine can easily cause roof fall,and deterioration is difficult to detect.When drilling holes for roof bolts,there is a relationship between the vibration of the drill rod and the properties of the rock being drilled.This paper analyzes transverse,longitudinal,and torsional vibrations in the drill rod by using vibration theory.Characteristic indexes for three kinds of vibration are determined.Using the finite element analysis software ABAQUS,a model for drill rod vibration during the drilling of roof bolt holes was established based on the geological and mining conditions in the Guyuan Coal Mine,northern China.Results from the model determined that the transverse and the longitudinal vibration decrease as the rock hardness decreases.In descending order,sandstone,sandy mudstone,mudstone,and weak interbeds cause progressively less vibration when being drilled.The ranking for strata that cause decreasing torsional vibration is slightly different,being,in descending order,mudstone,sandstone,sandy mudstone,and weak interbeds.These results provide a theoretical basis for predicting dangerous roof conditions and the presence of weak interbeds to allow for adjusting bolt support schemes.展开更多
The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s ...The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.展开更多
With rampant growth and improvements in drilling technology, drilling of blast holes should no longer be viewed as an arduous sub-process in any mining or excavation process. Instead, it must be viewed as an important...With rampant growth and improvements in drilling technology, drilling of blast holes should no longer be viewed as an arduous sub-process in any mining or excavation process. Instead, it must be viewed as an important opportunity to quickly and accurately measure the geo-mechanical features of the rock mass on-site, much in advance of the downstream operations. It is well established that even the slightest variation in lithology, ground conditions, blast designs vis-a-vis geologic features and explosives performance, results in drastic changes in fragmentation results. Keeping in mind the importance of state-of-the-art measurement-while-drilling （MWD） technique, the current paper focuses on integrating this technique with the blasting operation in order to enhance the blasting designs and results. The paper presents a preliminary understanding of various blasting models, blastability and other related concepts, to review the state-of-the-art advancements and researches done in this area. In light of this, the paper highlights the future needs and implications on drill monitoring systems for improved information to enhnnrp th~ hl^tin~ r^HIt~展开更多
A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at roo...A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at room temperature with different lengths in 108 mm, 100 mm, 90 ram, 83.5 mm, 80 ram, 74.5 mm, 70 mm for the polycarbonate bars, and the curves of ratios A2/A1 between two ends of a viscoelastic bar versus frequencies are obtained, furthermore, the corresponding 3 dB bandwidth and the storage and loss modulus can be calculated. Sufficient number of obtained complex Young＇s modulus at different frequency allows us to calculate other ones using the least square method. If the step of the tested frequency is 5 Hz, the maximum error of results can be less than 6%. By comparison with the measurement methods which the previous literature mentioned, this new method simplifies the calculation, and the physical meaning appears apparently and clearly.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 10472067)
文摘The analysis of kinematics and dynamics of an elastic rod with circular cross section is studied on the basis of exact Cosserat model under consideration of the tension and shear deformation of the rod. The dynamical equations of a rod with arbitrary initial shape are established in general form. The dynamics of a straight rod under axial tension and torsion is discussed as an example. In discussion of static stability in the space domain the Greenhill criteria of stability and the Euler load are corrected by the influence of tension and shear strain. In analysis of dynamical stability in the time domain it is shown that the Lyapunov and Euler stability conditions of the rod in space domain are the necessary conditions of Lyapunov＇s stability in the time domain. The longitudinal, torsional and lateral vibrations of a straight rod based on exact model are discussed, and an exact formula of free frequency of lateral vibration is obtained. The free frequency formulas of various simplified models, such as the Rayleigh beam, the Kirchhoff rod, and the Timoshenko beam, can be seen as special cases of the exact formula under different conditions of simplification.
基金the National Natural Science Foundation of China(Nos.51104055,51274087,51604094 and 51674098)
文摘Structural deterioration in the roof in an underground mine can easily cause roof fall,and deterioration is difficult to detect.When drilling holes for roof bolts,there is a relationship between the vibration of the drill rod and the properties of the rock being drilled.This paper analyzes transverse,longitudinal,and torsional vibrations in the drill rod by using vibration theory.Characteristic indexes for three kinds of vibration are determined.Using the finite element analysis software ABAQUS,a model for drill rod vibration during the drilling of roof bolt holes was established based on the geological and mining conditions in the Guyuan Coal Mine,northern China.Results from the model determined that the transverse and the longitudinal vibration decrease as the rock hardness decreases.In descending order,sandstone,sandy mudstone,mudstone,and weak interbeds cause progressively less vibration when being drilled.The ranking for strata that cause decreasing torsional vibration is slightly different,being,in descending order,mudstone,sandstone,sandy mudstone,and weak interbeds.These results provide a theoretical basis for predicting dangerous roof conditions and the presence of weak interbeds to allow for adjusting bolt support schemes.
基金the National Natural Science Foundation of China (10472067)
文摘The stability and vibration of an elastic rod with a circular cross section under the constraint of a cylinder is discussed. The differential equations of dynamics of the constrained rod are established with Euler＇s angles as variables describing the attitude of the cross section. The existence conditions of helical equilibrium under constraint are discussed as a special configuration of the rod. The stability of the helical equilibrium is discussed in the realms of statics and dynamics, respectively. Necessary conditions for the stability of helical rod are derived in space domain and time domain, and the difference and relationship between Lyapunov＇s and Euler＇s stability concepts are discussed. The free frequency of flexural vibration of the helical rod with cylinder constraint is obtained in analytical form.
文摘With rampant growth and improvements in drilling technology, drilling of blast holes should no longer be viewed as an arduous sub-process in any mining or excavation process. Instead, it must be viewed as an important opportunity to quickly and accurately measure the geo-mechanical features of the rock mass on-site, much in advance of the downstream operations. It is well established that even the slightest variation in lithology, ground conditions, blast designs vis-a-vis geologic features and explosives performance, results in drastic changes in fragmentation results. Keeping in mind the importance of state-of-the-art measurement-while-drilling （MWD） technique, the current paper focuses on integrating this technique with the blasting operation in order to enhance the blasting designs and results. The paper presents a preliminary understanding of various blasting models, blastability and other related concepts, to review the state-of-the-art advancements and researches done in this area. In light of this, the paper highlights the future needs and implications on drill monitoring systems for improved information to enhnnrp th~ hl^tin~ r^HIt~
基金supported by the Fundamental Research Funds of China for the Central Universities(GK201001008)
文摘A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at room temperature with different lengths in 108 mm, 100 mm, 90 ram, 83.5 mm, 80 ram, 74.5 mm, 70 mm for the polycarbonate bars, and the curves of ratios A2/A1 between two ends of a viscoelastic bar versus frequencies are obtained, furthermore, the corresponding 3 dB bandwidth and the storage and loss modulus can be calculated. Sufficient number of obtained complex Young＇s modulus at different frequency allows us to calculate other ones using the least square method. If the step of the tested frequency is 5 Hz, the maximum error of results can be less than 6%. By comparison with the measurement methods which the previous literature mentioned, this new method simplifies the calculation, and the physical meaning appears apparently and clearly.
