Based on the geometrically nonlinear theory of axially extensible elastic rods, the governing equations of post_buckling of a clamped_free rod with variable cross_sections, subjected to a combined load, a concentrated...Based on the geometrically nonlinear theory of axially extensible elastic rods, the governing equations of post_buckling of a clamped_free rod with variable cross_sections, subjected to a combined load, a concentrated axial load P at the free end and a non_uniformly distributed axial load q, are established.By using shooting method, the strong nonlinear boundary value problems are numerically solved. The secondary equilibrium paths and the post_buckling configurations of the rod with linearly varied cross_sections are presented.展开更多
In engineering practice,there are many factors causing the vibration to which rods are usually subjected.Generally,the vibration of elastic rods motivated by determined vibration excitations can be controlled effectiv...In engineering practice,there are many factors causing the vibration to which rods are usually subjected.Generally,the vibration of elastic rods motivated by determined vibration excitations can be controlled effectively.However,the working frequency of vibration excitation may vary due to environmental changes,the working conditions of equipment,and other factors.Consequently,it remains a challenge to restrict the longitudinal vibration of elastic rods within a wide frequency band.In order to meet the relevant engineering requirements and address the existing limitations,the longitudinal vibration control of an elastic rod within a wide frequency band is explored in this study through an adjustable stiffness internal support.To achieve this purpose,the variable stiffness longitudinal vibration control theory of the elastic rod is validated.The model of an adjustable stiffness internal support is designed,constructed,and tested,demonstrating that the stiffness coefficients of the adjustable stiffness internal support can be effectively controlled.Through the adjustable stiffness internal support,the experiment on longitudinal vibration control of the elastic rod is designed and performed.It leads to the conclusion that the adjustable stiffness internal support within the adjustable working region is effective in restricting the longitudinal vibration within a wide frequency band of the elastic rod.Furthermore,the existence of the adjustable working region in the experiment demonstrates the effectiveness of the adjustable stiffness internal support intended for the variable stiffness longitudinal vibration control of an elastic rod.To sum up,this study provides insights into an adjustable stiffness mechanism for applying the theory of variable stiffness longitudinal vibration control on an elastic rod in engineering practice.展开更多
The key technique of a kinetic energy rod(KER) warhead is to control the flight attitude of rods. The rods are usually designed to different shapes. A new conceptual KER named profiled rod which has large L/D ratio is...The key technique of a kinetic energy rod(KER) warhead is to control the flight attitude of rods. The rods are usually designed to different shapes. A new conceptual KER named profiled rod which has large L/D ratio is described in this paper. The elastic dynamic equations of this profiled rod flying at high velocity after detonation are set up on the basis of Euler-Bernoulli beam, and the aeroelastic deformation of profiled rod is calculated by semi-analytical method for calculating the vibration characteristics of variable cross-section beam. In addition, the aeroelastic deformation of the undeformed profiled rod and the aeroelastic deformation of deformed profiled rod which is caused by the detonation of explosive are simulated by computational fluid dynamic and finite element method(CFD/FEM), respectively. A satisfactory agreement of these two methods is obtained by the comparison of two methods. The results show that the semi-analytical method for calculating the vibration characteristics of variable cross-section beam is applied to analyze the aeroelastic deformation of profiled rod flying at high velocity.展开更多
A slender rod suffers global vibration in impact.In this study,we present the experimental,numerical,and theoretical studies of the axial responses of a 316 stainless steel rod during vertical impact with a rigid flat...A slender rod suffers global vibration in impact.In this study,we present the experimental,numerical,and theoretical studies of the axial responses of a 316 stainless steel rod during vertical impact with a rigid flat.Combining the contact models and the one-dimensional(1D)wave equation,we first develop a semi-analytical vertical impact model for the rods based on a unified theoretical framework,which considers different geometries of the impacting end including the hemispherical nose,the truncated conical nose,and the flat end.Furthermore,we perform free-drop experiments on these rods and numerical simulations to verify the theoretical models.The results show that the strain-rate effect hardens the rod nose and should not be ignored even at a velocity as low as a few meters per second.After the proposal of a dynamic correction factor to adjust the quasi-static contact model,the theoretical,numerical,and experimental results agree well with one another.Also,the threedimensional(3D)FEM simulations show that the slight deviations between the experimental and the predicted results are due to the slight obliqueness of the rods in the drop.Additionally,we leverage the theoretical tool and FEM simulations to compare the mechanical responses of rods with different impacting ends,and suggestions about the selection of rod noses are obtained.展开更多
文摘Based on the geometrically nonlinear theory of axially extensible elastic rods, the governing equations of post_buckling of a clamped_free rod with variable cross_sections, subjected to a combined load, a concentrated axial load P at the free end and a non_uniformly distributed axial load q, are established.By using shooting method, the strong nonlinear boundary value problems are numerically solved. The secondary equilibrium paths and the post_buckling configurations of the rod with linearly varied cross_sections are presented.
基金Supported by the Fundamental Research Project of SIA(Grant No.2022JC1G04)National Natural Science Foundation of China(Grant Nos.52401364 and 52205091)。
文摘In engineering practice,there are many factors causing the vibration to which rods are usually subjected.Generally,the vibration of elastic rods motivated by determined vibration excitations can be controlled effectively.However,the working frequency of vibration excitation may vary due to environmental changes,the working conditions of equipment,and other factors.Consequently,it remains a challenge to restrict the longitudinal vibration of elastic rods within a wide frequency band.In order to meet the relevant engineering requirements and address the existing limitations,the longitudinal vibration control of an elastic rod within a wide frequency band is explored in this study through an adjustable stiffness internal support.To achieve this purpose,the variable stiffness longitudinal vibration control theory of the elastic rod is validated.The model of an adjustable stiffness internal support is designed,constructed,and tested,demonstrating that the stiffness coefficients of the adjustable stiffness internal support can be effectively controlled.Through the adjustable stiffness internal support,the experiment on longitudinal vibration control of the elastic rod is designed and performed.It leads to the conclusion that the adjustable stiffness internal support within the adjustable working region is effective in restricting the longitudinal vibration within a wide frequency band of the elastic rod.Furthermore,the existence of the adjustable working region in the experiment demonstrates the effectiveness of the adjustable stiffness internal support intended for the variable stiffness longitudinal vibration control of an elastic rod.To sum up,this study provides insights into an adjustable stiffness mechanism for applying the theory of variable stiffness longitudinal vibration control on an elastic rod in engineering practice.
文摘The key technique of a kinetic energy rod(KER) warhead is to control the flight attitude of rods. The rods are usually designed to different shapes. A new conceptual KER named profiled rod which has large L/D ratio is described in this paper. The elastic dynamic equations of this profiled rod flying at high velocity after detonation are set up on the basis of Euler-Bernoulli beam, and the aeroelastic deformation of profiled rod is calculated by semi-analytical method for calculating the vibration characteristics of variable cross-section beam. In addition, the aeroelastic deformation of the undeformed profiled rod and the aeroelastic deformation of deformed profiled rod which is caused by the detonation of explosive are simulated by computational fluid dynamic and finite element method(CFD/FEM), respectively. A satisfactory agreement of these two methods is obtained by the comparison of two methods. The results show that the semi-analytical method for calculating the vibration characteristics of variable cross-section beam is applied to analyze the aeroelastic deformation of profiled rod flying at high velocity.
基金supported by the National Natural Science Foundation of China(Grant Nos.12102046 and 12272203)the Young Elite Scientists Sponsorship Program by China Association for Science and Technology(CAST)(Grant No.YESS20220046)China National Nuclear Corporation(CNNC)Young Talents Program(Grant No.2022-379-3-THU-YE)。
文摘A slender rod suffers global vibration in impact.In this study,we present the experimental,numerical,and theoretical studies of the axial responses of a 316 stainless steel rod during vertical impact with a rigid flat.Combining the contact models and the one-dimensional(1D)wave equation,we first develop a semi-analytical vertical impact model for the rods based on a unified theoretical framework,which considers different geometries of the impacting end including the hemispherical nose,the truncated conical nose,and the flat end.Furthermore,we perform free-drop experiments on these rods and numerical simulations to verify the theoretical models.The results show that the strain-rate effect hardens the rod nose and should not be ignored even at a velocity as low as a few meters per second.After the proposal of a dynamic correction factor to adjust the quasi-static contact model,the theoretical,numerical,and experimental results agree well with one another.Also,the threedimensional(3D)FEM simulations show that the slight deviations between the experimental and the predicted results are due to the slight obliqueness of the rods in the drop.Additionally,we leverage the theoretical tool and FEM simulations to compare the mechanical responses of rods with different impacting ends,and suggestions about the selection of rod noses are obtained.
