The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading ...The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.展开更多
The telescopic boom is the main bearing force component of the crane.The rationality of the design will directly affect the performance of the machine and safety.The telescopic boom is a typical thin-walled plate and ...The telescopic boom is the main bearing force component of the crane.The rationality of the design will directly affect the performance of the machine and safety.The telescopic boom is a typical thin-walled plate and shell structure.Its main form of damage is the occurrence of buckling,resulting in decreased carrying capacity,or even a security incident.In order to meet the lifting weight and height,to ensure the stability of the telescopic boom has become a major problem of the designer.There are many factors that affect the critical load of the telescopic boom,including support method,inertia moment,length and material.When the support mode,material and length are determined,the maximum factor affecting the buckling critical load is the inertia moment.In this paper,the influence of the section size on the buckling critical load of the telescopic boom is analyzed by using the inertia moment of section method ande finite element method.And the sensitivity analysis is carried out on this basis.The results of the analysis can provide designers with design reference basis.Then a reasonable cross-sectional size can be used to improve the buckling resistance capacity of the telescopic boom.展开更多
By the Lyapunov direct method, dynamic stability of two conservative systems of finite degrees of freedom with one parameter is analyzed. Two Lyapunov functions are proposed for the two systems, respectively. When the...By the Lyapunov direct method, dynamic stability of two conservative systems of finite degrees of freedom with one parameter is analyzed. Two Lyapunov functions are proposed for the two systems, respectively. When the number of degree of freedom the two systems tends to infinite, the two systems can simulate dynamic stability of a compressed elastic column with one end fixed and the other clamped in rotation. In the sense of the Lyapunov stability, the column is proved to be dynamically stable when the load equals to the Euler critical load.展开更多
Buckling is the primary cause of failure of a side member in condition of overloading,so buckling stability should be taken into consideration in the design optimization of side member.On the other hand,lightweight is...Buckling is the primary cause of failure of a side member in condition of overloading,so buckling stability should be taken into consideration in the design optimization of side member.On the other hand,lightweight is always a pursuing objective of manufacturer of automobile seat.Thus both the buckling stability and lightweight are considered in the suggested design optimization method of the side member of automobile seats.The method has two design phases.Firstly,the optimal shape of back curve by using shape optimization was obtained in which the lightweight of the side member was set to be the design objective.Secondly,optimal size and distribution of grooves on side member was obtained by topography optimization in which the buckling critical load was set to be the design objective.A typical design example shows that the buckling critical load of the optimal side member is increased by 25.98%,and the weight is decreased by 3.7% simultaneously.展开更多
基金Project supported by the Natural Science and Engineering Research Council (NSERC) of Canada (No.NSERC-RGPIN204992)
文摘The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.
基金supported by the National Natural Science Foundation of China (51575370)Natural Science Foundation of Shanxi Province (201901D111236)Nanchong 2023 Municipal Science and Technology Plan Project (23YYJCYJ0023)。
文摘The telescopic boom is the main bearing force component of the crane.The rationality of the design will directly affect the performance of the machine and safety.The telescopic boom is a typical thin-walled plate and shell structure.Its main form of damage is the occurrence of buckling,resulting in decreased carrying capacity,or even a security incident.In order to meet the lifting weight and height,to ensure the stability of the telescopic boom has become a major problem of the designer.There are many factors that affect the critical load of the telescopic boom,including support method,inertia moment,length and material.When the support mode,material and length are determined,the maximum factor affecting the buckling critical load is the inertia moment.In this paper,the influence of the section size on the buckling critical load of the telescopic boom is analyzed by using the inertia moment of section method ande finite element method.And the sensitivity analysis is carried out on this basis.The results of the analysis can provide designers with design reference basis.Then a reasonable cross-sectional size can be used to improve the buckling resistance capacity of the telescopic boom.
基金supported by the Research Fund for the Doctoral Program of Higher Education of China (20120009110019)
文摘By the Lyapunov direct method, dynamic stability of two conservative systems of finite degrees of freedom with one parameter is analyzed. Two Lyapunov functions are proposed for the two systems, respectively. When the number of degree of freedom the two systems tends to infinite, the two systems can simulate dynamic stability of a compressed elastic column with one end fixed and the other clamped in rotation. In the sense of the Lyapunov stability, the column is proved to be dynamically stable when the load equals to the Euler critical load.
基金National Natural Science Foundation of China(No.50875174)Shanghai Leading Academic Discipline Project,China(No.S30504)The Innovation Fund Project for Graduate Student of Shanghai,China(No.J WCXSL1002)
文摘Buckling is the primary cause of failure of a side member in condition of overloading,so buckling stability should be taken into consideration in the design optimization of side member.On the other hand,lightweight is always a pursuing objective of manufacturer of automobile seat.Thus both the buckling stability and lightweight are considered in the suggested design optimization method of the side member of automobile seats.The method has two design phases.Firstly,the optimal shape of back curve by using shape optimization was obtained in which the lightweight of the side member was set to be the design objective.Secondly,optimal size and distribution of grooves on side member was obtained by topography optimization in which the buckling critical load was set to be the design objective.A typical design example shows that the buckling critical load of the optimal side member is increased by 25.98%,and the weight is decreased by 3.7% simultaneously.
