Lyapunov＇s first method,extended by Kozlov to nonlinear mechanical systems,is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative fo...Lyapunov＇s first method,extended by Kozlov to nonlinear mechanical systems,is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative forces.The cases with a tensor of inertia or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position.This fact renders the impossible application of Lyapunov＇s approach in the analysis of the stability because,in the equilibrium position,the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not fulfilled.It is shown that Kozlov＇s generalization of Lyapunov＇s first method can also be applied in the mentioned cases on the conditions that,besides the known algebraic expression,more are fulfilled.Three theorems on the instability of the equilibrium position are formulated.The results are illustrated by an example.展开更多
A fan casing model of cantilever circular thin shell is constructed based on the geometric characteristics of the thin-walled structure of aero-engine fan casing. According to Donnelly＇s shell theory and Hamilton＇s ...A fan casing model of cantilever circular thin shell is constructed based on the geometric characteristics of the thin-walled structure of aero-engine fan casing. According to Donnelly＇s shell theory and Hamilton＇s principle, the dynamic equations axe established. The dynamic behaviors are investigated by a multiple-scale method. The effects of casing geometric parameters and motion parameters on the natural frequency of the system are studied. The transition sets and bifurcation diagrams of the system are obtained through a singularity analysis of the bifurcation equation, showing that various modes of the system such as the bifurcation and hysteresis will appear in different parameter regions. In accordance with the multiple relationship of the fan speed and stator vibration frequency, the fan speed interval with the casing vibration sudden jump is calculated. The dynamic reasons of casing cracks are investigated. The possibility of casing cracking hysteresis interval is analyzed. The results show that cracking is more likely to appear in the hysteresis interval. The research of this paper provides a theoretical basis for fan casing design and system parameter optimization.展开更多
通过进行带机匣测点的滚动轴承故障模拟实验,获取滚动轴承在故障状态条件下,轴承座测点和机匣测点的振动数据。分析结果显示,相对于轴承座,机匣上的振动信号成分复杂,轴承故障特征不明显,直接进行包络解调无法提取故障特征。通过奇异值...通过进行带机匣测点的滚动轴承故障模拟实验,获取滚动轴承在故障状态条件下,轴承座测点和机匣测点的振动数据。分析结果显示,相对于轴承座,机匣上的振动信号成分复杂,轴承故障特征不明显,直接进行包络解调无法提取故障特征。通过奇异值分解(singular value decomposition,SVD),差分谱中各峰值处奇异值可以表征不同成分的信号。当轴承故障信号微弱时,第一个峰值处的奇异值重构信号往往代表转频及其调制信号分量,选取该靠后峰值处的奇异值进行信号重构可以有效提取轴承故障特征信号。研究内容为实际基于机匣测点信号的航空发动机滚动轴承故障特征提取提供了一种新的方法。展开更多
The main purpose of this paper is to extend the result obtained by Beirao da Veiga(2000)from the whole-space case to slip boundary cases.Denote by a two components of the velocity u.To fix ideas setū=(u_(1),u_(2),0)(...The main purpose of this paper is to extend the result obtained by Beirao da Veiga(2000)from the whole-space case to slip boundary cases.Denote by a two components of the velocity u.To fix ideas setū=(u_(1),u_(2),0)(the half-space)orū=?_(1)ê_(1)+?_(2)ê_(2)(the general boundary case(see(7.1))).We show that there exists a constant K,which enjoys very simple and significant expressions such that if at some timeτ∈(0,T)one has lim sup_(t→^(τ)-0)‖ū(t)‖_(L^(3)(Ω))^(3)<‖ū(τ)‖_(L^(3)(Ω))^(3)+K,then u is continuous atτwith values in L^(3)(Ω).Roughly speaking,the above norm-discontinuity of merely two components of the velocity cannot occur for steps'amplitudes smaller than K.In particular,if the above condition holds at eachτ∈(0,T),the solution is smooth in(0,T)×Ω.Note that here there is no limitation on the width of the norms‖ū(t)‖_(L^(3)(Ω))^(3)·So K is independent of these quantities.Many other related results are discussed and compared among them.展开更多
基金supported by the Ministry of Science and Technological Development of the Republic of Serbia (Nos. ON174004,ON174016,and TR335006)
文摘Lyapunov＇s first method,extended by Kozlov to nonlinear mechanical systems,is applied to study the instability of the equilibrium position of a mechanical system moving in the field of conservative and dissipative forces.The cases with a tensor of inertia or a matrix of coefficients of the Rayleigh dissipative function are analyzed singularly in the equilibrium position.This fact renders the impossible application of Lyapunov＇s approach in the analysis of the stability because,in the equilibrium position,the conditions of the existence and uniqueness of the solutions to the differential equations of motion are not fulfilled.It is shown that Kozlov＇s generalization of Lyapunov＇s first method can also be applied in the mentioned cases on the conditions that,besides the known algebraic expression,more are fulfilled.Three theorems on the instability of the equilibrium position are formulated.The results are illustrated by an example.
基金supported by the National Natural Science Foundation of China(No.10632040)
文摘A fan casing model of cantilever circular thin shell is constructed based on the geometric characteristics of the thin-walled structure of aero-engine fan casing. According to Donnelly＇s shell theory and Hamilton＇s principle, the dynamic equations axe established. The dynamic behaviors are investigated by a multiple-scale method. The effects of casing geometric parameters and motion parameters on the natural frequency of the system are studied. The transition sets and bifurcation diagrams of the system are obtained through a singularity analysis of the bifurcation equation, showing that various modes of the system such as the bifurcation and hysteresis will appear in different parameter regions. In accordance with the multiple relationship of the fan speed and stator vibration frequency, the fan speed interval with the casing vibration sudden jump is calculated. The dynamic reasons of casing cracks are investigated. The possibility of casing cracking hysteresis interval is analyzed. The results show that cracking is more likely to appear in the hysteresis interval. The research of this paper provides a theoretical basis for fan casing design and system parameter optimization.
文摘通过进行带机匣测点的滚动轴承故障模拟实验,获取滚动轴承在故障状态条件下,轴承座测点和机匣测点的振动数据。分析结果显示,相对于轴承座,机匣上的振动信号成分复杂,轴承故障特征不明显,直接进行包络解调无法提取故障特征。通过奇异值分解(singular value decomposition,SVD),差分谱中各峰值处奇异值可以表征不同成分的信号。当轴承故障信号微弱时,第一个峰值处的奇异值重构信号往往代表转频及其调制信号分量,选取该靠后峰值处的奇异值进行信号重构可以有效提取轴承故障特征信号。研究内容为实际基于机匣测点信号的航空发动机滚动轴承故障特征提取提供了一种新的方法。
基金supported by Portuguese Foundation for Science and Technology(Portugal)(Grant No.UIDB/MAT/04561/2020)supported by National Natural Science Foundation of China(Grant No.12001429)。
文摘The main purpose of this paper is to extend the result obtained by Beirao da Veiga(2000)from the whole-space case to slip boundary cases.Denote by a two components of the velocity u.To fix ideas setū=(u_(1),u_(2),0)(the half-space)orū=?_(1)ê_(1)+?_(2)ê_(2)(the general boundary case(see(7.1))).We show that there exists a constant K,which enjoys very simple and significant expressions such that if at some timeτ∈(0,T)one has lim sup_(t→^(τ)-0)‖ū(t)‖_(L^(3)(Ω))^(3)<‖ū(τ)‖_(L^(3)(Ω))^(3)+K,then u is continuous atτwith values in L^(3)(Ω).Roughly speaking,the above norm-discontinuity of merely two components of the velocity cannot occur for steps'amplitudes smaller than K.In particular,if the above condition holds at eachτ∈(0,T),the solution is smooth in(0,T)×Ω.Note that here there is no limitation on the width of the norms‖ū(t)‖_(L^(3)(Ω))^(3)·So K is independent of these quantities.Many other related results are discussed and compared among them.
