Thermoelastic Coupling Vibration And Stability Of Rotating Elastic And Viscoelastic Sector Plates

Sector plates,as the rotating mechanical structures,including annular and circular sector plates,have been mainly used in the rapid commutation mechanism,balancing mechanism and vibration crushing mechanism in the engineering fields of aviation,aerospace,transportation and mining machinery.Under rotating working condition,due to the influence of inertial force,operating temperature and geometric assembly precision,sector plates are prone to instability of transmission and operation,which affects the normal operation of mechanical structure.It is of great theoretical and engineering significance to study dynamic characteristics of sector plates.However,in the research field of transverse vibration characteristics of rotating mechanical structures,more achievements have been made in the field of axisymmetric circular and annular plates,and less in the field of non-axisymmetric annular and circular sector plates.Based on this,dynamics characteristics of annular and circular sector plates are studied in this paper,taking into account such factors as operating temperature,follower force,geometric assembly error and viscoelastic material characteristics.The main research work is listed as follows:(1)The thermoelastic coupling transverse vibration of rotating elastic sector plates is studied.Considering temperature change and based on the theory of small deflection bending of elastic thin plate and the heat conduction equation containing strain,the non-axisymmetric thermoelastic coupling differential equation of motion of rotating sector plates is established.The mode equation and boundary conditions are discretized by differential quadrature method.The effects of the dimensionless angular speed,the geometric parameters of plate and the thermoelastic coupling coefficient on the dimensionless complex frequencies of rotating sector plates are studied by calculating the eigenvalue equation.The effects of the geometric parameters and the thermoelastic coupling coefficient on the stability of rotating sector plates are analyzed.The corresponding types of instability and critical angular speed are obtained.(2)The thermoelastic coupling vibration of rotating elastic sector plates with non-uniform follower force is investigated.The differential equation of thermoelastic coupling transverse vibration of rotating sector plates with non-uniform follower force is established.The variation of the dimensionless complex frequencies of rotating sector plates with basic follower force is calculated under the different dimensionless angular speed,thermoelastic coupling coefficient and boundary conditions.The effects of uniform and non-uniform follower forces on the stability of sector plates are compared and analyzed.The corresponding types of instability and critical load are obtained.(3)The thermoelastic coupling vibration characteristics and stability of rotating elastic sector plates with geometric eccentricity are analyzed.The non-axisymmetric differential equation of thermoelastic coupling transverse vibration of eccentric rotating sector plates is established.The middle internal forces containing eccentricity and rotation angular speed are calculated.The eigenvalue equation containing boundary conditions is discretized by the differential quadrature method.The variation of the dimensionless complex frequencies of rotating sector plates with the dimensionless angular speed is analyzed in the case of different eccentricities.The types of instability of eccentric rotating sector plates are discussed,and the critical angular speed of sector plate with different conditions is obtained.(4)The parametric vibration and dynamic stability of elastic sector plates with periodically varying rotating angular speed are studied.The differential equation of transverse vibration of rotating sector plates with rotating angular speed of periodic variation is established,and the second order periodic coefficient differential equations are obtained by using the differential quadrature method to discretize the radial and circumferential variable.The effects of the geometric parameters and the average rotating angular speed on the unstable region of sector plates are analyzed by using the Floquet theory and the Runge-Kutta method.(5)The transverse vibration characteristics of rotating viscoelastic sector plates are examined.The differential equation of motion of rotating viscoelastic sector plates constituted by the elastic behavior in dilatation and the Kelvin-Voigt laws for distortion is established.The differential equation of thermoelastic coupling vibration of rotating viscoelastic sector plates is deduced.The eigenvalue equation of the rotating viscoelastic sector plates is calculated.The effects of the geometric parameters and the dimensionless dimensionless delay time on the stability and critical angular speed of plates are analyzed.The types of instability and critical angular speed in the case of thermoelastic coupling and uncoupling are obtained by numerical calculation.(6)The thermoelastic coupling vibration characteristics of rotating sector sandwich plates are studied.The rotating sector sandwich plates with middle viscoelastic sandwich layer and upper and lower elastic constraint layers are employed as the research objects,and the differential equation with the dimensionless delay time is established by using the constitutive equations of elasticity and viscoelasticity.The variation of the dimensionless complex frequencies of rotating sector sandwich plates with the dimensionless angular speed and the geometric parameters is calculated.The transverse vibration characteristics of rotating sector sandwich plates in the case of thermoelastic coupling and uncoupling are compared.The types of instability of sector sandwich plates with the different layer thickness ratios are obtained.The theoretical research results of this paper provide a theoretical basis for structural optimization and dynamic analysis of sector plates.The results are also important for improving performance of mechanical transmission.