The free vibration analysis of a rotating sandwich conical shell with a reentrant auxetic honeycomb core and homogenous isotropic face layers reinforced with a ring support is studied.The shell is modeled utilizing th...The free vibration analysis of a rotating sandwich conical shell with a reentrant auxetic honeycomb core and homogenous isotropic face layers reinforced with a ring support is studied.The shell is modeled utilizing the first-order shear deformation theory(FSDT)incorporating the relative,centripetal,and Coriolis accelerations alongside the initial hoop tension created by the rotation.The governing equations,compatibility conditions,and boundary conditions are attained using Hamilton’s principle.Utilizing trigonometric functions,an analytical solution is derived in the circumferential direction,and a numerical one is presented in the meridional direction via the differential quadrature method(DQM).The effects of various factors on the critical rotational speeds and forward and backward frequencies of the shell are studied.The present work is the first theoretical work regarding the dynamic analysis of a rotating sandwich conical shell with an auxetic honeycomb core strengthened with a ring support.展开更多
A lumped parameter-rigid elastic coupled dynamic model of two-stage planetary gears for a hybrid car is established through the inter-stage coupled method,in which the supports of the ring gear of planet set Ⅱ are re...A lumped parameter-rigid elastic coupled dynamic model of two-stage planetary gears for a hybrid car is established through the inter-stage coupled method,in which the supports of the ring gear of planet set Ⅱ are represented as an elastic foundation with radial and tangential uniform distributed stiffness,and the ring gear of planet set Ⅱ is modeled as an elastic continuum body. The natural frequencies based on the eigenvalue problem of dynamic model of planetary transmission are solved and the associated vibration modes are discussed. The rules are revealed which are the influences of the ring gear elastic supports stiffness and rim thickness on natural frequencies of planetary transmission. The theoretical analysis indicates that the vibration modes of planetary transmission with thin-walled ring gear on elastic supports are classified into seven types: Ⅰ/Ⅱ stage coupled rotational mode,Ⅰ stage translational mode,Ⅰ stage planet mode,Ⅱ stage translational mode,Ⅱ stage degenerate planet mode,Ⅱ stage distinct planet mode and purely ring gear mode. For each vibration mode, its properties are summarized. The numerical solutions show that the elastic supports stiffness and rim thickness of the ring gear of planet set Ⅱ have different influences on natural frequencies.展开更多
文摘The free vibration analysis of a rotating sandwich conical shell with a reentrant auxetic honeycomb core and homogenous isotropic face layers reinforced with a ring support is studied.The shell is modeled utilizing the first-order shear deformation theory(FSDT)incorporating the relative,centripetal,and Coriolis accelerations alongside the initial hoop tension created by the rotation.The governing equations,compatibility conditions,and boundary conditions are attained using Hamilton’s principle.Utilizing trigonometric functions,an analytical solution is derived in the circumferential direction,and a numerical one is presented in the meridional direction via the differential quadrature method(DQM).The effects of various factors on the critical rotational speeds and forward and backward frequencies of the shell are studied.The present work is the first theoretical work regarding the dynamic analysis of a rotating sandwich conical shell with an auxetic honeycomb core strengthened with a ring support.
基金Innovation Funded Project of Fujian Province,China(No.2015C0030)Natural Science Foundation of Guangdong Province,China(No.S2013020013855)
文摘A lumped parameter-rigid elastic coupled dynamic model of two-stage planetary gears for a hybrid car is established through the inter-stage coupled method,in which the supports of the ring gear of planet set Ⅱ are represented as an elastic foundation with radial and tangential uniform distributed stiffness,and the ring gear of planet set Ⅱ is modeled as an elastic continuum body. The natural frequencies based on the eigenvalue problem of dynamic model of planetary transmission are solved and the associated vibration modes are discussed. The rules are revealed which are the influences of the ring gear elastic supports stiffness and rim thickness on natural frequencies of planetary transmission. The theoretical analysis indicates that the vibration modes of planetary transmission with thin-walled ring gear on elastic supports are classified into seven types: Ⅰ/Ⅱ stage coupled rotational mode,Ⅰ stage translational mode,Ⅰ stage planet mode,Ⅱ stage translational mode,Ⅱ stage degenerate planet mode,Ⅱ stage distinct planet mode and purely ring gear mode. For each vibration mode, its properties are summarized. The numerical solutions show that the elastic supports stiffness and rim thickness of the ring gear of planet set Ⅱ have different influences on natural frequencies.
