Existence of global solutions for vibration equations of a rotating thin-walled beam with C-F boundary
As the heart of large aircraft,aero-engines provide power for large aircraft and are an important pillar of aviation development.At the same time,the construction level of aero-engines is also an important manifestation of the national strength,technology and industrial.The most important component of aero-engine is engine blade,which is mainly reflected in the vibration fault of rotor blade when rotating at high speed.In order to research the vibration of the rotor blade during high-speed rotation,a vibration equation of a circular-section rotating thin-walled beam is considered with C-F boundary conditions,where the C-F boundary is the clamped boundary at the left and the free boundary at the right.Firstly,the vibration equations were reduced to vector equations,and the definition of the weak solution was given.Secondly,the approximate solution of vibration equation was constructed by Faedo-Galerkin method and the existence and uniqueness of the approximate solution was proved by using the existence theory of the ordinary differential equation.Finally,by using the energy method and the Gronwall inequality,the consistent estimation of approximate solutions was obtained,and the existence and uniqueness of the global weak solution was proved.By applying Gagliardo-Nirenberg inequality,Young inequality and Holder inequality,the higher order estimation of global weak solutions was deduced,and the existence of global strong solutions was proved.
rotating thin-walled beamrotor bladeC-F boundarystrong solutionsthe energy method
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