Dynamic Modeling And Vibration Control Of Flexible Arm With Enhanced Active Layer Constrained Damping Treatment

Space arm is a kind of common devices in the aerospace field,which is used to do some tasks such as things grabbing,maintenance.Because of the large sizes and flexibilities,the external force can lead the arm to vibrate easily.The arm needing a long time to return to a stable condition brings an inefficiency result.It is necessary to make a vibration control of space arm.In this paper,an active-passive hybrid vibration control technology called as enhanced active constrained layer damping(EACLD)treatment is applied to structural vibration suppression of a typical rigid-flexible coupled hub-beam system.The EACLD treatment was developed based on the traditional ACLD treatment by adding two edge elements onto the sandwich structures that contains three layers: the active piezoelectric layer,the passive viscoelastic material(VEM)layer,and the base layer.Each edge element is modelled as an equivalent spring-point mass system so that the stiffness and mass effects of both edge elements of the system are included.In this paper,the basic theories of piezoelectric and viscoelastic materials are introduced including the constitutive equation of piezoelectric materials under four different boundary conditions and the description of several common viscoelastic damping models,such as GHM model and complex modulus model.The complex modulus model and the piezoelectric constitutive equation under the second boundary condition are selected.The longitudinal shrinking of the flexible beam caused by the transverse displacement is considered so that the high-order geometrically nonlinear terms are obtained.By using the Euler-Bernoulli beam theory and describing the VEM with a complex shear modulus,and using the assumed mode method together with Lagrange's equations,the discrete high-order rigid-flexible coupled dynamic equations of the system with EACLD treatment are derived in the closed-loop case with a PD controller.Based on the new dynamic model,the dynamic behavior of the rotating EACLD beam is analyzed and compared with traditional ACLD beam in the time domain.Vibrations of the first three modes of frequency and damping ratio with angular velocity of EACLD beam and ACLD beam are calculated.The effects of coverage ratio of the control layer,edge element mass,edge element stiffness,edge element location and control gains on the dynamic responses of system are investigated.The results obtained show that the influences of edge element stiffness and mass can be helpful to the design of structural vibration control.