Study On Damping Characteristics Of Magnetic Rubber Layer Damping Treatment

Passive constrained layer damping treatments(PCLD) have been extensively utilized,for many years,to damp out the vibration of flexible structures ranging from simple beams to complex space structures.With an increasing need for the vibration and noise control,the importance for the vibration damping materials is mounting.But the conventional damping materials have two weighty drawbacks.One is that it takes much labor to install,and the other is that it can exhibit high damping performance only at limited frequencies and temperatures.To overcome these drawbacks,a new type of magnetic rubber layer damping treatment(MRLD) has been developed.Different from PCLD,magnetic rubber powder is applied as damping material in MRLD.The magnetic rubber powder is easily attached to the vibrating steel body by the magnetic attractive force not by adhere bonding.During vibrating,a relative motion of displacement takes place and a resulting sliding friction is generated on the interface between the magnetic rubber layers and the vibrating body.The sliding friction has an effect of dissipating a portion of vibration energy as thermal energy.Thereby the damping performance of the MRLD is caused by the frictional loss together with the shear deformation of rubber material,while that of the PCLD is only by the shear deformation of damping material.Several vibration analytical models of the beam with PCLD treatment are firstly derived.One is the classical Cum analytical approach to obtain the transverse displacement and shear strain of damping layer involved in solving a cubic equation for a single sandwich beam or a four power equation for a double sandwich beam.Another is an improved assumed-function method,based the second minimized energy principle to reduce the number of the unknown coefficients.Moreover,for the vibration analysis of PCLD plates or cylindrical shells,the assumed function approaches are used to obtain the response of plates or shells under a given sinusoidally-varying excitation.Secondly,the technique of the equivalent damping is applied to give an estimate of the system modal loss factorη^MRLD of the MRLD structure.Since sliding regions vary with vibratory amplitude and time t during a vibrating cycle,it is difficult to find the exact solutions to vibratory response of MRLD structures,η^MRLD of the MRLD is computed based on the derived equations of the PCLD structures by equating the loss energy of the MRLD to the energy loss of PCLD in a vibrating cycle.A concept known as "equivalent loss factor",β^*,is to be introduced to determineη^MRLD.In this concept,if the transverse vibration responses of the MRLD structures are the same as that of PCLD with rubber material loss factor beingβ^* when the host structure is subjected to the same sinusoidally-varying transverse excitation,the energy dissipated per cycle by MRLD structures is equal to that by PCLD structures.Thusη^PCLD ofβ^* is considered asη^MRLD.The iteration procedures are to used to find the value ofβ^*.Finally,the fundamentals and the underlying phenomena associated with the MRLD are then investigated theoretically and experimentally.Some of valuable results are obtained as follows.(1) The damping property of MRLD significantly depends on exterior excitated force F and loss factor,β,of magnetic rubber material.Forβis less than a critical valueβ_cri of about 0.8255,η^MRLD does have apparent dependence on F butη^PCLD doesn't.η^MRLD increases similarly in proportion to F in the beginning during slip occurs,whileη^MRLD decreases as F continues to rise,resulting in the loss factor of MRLD is less than that of PCLD.There also exists a valid region range of excitation force,where the MRLD has superior damping ability to the PCLD.However,forβis above the critical valueβ_cri,η^MRLD is always less thanη^PCLD when slide occurs.The critical value,β_cri,is identical for other different physical and geometrical parameters,such as magnetic force F_m,shear modulus,damping layer thickness.The quadratic function theorem is applied to explained why the critical value ofβ_cri about 0.8255 exists.(2) Under a given excited force F,for small G_v^* MRLD is the same as PCLD. Increasing G_v^* makes damping layers slide,as a result,MRLD shows itself better damping than that of PCLD in the beginning whereasηdecreases as G_v^* continues to rise untilηof MRLD is less than that of PCLD.Moreover,increasing F makes the valid region of G_v^*,for which MRLD exceeds PCLD in damping property,move to the region of small G_v^*.So does the corresponding optimal shear modulus G_vopt^* for which the maximal damping can be obtained using MRLD.(3)η^MRLD of MRLD has a peak value on frictional force F_s.It is mainly by changing the slip region of damping layer that frictional force Fs exposes effect on the system modal damping ability.At the same resonant frequency,the available maximal modal loss factor is the same although excitating force F is different.(4) For MRLD cylindrical shell with given data,the starting slip excitation force F₀ is 3-4 times difference among the first 11 modes from 1000 Hz to 3365Hz while the valid excitating force F under which MRLD exceeds PCLD in damping property is large as 16-20 times as F₀.The damping improvement of the shell for the first several modes can be achieved simultaneously by using MRLD,but it can not for MRLD plates.Such evaluations are used to determine the merits and limitations of the MRLD treatment and develop design guidelines.