Dynamic Research Of Thin Wall Structure With Constrained Layer Damping Treatment Based On Transfer Matrix Method

Thin-walled structures are widely used in industries such as automobile,aerospace,submarine etc.because they can withstand large loads with relatively small weight.These structures usually work under coupled airflow-stress-sound-thermo field with high static and dynamic stress,and they are likely to vibrant when exposed to external excitations.That,as a result,not only cause noise radiated from thin-walled structures,producing noise pollution,but also cause vibration damage due to increased vibration stress,which affects the structures' service life.Therefore it is necessary to introduce vibration absorbing treatment to thin-walled structures.Viscoelastic damping materials,with high damping characteristics,can effectively inhibit resonance response,which makes them ideal materials to control vibration in modern thin-walled structures.There are two typical structural damping forms,i.e.unconstrained layer damping and constrained layer damping,the later is able to dissipate more energy than the former,hence better damping effect,but it causes larger added weight.Most thin-walled structures are demanding on weight,because larger added weight can severely affect their performance.Therefore it is significant for the damping theory and engineering application to improve traditional constrained damping structure in order to achieve better damping effect with less weight.To meet the damping and lightweight requirements of thin-walled structures,with rectangular thin plates and cylindrical shell as research objects,this paper investigated the damping mechanism of constrained layer damping structures,and illustrated regular patterns of effect of performance parameters and thickness of damping and constraining material on the vibration characteristics of structures.Traditional transfer matrix method is improved and applied to multi-layer constrained damping structure and partially covered damping structure,furthermore,structural vibration characteristics of both structures are investigated,which provided theoretical support to lightweight design of thin-walled damping structures.In addition,vibration characteristics of constrained damping cylindrical shell at rotating state were investigated and the effect of rotating speed on the structural damping are illustrated.The main contents of this paper are as follows:The energy dissipation mechanism of viscoelastic material has been analyzed,and according to its constitutive relation,dynamic equations of both unconstrained and constrained layer damping have been established using complex constants model.For simply-supported boundary condition,the equations were solved by analytical method,and its effectiveness was confirmed by a numerical example.Moreover,accurate dynamic equations of constrained damping structure has been obtained,which provided guidance for establishing dynamic equations of multi-layer constrained damping structure and partially covered damping structure.The transfer matrix method has been improved,in which state vector and boundary condition vector were set separately,and they are connected by an association matrix,simplifying the solution of the transfer matrix.The accuracy of the improved transfer matrix method(ITMM)has been confirmed by a thin-walled cylindrical shell numerical example.This method has been applied to constrained damping plate and constrained damping cylindrical shell structures,and compared to analytical and finite element method,the ITMM is superior in terms of simplicity and accuracy.This is more remarkable in multiple degree of freedom systems,which provided reliable method for the vibration characteristics analysis of multi-layer constrained damping structure and partially covered damping structure.Damping mechanism of the constrained damping structure has been investigated systematically.The equations of unconstrained and constrained layer damping plates were solved through ITMM,and the effect of material parameters(Poisson's ratio,elasticity modulus,density and thickness etc.)on the structural vibration characteristics was analyzed.What's more,intrinsic frequency and loss factor of damping material and constraining material were obtained in various thickness combinations of the two materials,and added mass of different combination were compared.The results show that the selection of damping material and constraining material can affect the structural vibration characteristics a lot.If appropriate thicknesses were chose,better damping effect can be achieved with less material.Also,the necessity of material selection and thickness optimization of damping materials were illustrated.The experimental validation is carried out for the constrained damping plate and muitilayer constrained damping plate.The validity and effectiveness of the improved transfer matrix method and the results of this paper are verified.Based on the basic assumption of constrained damping structure,the author analyzed the inner stress and strain of multi-layer damping structure,and established the general dynamic equations of multi-layer constrained plate and cylindrical shell.The results show that as long as the thickness of damping material and constraining material is the same,the ITMM can solve the equations of constrained damping structure of any layer.Comparison of structural vibration characteristics of different layers shows that multi-layer damping structure can achieve better damping effect.Further,the impact of the number of layers and layout of damping material on the vibration characteristics were investigated.The constrained damping cylindrical shell was taken as research object,and the dynamic equations of axial segmental covered damping structure were established.Then the transfer matrix method was further improved,and based on this,the state vector and boundary conditions of multi-layer damping material covered segments were introduced to the uncovered segments,and re-established the transfer matrix of each segment such that the order of transfer matrix of any segment is equal.Thereby the transfer matrix method of segmental covered multi-layer damping structure is established,which can analyze the vibration characteristics of partially covered damping structure of any segment,any layer.This method was confirmed by a numerical example.The impact of cover location and cover area of damping material on the structural vibration characteristics has been studied,which illustrated that partially covered structure is superior.The vibration characteristics of rotating cylindrical shell were also investigated,in which static stress and inner stress were neglected and the dynamic equations of rotating cylindrical shell were simplified.This was confirmed by a numerical example.On this basis,dynamic equations of constrained damping cylindrical shell at rotating state were established.Then its wave-vibration characteristics were investigated and the impact of forward and backward traveling and rotating velocity on the damping effect were studied.