Vibro-Acoustic Analysis Of Ribbed Plate Structures And The Associated Strutural-Acoustic Coupled System

Ribbed plate structures are the main structural components of mechanical engineering,vehicle engineering,marine engineering,aerospace engineering and other engineering systems,so it is of great theoretical significance and applied value to study their vibration and acoustic characteristics.In this thesis,surrounding the dynamic model establishment,wave propagation mechanism and vibration-acoustic coupling properties of ribbed Kirchhoff thin plate,ribbed Mindlin thick plate and ribbed plate-acoustic cavity coupling system are systematically studied.The main research works of this thesis are as follows:(1)The dynamic model is established for the vibration response of orthogonal ribbed Kirchhoff thin plates with fully clamped,fully simply supported and arbitrary combination of clamped and simply supported boundary conditions.In the modeling process based on the finite integral transformation method,there is no need to manually select the modal functions of the plate and the beam.And the general solution of the vibration response model of orthogonal ribbed plate with various combinations of clamped and simply supported boundary conditions can be also obtained.The vibration response of the ribbed isotropic plate is compared with that of an orthotropic plate,and similarities between the responses are discussed.The findings confirm that an orthogonal ribbed isotropic plate can be used to replace an orthotropic plate with similar vibration properties.(2)An analytical solution utilizing the double finite cosine integral transformation technique is presented for the study of the free and force vibration of a ribbed plate having a completely free boundary condition on all its edges.And the vibration modes of the free-free base plate can be classified into four mode groups according to the symmetric properties of the plate with respect to the two middle lines parallel to the two pairs of the plate edges such as double symmetric,double anti-symmetric,symmetric/anti-symmetric and anti-symmetric/symmetric.Effects of rib insertion on the four mode groups of plate are then studied.It is found that the effect of rib insertion on the modal vibration varies from case to case and depends upon the role that the rib plays in the modal vibration.In general,both rib's mass and stiffness take part in the plate modal vibration and their combined effect on the modal vibration depends upon which one plays a more prominent role.(3)Since Kirchhoff's thin plate theory ignores the effects of transverse shear deformation and rotatory inertia,the vibration prediction error will gradually increase with the increase of frequency or thickness of the plate.The dynamic model of the ribbed Mindlin plate with higher vibration prediction accuracy is established by using the modal solution approach.The model is utilized to evaluate the prediction discrepancy using a thin(ribbed)plate model.It is found that using the thin plate model would yield a less than 5 percent error when the ratio of the plate bending wave length to thickness is greater than 12 times.It is also found that shear deformation of the plate plays a more dominant role in affecting the prediction accuracy of a ribbed plate than the rotatory inertia,which is the main factor causing the difference between the results predicted using Mindlin and Kirchhoff plate models.(4)An analytical solution utilizing a double finite sine integral transformation technique is presented in this study for the vibration prediction of the ribbed plate with various boundary conditions by using Mindlin thick plate theories.And the general solution of the vibration response model of the ribbed Mindlin plate with various combinations of clamped and simply supported boundary conditions is also obtained.The models are utilized for the study of the effects of shear deformation and rotatory inertia on the energy flow across the beam/plate interface of the ribbed plate.It is found that the inclusion of rotatory inertia of the beam and the plate on the model will only affect the energy flow component controlled by the moment coupling but not that controlled by the shear force coupling.Whilst the inclusion of the shear deformation of the beam and the plate is mainly lead to a decreasing amplitude of the energy flow for the mode group where the beam is located away from both the nodal and the anti-nodal positions of the modes,with an exception of shear deformation of the plate which also lead to an increased amplitude for the mode group where the beam locates at the anti-nodal position of the modes.(5)An analytical solution is presented for the study of vibration response of a ribbed Mindlin plate having a completely free boundary condition by utilizing the finite cosine integral transformation technique.The validity of the model is evaluated by comparing the calculated natural frequency and forced vibration responses of the ribbed plate with those calculated using finite element analysis and experimental results,and it is found that they are in good agreement with each other.Thus,it lays a good foundation for the engineering application of the theoretical model.It is found that only when the rib plays as a stiffness attachment and the distance between the excitation source and the rib is less than a quarter of the bending wavelength,the vibration response will be controlled by both the plate stiffness and the beam stiffness.(6)An analytical solution is presented in this study for the vibro-acoustic analysis of a coupled ribbed Mindlin plate-cavity system due to an internal point sound source excitation.The analytical solution is validated by comparing the result with that obtained using finite element analysis.Generally good agreements are found between the results.The theoretical model is further extended to a multiple plate-acoustic cavity coupling system,and the corresponding numerical simulation verification is carried out.Then,the model is used to study the sound transmission either to a single ribbed-plate or multiple ribbed-plates separated by air gaps.Results demonstrate that the rib insertion are more effective to reduce the energy transmission to the plate controlled by the plate control modes.Whereas the attenuation of the energy transmission to the plates is more effective for the cavity control modes when multiple ribbed panels with air gaps are used.Finally,the vibration and vibro-acoustic coupling characteristics of ribbed plates are summarized,and the focus of the follow-up research work is pointed out.