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A Study On The Vibration And Transient Response Of Frames By The Method Of Reverberation Ray Matrix

Posted on:2010-04-04Degree:DoctorType:Dissertation
Country:ChinaCandidate:F X MiaoFull Text:PDF
GTID:1102360302466625Subject:Solid mechanics
Abstract/Summary:PDF Full Text Request
The researches on dynamic response of composite structures are important, since all kinds of new composite materials are increasingly used in many industry departments. In recently years, the Method of Reverberation Ray Matrix (MRRM) has been successfully used to solve dynamic response of frames and wave propagation in layered media. By Neumann series expansion in inversion of the structural matrix the singularity problem is avoided. It is an effective method in solving dynamic problems and has broad prospective. However, the studies on vibration modal analysis of frames by means of the MRRM and transient dynamic response of frames made of laminated composite beams have not been reported yet. The failure mechanism of laminated composites is more complicated than isotropic materials due to non-homogeneity and inter-laminar stresses so that the composite structure is more sensitive to dynamic load than the isotropic material. It is important in theory and in application to find effective method to analyze dynamic response of laminated composite structures. The present work proposes a method which has been proved to be applicable in solving the natural frequency and the corresponding mode of any order for isotropic frames. And the present study extends the MRRM for dynamic analysis of frames made of laminated composite beams.In terms of the MRRM and the adjoint matrix of the coefficient matrix of the governing equation, a procedure is proposed to obtain the vibration mode with wave theory. A new modal analysis procedure is proposed based on MRRM. The natural frequencies and the corresponding modes for a simply supported beam, aΓtype frame and a plane frame made of 17 aluminum bars are calculated with the method and verified by comparing with the results obtained with FEM of ANSYS. The accuracy of the natural frequencies and vibration modes obtained by MRRM are verified. The solution obtained satisfies the differential equation of the element beam and the equilibrium and compatibility conditions at the nodes. It is the exact solution of the vibration mode. It provides a new effective method for natural frequency and vibration modal analysis of complex frames.The MRRM is applied for the first time to transient dynamic analysis of laminated composite beam. The formula for asymmetrically laminated beam based on classical beam theory and the first order shear deformation theory are derived respectively. The dynamic responses under the plane strain or the plane stress hypothesis for the beam are calculated respectively. It is shown that the velocity responses under smooth triangle force pulse coincide well with that of FEM and spectrum element method. Therefore the MRRM which is used for the transient analysis of asymmetrically laminated beam is verified.Axial-bending coupling effect and axial-bending-shear coupling effect in asymmetrically laminated beam are analyzed by MRRM. The velocity responses under half cycle and rectangular force pulse with different laminate configurations are calculated. It is found that with the increase of the axial-bending coupling coefficient and axial-bending-shear coupling coefficient, the axial or transverse load can cause transverse or axial dynamic response, the amplitude of the coupling response increases with the increase of coupling coefficient apparently. The influences caused by other parameters on dynamic response are also analyzed.The MRRM formula for dynamic responses of laminated frames based on classical beam theory and the first order shear deformation theory are derived. The MRRM for the analysis of laminated frames is verified by the force and moment balance at a node of a 17-bar laminated frame. It is found that the effect of axial-bending coupling is also evident in analysis of laminated frames. The variations of the transient responses for laminated frames under the two theories due to change of other parameters are also investigated.
Keywords/Search Tags:Reverberation ray matrix method, modal analysis, elastic wave, asymmetrically laminated composite beam and frame, transient dynamic response
PDF Full Text Request
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