| The environmental vibration and noise pollution of the building are harmful to people daily life.In order to suppress the vibration transmission and noise,the vibration characteristics of the structure need to be analyzed and calculated.The bottom building can be regarded as the rectangular plates and their coupling structures on elastic foundation.In order to simplify the calculation,Kirchhoff theory is mostly used for the study of the dynamic behavior of the plate structure on the elastic foundation.With the increase of plate thickness,the effect of shear deformation and moment of inertia cannot be ignored.Therefore,more accurate plate theory is needed to analyze and calculate.As one of the important factors affecting the vibration characteristics of structures,boundary conditions play an important role in the vibration study of structures.It is important to study the vibration modeling for the plate and its coupled structure on elastic foundation subjected to arbitrary boundary by using the Mindlin-Reissner theory.The influencing factors for the vibration characteristics of the whole structure need to be analyzed.For the plate structure on two parameter foundation,settlement problem of soil outside the plate can be ignored when the boundary condition is rigid constraint,but it may cause a big error when the boundary is free.At the same time,less work has been done to investigate the vibration of the thick coupled plate on elastic foundation.Therefore,this paper,around the above problems,in consideration of the arbitrary setting of boundary conditions and the influence of the settlement of the foundation outside the plate,seeks a unified solution for the vibration analysis of rectangular thick plates and their coupled structures on elastic foundation,which provides a research foundation for the vibration analysis of the related structures in engineering.The main research work has been carried out in this dissertations:(1)Based on Mindlin theory,Winkler foundation model and two parameter foundation model are selected to solve the vibration of plate on foundation.The lateral,rotating and torsional elastic components are set around the plate.By setting the corresponding parameters to simulate arbitrary boundary constraint state.The displacement function and two rotations functions can be expressed by using the improved Fourier series.Combining with Hamilton principle,the unified analysis model of the vibration of the rectangular plate on elastic foundation is established.The necessity of this method is determined by comparing with the calculation results of Kirchhoff thin plate theory.Further,the numerial results are presented to validate the fast convergence and accuracy;(2)Considering the influence of the settlement of the foundation outside the plate,the analysis model of the rectangular thick plate on the two parameter foundation is established.Through parametric analysis,the influence of the settlement of the foundation outside the plate on the vibration characteristics of the structure is studied under the condition of free boundary or elastic boundary;(3)The displacement function of in-plane vibration is described by the improved Fourier series,and the vibration model of in-plane rectangular thick plate is established,which provides theoretical support for the research of the modeling method of thick coupling plate on elastic foundation;(4)The vibration calculation model of the coupling plate on the elastic foundation is established with and without considering the in-plane vibration.Through numerical analysis,the necessity of considering the in-plane vibration of the thick plate is determined.Comparison with finite element results,verify that this model is suitable for calculation of vibration characteristics under arbitrary boundary conditions. |
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