The Global Vibration Research Of Rectangle Thin Plate And L-Shape Coupling Plate On Elastic Foundation

As a common structural unit,rectangular thin plate and its coupling structure on elastic foundation are widely used in engineering construction.In addition,many of these large and complex engineering structural components,such as space launch pad,building foundation floor slab and rigid pavement of expressways,can be considered or simplified as plate structures for mechanical analysis and design.Most of the researches on the dynamic behavior of plate structure on elastic foundation are limited to several classical boundary conditions or their combined forms.The vibration solution of the two-parameter upper plate structure with free boundary or elastic boundary usually ignores the influence of the settlement of the foundation outside the plate,resulting in a large error.Meanwhile,the vibration study of coupled plate structure on elastic foundation is not enough.Therefore,in view of the deficiencies mentioned above,this paper gives full consideration to the arbitrary setting of boundary conditions and the influence of the settlement of the foundation outside the plate,and seeks the global and unified solution method for the vibration analysis of rectangular thin plate and L-shaped coupled plate on elastic foundation,so as to provide a research foundation for the correlation analysis of engineering structure vibration.the following research work has been carried out:(1)Based on the Winkler foundation model and the two-parameter foundation model,the transverse and torsional elastic components and parameter setting are used to simulate the state and category of arbitrary boundary constraints,and the bending displacement function is described as an improved Fourier series to establish the vibration analysis model of rectangular thin plate on the elastic foundation that can adapt to the setting of arbitrary boundary conditions.Through parametric analysis,the convergence and accuracy of the model have been verified from the perspectives of different boundary conditions,dimension parameters and mode shapes.(2)According to the assumption of Vlazov,settlement of the foundation outside the plate in each region is represented as the product of the displacement of the plate edge and the plate angle and an exponential attenuation function,and the global vibration model of the rectangular thin plate on the two-parameter foundation is established based on Hamilton principle.By means of parametric analysis,the influence of the settlement of the foundation on the structural vibration characteristics under the condition of free boundary and elastic boundary has been investigated.(3)Longitudinal and tangential elastic components are used to simulate the states and categories of arbitrary boundary constraints,and the in-plane displacement function is described as an improved Fourier series to verify the effectiveness of the in-plane vibration model of rectangular thin plates,which provided theoretical support for the research of L-shape coupling plate modeling method on elastic foundation.(4)As a part of the basic research on vibration transfer of coupled structure on elastic foundation,the global vibration model of L-shape coupling plate on elastic foundation was established considering the interaction between in-plane vibration and out-of-plane vibration.Through parametric analysis,the model has been proved to be suitable for the vibration behavior analysis of arbitrary coupling conditions,boundary conditions,coupling included angles and different elastic foundation models.