The Bending And Steady-state Vibration Of Four Free Edges Rectangular Plate Considering The Tangential Friction On The Winkler Foundation

Plates on elastic foundation are the basic components of civil engineering structures,such as the foundation of building structures,airport runways,dock floors,and highway rigid pavements.The calculation of these engineering structures can simplify the calculation of elastic foundation plate,and therefore,be accurate and reasonable.Its calculation is very important.There are many existing elastic foundation models.The Winkler foundation model has simple assumptions,clear conditions and easy calculation.Although there are certain defects,it is widely applied in practical engineering because of the practicality of fitting projects.In this paper,the research on the bending of the plate on the Winkler foundation considering the horizontal friction has been studied.This is a supplement to the research field of soil-static interaction and has a high reference value for engineering practice.According to relevant literature,the key to the analysis and solution of the static and dynamic problems on the elastic foundation plate is to find a deflection function that can satisfy the four-sided free boundary condition.Based on the Winkler foundation model,the control of the rectangular plate considering the tangential friction force is established.The equation is then deduced by the double Fourier series expansion.Then the Matlab software is used to program and calculate the numerical solution of the Four free edges rectangular plate bending considering the tangential friction on the Winkler foundation.By comparing with the corresponding examples,the effect of tangential friction on the bending of the plate was analyzed,and the related sensitivity factors were studied.Then,based on this,the steady-state vibration of the four free edges rectangular plate considering the tangential friction on the Winkler foundation is studied,and the effect of tangential friction on the steady-state vibration of the plate is analyzed,then,the effects of different excitation force frequencies and related sensitivity factors on the steady-state vibration of the plate were studied.The double Fourier series expansion method has a clear theory,a simple method,and has a wide range of applications in mechanics.When solving the bending and steady-state vibration problems of the four free edges rectangular plate considering the tangential friction on the Winkler foundation,the theory is clear,the calculation is simple,the result is accurate,and the convergence speed is fast.It can be extended to solve various related problems,has a broad application prospects.