Vibration Response And Transfer Analysis Of L-shaped Thin Plate On Elastic Foundation

The structural vibration and sound transmission of indoor transformer engineering can be abstracted as a coupled structure vibration response and transmission analysis problem on elastic foundation.Research on the dynamic behavior of coupled-plate structures is often limited to classical boundary conditions,and the solution methods are not uniform;at the same time,the vibration research of coupled-plate structures on elastic foundations is insufficient.In view of the above-mentioned research deficiencies,this paper conducts a systematic study on the vibration response and transmission analysis of the L-shaped thin plate.The main work is as follows:1.Using Winkler foundation model,the rectangular thin plate boundary is expressed as a combination of transverse spring and torsion spring to simulate elastic boundary conditions,and the transverse displacement function is expressed as an improved two-dimensional Fourier series form(two-dimensional Fourier cosine series And the linear combination of eight auxiliary series),and finally use the energy variation method to derive the matrix expression of the vibration equation of the structure.Through the analysis of the harmonic response of the rectangular thin plate modal analysis,and the comparison with the results of the finite element method,the correctness and effectiveness of this method are verified,and the changes in the number of resonance peaks at different excitation points and different response points are further explored.2.According to the idea of single plate vibration analysis on elastic foundation,Winkler foundation model is still used to establish a displacement model that satisfies arbitrary boundary conditions.Unlike thin plates,since the influence of in-plane vibration cannot be ignored for L-shaped thin plates,the surface must also be established.The displacement function model of internal vibration(in-plane vibration displacement can be expressed by a two-dimensional modified Fourier series).In addition,four types of coupling springs are introduced at the connection of the two plates to fully consider the bending moment,transverse shear,and in-plane there are four coupling effects of longitudinal force and in-plane shear force.Finally,the response matrix is solved by the energy variation method.The accuracy of the method is verified by analyzing the calculation example of the L-shaped thin plate and comparing it with the result of the finite element method.Further explore the influence of the location of the excitation point,the coupling condition and the coefficient of the foundation machine tool on the structural vibration.3.For the energy transfer analysis of the L-shaped thin plate on the elastic foundation,first follow the theoretical framework of vibration response,and then solve the internal force field of the L-shaped thin plate on the elastic foundation(including bending moment,transverse shear,torque,in-plane normal stress and in-plane shear,etc.)distribution.Finally,the input power of the structure,the transmitted power and the structural sound intensity components of each point are solved.The influence of the position of the excitation point,the damping ratio of the structure,the coupling stiffness and the foundation bed coefficient on the input power and the transmitted power of the structure is explored through the analysis of examples.In addition,through the power flow streamline diagram,the energy propagation path and propagation law of the L-shaped thin plate are identified,and the influence of the excitation frequency and the position of the excitation point on the power flow distribution of the L-shaped plate is explored.