The Static And Dynamic Nonlinear Mechanical Analysis Of The Rectangular Sandwich Plates

The dissertation conducted a series of research and analysis for the nonlineardynamic and static mechanics problems of the rectangular sandwich plates. Its maincontents include: the large deflection bending, the nonlinear free vibration of the beamsandwich plates, and the nonlinear free vibration of the rectangular sandwich plates whichare simply supported at four sides and without displacement.The basic large deflection bending equations for the rectangular sandwich plates aresimplified to achieve the beam sandwich plate’s large deflection bending equations whichwill be solved under the boundary condition of two long sides simply supported andwithout displacement. As a result, a transcendental equation about the parameters n relatedto the stress can be obtained to conduct numerical calculation. The value of the parametersn will be calculated by means of the trial. Further more, the deflection curve equation, theload deflection curve and the load stress curve were found out.The basic nonlinear free vibration equations for the rectangular sandwich plates aresimplified to get the beam sandwich plate’s nonlinear free vibration equations. Based onthe hypothesis of the time mode, the unknown function was assumed as the form ofseparation for the unknown space function and the harmonic time function. Aftereliminating the time function, the control equation of the space mode which will be solvedby means of the modified iteration method can be obtained. A analytical solution ofvibration mode will be found out to achieve the relationship curve for theamplitude-frequency. It was discussed further that how the shear parameters impact thevibration.The basic nonlinear free vibration equations for the rectangular sandwich plates aresimplified by introducing the new function. Using the same method as the beam sandwichplates, this part solved the vibration equations in the condition of simply supported at foursides and without displacement. Then, an analytical solution of vibration mode and therelationship curve for the amplitude-frequency can be obtained in order to find out theinfluence of the shear parameters and the ratio of length to width on the vibration. Besides, the beam sandwich plates and the sandwich plates simply supported at four sides arecompared further more.