Analysis Of Static And Dynamic Behaviors For Fiber-metal Laminated Macro And Micro Beams

Engineering application have revealed that, compared to traditional materials, the advantages of the composite materials are incomparable, and therefore composites have a broad prospect in engineering application. Micro and nano scale experimental studies have shown that there is a phenomenon of size effect of micro and nano structures, and this phenomenon can be explained effectively by modified couple stress theory. The fiber metal laminated macro and micro beams are the research objects on this thesis. Considering its applications macroscopic and microscopic research, the mechanical model of FML macro beam under moving load as well as the nonlinear mechanics model of FML micro beam in the thermal environment are established, and effective methods are adopted to solve the problem.Based on Euler-Bernoulli beam theory and the von Karman geometric nonlinear theory, the nonlinear dynamic equations of the fiber metal laminated beams under the action of the moving loads and the steady temperature field are established by using Hamilton principle. Galerkin method and Newmark method are introduced to discrete the nonlinear governing equation on the space on the time domain, respectively, and the nonlinear algebraic equations are solved by iterative method. The influence of the speed of load, temperature, geometric nonlinearity and the type of load on the dynamic responses of the fiber metal laminated beam are discussed.By modeling the cracks as the torsion springs, the dynamic equation of the cracked fiber metal laminated beams with vibration absorber carrying moving loads is established by Hamilton principle. The modal expansion method and Newmark method is adopted to solve the governing equation numerically. Based on the dynamic response of the structure and continuous wavelet transform, the cracks are detected. The influence of the depth and location of the crack, the location and stiffness of the vibration absorber on the free vibration frequency, the response of the deflection of the beam are discussed, and the load speed, scaling factor influence on the precision of crack detection are analyzed.Based on Timoshenko beam theory, the von Karman geometric nonlinear theory and the modified couple stress theory for composites, the nonlinear governing equations of the fiber metal laminated beams are established by Hamilton principle. The analytical and numerical method are used to solve the equations, respectively. By introducing an auxiliary function, the problem of the thermal buckling and post-buckling are figured out, and by introducing differential quadrature method, the problem of the thermal buckling is worked out. The influence of the ratio of the thermal expansion coefficient of the fiber layer and scale parameter on the thermal buckling and post-buckling are discussed.Adopting non Fourier heat conduction theory, the one-dimensional heat conduction equation of the FML micro beam along the thickness direction are established. Based on Timoshenko beam theory, von Karman geometric nonlinear theory and the modified couple stress theory for composites, the nonlinear dynamic equations of the fiber metal laminated micro beams under thermal shock are founded. The differential quadrature method and Newmark method are introduced to discrete the equations in spatial and time domain, respectively, and the algebraic equations are solved by iteration method numerically. The relaxation time on the heat transfer process are discussed, and the influence of the size parameters as well as the geometric nonlinearity on the deflection responses of the micro beam are discussed.