Abstract:Beam structures in engineering system are usually suffered by various complex loads, and these loads induces many kinds of forced vibration of beam structures in this environment inevitably. When forced vibrations are occurred, these forced vibrations are affected by many factors such as temperature, humidity, electromagnetic field, cracks, etc., and these factors constitute multiphysical fields of beam structures. In multiphysical fields’ environment, as a good analytical mathematical tool, the Green’s function method has advantages to solve multifield coupled forced vibrations of beam structures, and has good performances to discuss vibration characteristics and coupled characteristics of beam structures under actions of external forces, electricity, heat and cracks are discussed. Compared with modal superposition method, the Green’s function method has advantages that it can obtain complete and high precision analytical solution, and has characteristics of good convergence and fast operation. This paper mainly reviewed a large number of theoretical and engineering research results of the Green’s function method on research problems of forced vibrations, thermodynamic coupled vibrations, electromechanical coupled vibrations, cracked beam vibrations, and so on.