Research On Some Problems Of Energy Finite Element Method

Energy finite element method (EFEM), based on wave theory,establishes the relationship between time average energy density and timeaverage power from the viewpoint of energy in order to analyse theproblem of vibro-acoustic coupling and vibration in built-up structures atmiddle and high frequencies regime. Compared with FEM, EFEM canovercome the problem of crowed modes and modal overlap at middle andhigh frequencies.As previous research on EFEM didn’t take the internal damping intoconsideration at the coupling point, this study considers it to simulate theactual conditions.Firstly, we establishes wave equation of simple three semi-infinitebeams coupled at arbitrary angles based on the theory of Euler-Bernoullibeam with internal damping taken into account. According to theequilibrium and continuity conditions of the junction, near-field amplitude,far-field amplitude and longitudinal wave amplitude subjected to flexuralwave and longitudinal wave excitations are derived. Due to theintroduction of internal damping coefficient, the near-field terms will beattenuated. Near-field power dissipation coefficients, reflection coefficientsand transmission coefficients are obtained from the relationship betweenthe vibration amplitude and the vibration power. The first example,three semi-infinite beam junctions coupled at arbitrary angles, is studied toreveal the effects of internal damping coefficient, coupled angles andexcitation frequency on near-field power dissipation coefficient. Thesecond example of the same structure analyses the effects of coupledangles and excitation frequency on reflection coefficients and transmissioncoefficients. Secondly, considering internal damping coefficient, this study usesthe similar approach to investigate the vibration power reflection relationsand transmission relations of three semi-infinite spatial beams coupled at90degree. An example reveals distributive characters of power coefficientsunder the excitations of z-flexural wave, longitudinal wave and torsionalwave respectively and the effects of excitation frequency on major powercoefficients in three cases are discussed.Finally, considering internal damping coefficient, a two dimensionalframe structure is studied and energy density distribution of flexural andlongitudinal waves is obtained by EFEM on the basis of above theory.