Some aspects and properties of the lateral vibration of sandwich beams are investigated, including the concept of apparent bending stiffness and shear modulus, allowing the sandwich beam dynamics to be approximately described by classical beam theory. A sixth order beam model is derived including boundary conditions, and the free and forced response of some beam configurations analyzed. The possibility of computing material parameters from measured eigenfrequencies, i. e. inverse analysis, is considered. The higher order model is also utilized for investigation of the energy propagation through sandwich composite beams and the transmission over different junctions.
The purpose of this work has been to evaluate the possibility of using modified lower order methods - such as the Bernoulli-Euler or Timoshenko beam theories with frequency dependent parameters - to calculate the response of sandwich beams subject to different end conditions. The models have been verified by measurements on a freely suspended asymmetric sandwich beam with aluminium laminates and a plastic foam core, indicating good agreement.
The flexural vibration of an asymmetric sandwich beam is modelled using Timoshenko theory with frequency dependent parameters. The advantage of this approach, as compared to using modified Bernoulli-Euler theory, is the independence of the frequency dependent parameters on the boundary conditions of the beam. Using Bernoulli-Euler theory, the apparent bending stiffness would have to depend on the particular end conditions of the beam configuration in order to achieve the best possible accuracy. Using instead Timoshenko theory, with frequency dependent bending stiffness and shear modulus parameters, this problem is avoided. The results are compared to measurements and to the results obtained from a previously derived 6th order sandwich beam theory, which takes into account the effects of pure bending of the entire beam, core shear and its coupling to the bending of the laminates, and rotational inertia. The possibility of implementing the approach in existing Timoshenko beam elements in commercial FEM programs is discussed.
The energy flow corresponding to the propagation of flexural waves in sandwich beam structures is investigated. A previously derived 6th order theory describing the bending of sandwich beams is utilized and important properties such as group velocity and energy transmission through joints are analyzed and compared to those expected from classical beam theory. The results could be applied in the method of statistical energy analysis (SEA) in order to predict the vibration level of different members of composite structures composing sandwich beam elements.
Various types of sandwich beams with foam or honeycomb cores are currently used in the industry, indicating the need for simple methods describing the dynamics of these complex structures. By implementing frequency-dependent parameters, the vibration of sandwich composite beams can be approximated using simple fourth-order beam theory. A higher-order sandwich beam model is utilized in order to obtain estimates of the frequency-dependent bending stiffness and shear modulus of the equivalent Bernoulli-Euler and Timoshenko models. The resulting predicted eigenfrequencies and transfer accellerance functions are compared to the data obtained from the higher-order model and from measurements.
The purpose of this study is to evaluate the possibility of using modified lower order methods - such as the Bernoulli-Euler or Timoshenko beam theories with frequency dependent parameters - to calculate the response of sandwich beams subject to different end conditions. The models have been verified by measurements on a freely suspended asymmetric sandwich beam with aluminum laminates and a plastic foam core, indicating good agreement.
Some basic parameters used in a traditional SEA calculation are coupling loss factors, modal densities, mobility and energy flow. For calculating the coupling loss factor the group velocity as well as the transmission coefficient for the energy flow from one structure to another must be known. These parameters are derived and discussed for some simple sandwich structures and are compared to the corresponding parameters for homogeneous structure.