求解声子晶体Euler梁弯曲振动能带结构的一种改进传递矩阵法

An Improved Transfer Matrix Method for Solving Bending Vibration Band Structure of Phononic Crystals Composed of Euler Beams

用于计算声子晶体Euler梁弯曲振动能带结构的传递矩阵法有如下缺点:待定参数无实际物理意义、传递矩阵的计算较为繁琐以及连续性条件的应用不直接等。为解决目前存在的问题,引入Krylov函数将待定参数转化为梁端位移、转角、弯矩和剪力4个具有明确意义的参数,使处理原胞内及原胞间不同材料梁连接位置的变形和受力连续条件直接化;并由此推导了形式较为简单的传递矩阵及相应的能带结构计算方法,并通过算例验证了该方法确适用于计算声子晶体Euler梁的弯曲振动能带结构。

The normal transfer matrix method for solving bending vibration band structure of phononic crystals composed of Euler beams had several defects,such as unknown parameters are without actual physical meanings,the continuity conditions are applied indirectly,and the computation of the transfer matrix are inconvenience,especially,in terms of multi-component problems.To overcome these problems,the Krylov functions were introduced to transform the unknown parameters into 4 initial parameters with explicit meanings of displacement,rotation angle,bending moment and shearing force of beam-ends.These lead to a natural and simple process when the deformation and force continuity conditions were handled within a primitive cell and between primitive cells.On this basis,the improved transfer matrix with a simple and regular form was derived,as well as the corresponding computational method of band structure.An illustrative example shows that the method is suitable for solving band structure of phononic crystals composed of Euler beams.