Investigations On Vibration Characteristics Of A Grillage Structure Using The Multi-reflection Method

The flexural wave propagation in a grillage structure with a propagating disturbance is studied firstly by the use of the multi-reflection method.The grillage structure consists of many beams intersecting each other at right angles.Each periodic binary beam consists of a finite repetition of alternating material A and material B.Based on the theory of multiple reflection,the paper verifies the effectiveness of the multi-reflection method by comparison with the finite element method.The details are as follows1.The research background and current situation of grilage structure are introduced.Secondly,Bloch theorem is given,and several methods for studying wave propagation characteristics are introduced.The multiple reflection method is emphasized.2.The multi-reflection method is applied to the periodic grid structure.A propagating wave is incident upon a discontinuity of a beam along the x axis and gives rise to transmitted and reflected waves.Here all of the transmitted and reflected waves of given flexural wave incident upon the beam at some specified location are found and superposed.These waves travel to the other beams as a bending wave in the direction of their partially reflected and partially transmitted.The relation between the wave-field of the incident wave and the wave-field of resulting waves on any beam is expressed.As an example,the application of the results to the analysis of a grillage structure with finite intersecting beams with a propagating disturbance is then demonstrated.3.Using the obtained functional relationship for numerical simulation,the result graph is basically consistent with the finite element method.A good agreement between the multi-reflection method and finite element method results on frequency response of the grillage structure validates the reliability of the multi-reflection method.4.The influences of the density and lattice constant on the band gaps of the grillage structures was analyzed by the energy band structure diagram obtained above.