Static And Dynamic Stability Of Typical Phononic Crystal Beams

Phononic crystal beam is a kind of new artificial composite dielectric structure composed of specific microstructural units.It exhibits a unique set of elastic wave regulation capabilities that component materials do not possess,and has been widely used in aerospace,ship,transportation and other engineering fields.In practical engineering applications,this kind of special structural beam will suddenly fail under the action of complex external loads.Once buckling occurs,the structure will collapse,which is far more dangerous than strength failure.Therefore,the stability of phononic crystal beam is an important aspect to be concerned and studied when the phononic crystal beam theory is applied in practice.In this paper,bragg-type phononic crystal beam and local resonant phononic crystal beam are taken as the research objects.Meanwhile,the paper has carried out a comprehensive study on the buckling characteristics and dynamic stability of phononic crystal beams by combining theoretical analysis,simulation calculation and experimental research,and revealed the relevant laws and behavior characteristics which are different from the traditional homogeneous beam structure.Finally,some useful measures are proposed to improve the stability of phononic crystal beams,which can be used to guide engineering practice.The main research work of this paper is as follows:1.The static buckling and natural characteristics of phononic crystal beams are studied.Based on the idea of first decomposition and then series,phononic crystal beams are divided into multi-section beams according to the beam cross-section geometry and beam material.The governing equation of buckling is established by using the transfer function method and the corresponding analytical solution is obtained.The free vibration frequencies,instability loads and corresponding modal shapes of phononic crystal beams are obtained through the displacement continuity and force balance conditions between the sub-beams.For local resonant phononic crystal beams,the idea of equivalent stiffness should be combined to equivalent the beam structure to a homogeneous beam,and the control equation should be derived and solved to obtain their natural and static buckling characteristics.2.The dynamic stability of phononic crystal beams is studied.Lyapunov dynamic instability criterion is used to judge the instability of bragg-type phononic crystal beams and the critical buckling load is obtained.Based on Hamilton’s principle,parametric vibration equations of phononic crystal beam structures under periodic loads are established by energy method in the form of Mathieu equation,and the critical vibration frequency equations of dynamic unstable regions are derived.For the local resonant phononic crystal beam,a calculation method of direct solution is summarized,which only needs the critical instability load and the transverse natural frequency of free vibration,the critical unstable region can be determined.The method not only simplifies the calculation process of critical vibration frequency,but also improves the calculation efficiency.3.Simulation verification is carried out for the above research.Using Abaqus finite element analysis software,the static buckling analysis and dynamic analysis of two kinds of phononic crystal beams are carried out and the critical load and the corresponding instability modes are obtained to verify the correctness of the theoretical results.The effects of different boundary constraints and cell parameters on the buckling characteristics and dynamic stability are investigated.Based on these effects,the corresponding measures to improve the stability are proposed.4.In terms of experimental research,samples of ABAB crystal beam and attached type local resonant phononic crystal beam are prepared,and the experimental platform is designed and built.The static buckling test and dynamic stability test of these two kinds of phononic crystal beams are carried out by using relevant experimental equipment,and the buckling mode,critical load and natural frequency distribution characteristics are investigated.The results are compared with the theoretical analysis and simulation analysis.In this paper,the static buckling and dynamic stability analysis of bragg-type phononic crystal beams and local resonant phononic crystal beams are carried out.and the critical buckling loads and buckling modes of two main types of phononic crystal beams are also revealed.It not only enriches the existing theoretical research contents of phononic crystal beams,but also provides a useful reference for the application design and research of such structures.