Design Of Static And Dynamic Properties Of Composite Sandwich Structures Under Compression

The buckling and vibration problems are the two most critical issues in the design of the sandwich panel and they directly determine the service performance of sandwich panel.Over the past few decades,there has been many studies on the buckling problem,and most of these early studies focused on isotropic sandwich structures.Besides,the established theoretical models have a certain degree of dispersion,and there are relatively few studies on the buckling of composite sandwich structures;so far,an accurate unified theoretical model for the buckling of composite sandwich beams/plates still remains to be established.Unlike thin-walled beam/plate structures,the mechanical behavior of sandwich structures reflects some unique properties.For example,the local failure modes of sandwich beam/panel are very important,and these local failure modes are likely to occur before or shortly after the global failure mode(i.e.,the local mode may have a similar or lower eigenvalue than the global mode);this phenomenon has already been noticed in the buckling problem but is still rarely studied in vibration problems.Regarding the vibration problem,most of the existing research focused on the free vibration of the sandwich beam/panel bearing no external load,and there are relatively few studies on the free vibration of the sandwich beam/panel subjected to an axial preloading.Based on the above background,in this paper,the vibration problems of sandwich beams/plates under an initial axial compression load and the buckling problems of composite sandwich beams/plates were respectively investigated,and the key independent parameters that affecting the dynamic and static properties of composite sandwich beams/plates were determined and analyzed.The potential connection between the buckling problem and the vibration problem was revealed,and a special new vibration mode migration phenomenon was discovered,that is,the vibration mode with the lowest frequency may migrate towards the initial higher-order vibration modes due to the presence of the compressive load during the vibration process of sandwich beam/plates.In this paper,based on the Winkler foundation model and the Airy stress function method,the new analytical models for the free vibration and the buckling problem of the compressed composite sandwich beams/plates with different applicable range were established respectively,and the accuracy of the theory were verified by comparison with numerical simulation and experimental results.Compared with the numerical or experimental methods,the analytical method has the advantage of being able to determine the influence of continuous changes of key parameters in a large range on structural properties,thus reflecting the mechanism of structural mechanical behavior more completely.Based on the above descriptions,this paper mainly carries out research work in the following four aspects:(1)Based on the Winkler foundation model and Timoshenko beam model,a new analytical model for the free vibration of compressed sandwich beam/panel was established,and the closed form expressions of the natural frequency were obtained,which takes into account both the transverse shear effect and the rotatory inertia effect in the facings.Then,based on the established theory,the independent parameters that affecting the dynamic properties of the sandwich panel were determined,and a special vibration mode migration phenomenon of the sandwich beam/panel was revealed.The effects of transverse shear and rotatory inertia on the natural frequencies were analyzed;the essential reasons of the modal migration phenomenon were explained and the connection between the buckling and vibration problems of sandwich beam/panel was discussed.Finally,the theoretical results in this part were compared with the numerical results in the literature to verify the accuracy.(2)The Winkler foundation method is generally applicable to the modeling of sandwich beam/panel with honeycomb cores and can be used to predict the symmetrical or the single-sided instability modes of structures.When the core is composed of isotropic materials,using the Winkler foundation method will introduce certain assumptions to the core;therefore,in this part,a high-precision modeling method was adopted to investigate the buckling problem of sandwich beams/plates.Based on the Airy stress function method and the Timoshenko beam model,an accurate unified analytical model for the buckling of composite sandwich beam/panel was established in this part.The Airy stress function method does not introduce additional assumptions about the core layer,so it has high accuracy,and the established model is applicable to both the three local and the global buckling mode of sandwich structures.Then,based on the newly established buckling theoretical model,the relationship between different buckling modes of the sandwich beam/panel and the influence of material and geometric parameters on the buckling properties were analyzed;the effects of the variation in the composite laminate bending stiffness and lay-up on the buckling properties were studied,and the effect of the transverse shear and the variation in composite laminate shear stiffness on the buckling loads were investigated.Finally,the accuracy of the model was verified by comparing with the theoretical and experimental results in the literature and the finite element results obtained in this paper.(3)Based on the theoretical model in the second part,the simplified formulas of the buckling stress of sandwich beam/panels for different buckling wavelengths were established respectively.Compared with the exact solutions established in the second part,these formulas have simpler forms and maintain sufficient accuracy.Then,based on the simplified formula,the buckling failure criteria of sandwich structures suitable for engineering applications under axial compressive loads and bending loads were established respectively.By introducing different hypotheses,the internal connection between the unified accurate buckling model established in the second part and some classical theories in history including the Winkler foundation method was revealed;on the one hand,it proves the correctness of the theory in this paper,and on the other hand,it evaluates the applicable range of these classical theories.The simplified buckling stress formulation established in this section will then be applied to the vibration investigations in part 4.(4)Based on the Airy stress function method and the Timoshenko beam model,an accurate analytical model suitable for the free vibration of the sandwich beam/plate with an isotropic core under initial axial compression load was established;the closed-form expression of the natural frequency was obtained,and the independent parameters that affecting the dynamic properties of the sandwich beam/plate were determined.The variation laws of symmetric,anti-symmetric and single-sided vibration properties were analyzed respectively.The reasons and conditions for the appearance of the vibration mode migration phenomenon of sandwich beams/plates were revealed,and the effects of the geometrical parameters,material parameters of sandwich beams/plates and the axial compressive loads on the vibration properties of the structure were studied.Finally,the applicability of the theoretical model established in this chapter is discussed.