Buckling and Free Vibration of Cylindrical Panels Under Non-Uniform Edge Loads

Abstract

Introduction of lightweight materials for different structural members of aerospace, marine, civil and automobile sectors are being made possible by utilizing nano reinforcements and addition of porosity in the bulk composite. Cylindrical curved panel structures are extensively utilized in different engineering applications owing to their better structural stability characteristics. Stability and dynamic behaviour analysis of these lightweight cylindrical panel structures is essential for the satisfactory design. In general, the buckling and dynamic characteristics of these panels are mostly studied under uniform edge load (UEL) conditions. However, the panels are exposed to nonuniform and partial edge loads in practical situation. Hence, the prediction of buckling and free vibration characteristics of the panels under different non-uniform edge loads (NELs) will help the designers in avoiding the failure of these structures. The buckling and free vibration characteristics of different nano composite panels namely, GPL reinforced porous, GPL reinforced porous core sandwich, CNT and GOP reinforced cylindrical panels under NELs are calculated using semi analytical method in the present study. Considering a higher order shear deformation theory, Hamilton’s principle is used to formulate the governing differential equations and buckling and free vibration solutions are obtained by employing the semi analytical method based on Galerkin’s approach. Initially, the membrane stress resultants due to the applied edge loads are represented through Airy’s stress function expansion. Then the stress resultants are evaluated through the minimisation of strain energy. Followed by this, equations of motion are obtained based on Hamilton’s principle and the stress resultants. The Eigen value problems of buckling and free vibration are solved using the semi analytical method.

Buckling and free vibration characteristics of graphene nano platelets (GPL) reinforced porous cylindrical panel under the inuence of NELs is studied rst. The distribution of GPL and porosity is varied in a layer wise fashion through the thickness. The effective mechanical properties are calculated using extended rule of mixture together with Halpin-Tsai micromechanics model and open-cell metal foam properties. It is found that the type of NEL greatly inuences the critical buckling load of the cylindrical panel. Further, the critical buckling load and natural frequency varies with a particular combination of porosity and GPL distributions. Next, a sandwich cylindrical panel with GPL reinforced porous core and metal facing sheets is analyzed. The effective mechanical properties are obtained by using properties of open cell foams and Halpin–Tsai micro mechanical model. Effects of nature of in-plane edge load, distribution of porosity and GPL, porosity coefcient, GPL loading, core to total thickness ratio are analyzed in detail. It is found that for the panel with high core thickness, even for the higher amount of porosity, the buckling resistance and free vibration frequency can be improved by properly tailoring the graded distribution of both the GPL and pores. Furthermore, a signicant variation in buckling load and free vibration frequencies is observed with respect to the type of in plane loading. Remarkable change in buckling mode and free vibration mode shape (with increase in the load intensity) is observed for panels having higher aspect ratio. The sandwich cylindrical panel with a core having a distribution of less porosity and high GPL content at the extreme surfaces provides maximum buckling strength and free vibration frequency value. Next, buckling and free vibration characteristics of agglomerated carbon nanotubes (CNTs) reinforced nano cylindrical panels are studied considering nonlocal elasticity theory. Effective material properties of the agglomerated CNT reinforced composite are obtained using a two-parameter micro-mechanics model while Eringen’s non-local theory is used to account the size effect. A comprehensive study is carried out to analyze the inuence of various degrees of agglomeration (complete, partial), nature of edge load , and non-local effects on the buckling and free vibration response of CNT reinforced nano cylindrical panel. The results revealed that non-local size effect leads to a reduction in stiffness and thus reduces buckling and dynamic characteristics. It is also observed that critical buckling load varies with type of in plane load. The reduction in natural frequency with increase in the edge load intensity is different for different type of NEL. Finally, the buckling and free vibration characteristics of graphene oxide powder (GOP) reinforced cylindrical panels are studied. Inuence of loading of GOP quantity, nature of grading of GOP, nature of non-uniform and partial edge loads on critical buckling coefcient and fundamental frequency and mode shapes are investigated. It is noted that the buckling and vibration characteristics are sensitive to the nature of GOP grading, GOP loading and nature of variation in edge loads. Furthermore, the fundamental buckling mode is not always the typical (1, 1) mode instead of that (2, 1) mode is observed as the buckling mode according to the variation in aspect ratio and nature of edge loads. It is found that near critical buckling load, the fundamental vibration mode changes to (2,1) from (1,1) for parabolic and partial edge loading cases for the panels with aspect ratio higher than 1.3.