张拉成形平面薄膜结构及其振动模态特征OA

Objective Space membrane antennas possess several inherent advantages that make them highly appealing for aerospace applications:Their very low mass reduces spacecraft launch weight and cost;their high packing efficiency allows compact folding and storage,which is critical when launch volume is limited;and their good environmental adaptability enables operation under extreme temperatures,vacuum,and radiation.Moti-vated by the growing interest in large planar membrane antennas,a dedicated planar membrane model was designed and fabricated,and a dy-namic modal test was conducted to evaluate its tension-formed structural performance. Methods Firstly,the form-finding process was used to determine the initial equilibrium shape of the membrane structure under a prescribed pre-stress,and the subsequent tension-forming process was used to tension the membrane to the target stiffness and geometry;both processes were simulated using the nonlinear finite element method(FEM).The tension-forming analysis explicitly modeled sliding-friction contact between the cables and their sleeves.To compare with the observed wrinkle patterns,an additional finite element analysis incorporating a wrinkling-corrected membrane constitutive model was performed to obtain the directions of the maximum principal stress under self-weight and initial pre-tension loads.A modal analysis of the test specimen was then conducted using FEM considering the added mass of the surrounding air in ground tests.Fi-nally,the planar membrane specimen was tensioned and tested under three loading cases:Initial pre-tension,low tension,and high tension.The measured wrinkle distributions and modal properties were compared with the numerical results. Results and Discussions The form-finding results showed that the short-span non-semicircular membrane had a more uniform stress distribution,whereas the short-span semicircular membrane exhibited relatively nonuniform stress near the corners,and its catenary radii deviated from the theoretical value.Therefore,the short-span non-semicircular configuration was adopted for subsequent finite element analyses and for the test specimen.In the tension-forming analysis,friction between the cables and sleeves altered both the direction and magnitude of the membrane prin-cipal stresses.The first principal stress shifted from the direction normal to the membrane edge toward the tangential direction.Friction also caused the minimum stress to occur at the cable mid-span and the maximum stress at the cable ends,while membrane stresses in the central re-gion exceeded those near the ends.Compared with the friction-free case,the stress at the cable ends remained almost unchanged,whereas the mid-span cable stress decreased.The normal stress in the x-direction of the central membrane element increased substantially,while the normal stress in the y-direction increased slightly relative to the friction-free case,and the von Mises equivalent stress increased with increasing friction coefficient.Modal analysis,which included the model's self-weight and an added air mass of 1.769 kg/m2,yielded the specimen's natural fre-quencies and mode shapes.Through the tensioning and modal tests,wrinkle distributions and modal frequencies were measured.Under initial pre-tension,numerous relatively large wrinkles formed in the upper central region,with fine,dense wrinkles along the inner side of the sleeves near the lower edge;increasing tension progressively improved membrane flatness.The wrinkle orientations agreed well with the directions of the maximum principal stress predicted by the wrinkling-corrected membrane constitutive model.Due to the geometric symmetry of the specimen and the high modal density resulting from the membrane's low bending stiffness,the first and second natural frequencies were very close,leading to easy mode coupling;apart from these coupled modes,the measured mode shapes and frequencies matched the numerical results closely,with frequency errors within 10%.These outcomes verify the reliability of the numerical methodology. Conclusions Friction between the cables and sleeves has a decisive influence on the stress distribution in both the membrane and the cables.The dynamic modal tests clearly captured the model's vibration characteristics under different load levels,and the results were compared with those from the finite element analyses.A detailed comparison between tests and simulations confirms that the tensioning system performs as intended and that the numerical model can reliably predict the actual structural response.