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At least 55 records · Page 3

Conical shell vibrations

Prediction of natural vibration frequencies and mode shapes of thin walled conical shells fixed at one end and free at other end

VIBRATIONAL FREQUENCY↗

On the Development of Shell Buckling Knockdown Factors for Stiffened Metallic Launch Vehicle Cylinders

From the 1920s to the early 1970s, many shell buckling experiments were conducted in an effort to understand the complex buckling behavior exhibited by thin-walled cylindrical shells, to provide data to correlate with new shell stability theories, and provide design guidelines. Typically, the experiments yielded buckling loads that were substantially lower than the corresponding analytical predictions, which were based on simplified linear bifurcation analyses of geometrically perfect shells with nominal dimensions and idealized boundary conditions. The seminal works by von Kármán and Tsien, by Donnell and Wan, and by Koiter identified small deviations from the idealized geometry of a shell, known as initial geometric imperfections, as a primary source of the discrepancy between corresponding analytical predictions and experimental results. However, the computational tools and capabilities at that time could not perform the nonlinear analyses needed to assess the effects of these imperfections on the buckling behavior of thin-walled shells. Thus, buckling design allowables were determined by establishing lower bounds to test data. Specifically, empirical design factors, that have become known as knockdown factors, were determined and were to be used in conjunction with linear bifurcation analyses for simply supported shells; that is, these empirical factors were used to "knock down" the value of the unconservative simplified analytical prediction. This approach to shell buckling design has proved satisfactory for most design purposes and remains prominent in industry practice, as evidenced by the extensive use of the NASA space vehicle design criteria and recommendations. Unfortunately, the current design guidelines have not been updated since they were first published in the late 1960s and may not be able to take full advantage of modern materials, precision manufacturing processes, and new structural concepts.

Hilburger, Mark W.↗

On the Theory of Anisotropic Shallow Shells

A numerical analysis of thin-walled shallow shells is presented. Equations of equilibrium and relations between deformations and stresses are included along with fundamental differential equations.

Ambartsumyan, S. A.↗

Nonlinear vibration of cylindrical shells

The large amplitude vibration of a thin-walled cylindrical shell is analyzed. A perturbation method is used to solve the steady-state forced vibration problem. The simply-supported boundary conditions and the circumferential periodicity condition are satisfied. The resulting solution indicates that in addition to the fundamental mode, the response contains asymmetric modes as well as axisymmetric modes with the frequency twice that of the fundamental mode. Vibrations involving a single driven mode response are investigated. The results indicate that the nonlinearity is either softening or hardening depending on the mode. The vibrations involving both a driven mode and a companion mode are also investigated. An experimental investigation is conducted, and the results are in qualitative agreement with the theory. 'Nonstationary' response is detected at some frequencies for large amplitude response in which the amplitude drifts from one value to another. Various nonlinear phenomena are observed and comparisons with the theoretical results are made.

Chen, J. C.↗