Buckling of sandwich cylindrical shells with shear deformable core through nondimensional parameters
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Equations of motion for flutter and stability of coaxial elastic circular cylindrical shells between which flows compressible fluid
Finite element computer programs were developed to determine thermal stresses and metal movement during butt welding of flat plates and bead-on-plate welding along the girth of a cylindrical shell. Circular cylindrical shells of 6061 aluminum alloy were used for the tests. Measurements were made of changes in temperature and thermal strains during the welding process.
Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.
Sanders equation for circular cylindrical elastic shell reduced to fourth order PDE
Cylindrical shell segments supersonic flutter boundaries engineering estimates related to Saturn 5 booster, obtaining thickness requirement as function of panel geometry
Cylindrical shell segments supersonic flutter boundaries engineering estimates related to Saturn 5 booster, obtaining thickness requirement as function of panel geometry
Partial differential equations for linear behavior of elastically isotropic circular cylindrical shell under edge and surface loading - structural dynamics
Equations for thermoelastic and viscoelastic cylindrical sandwich shells
Modeling of flexural and membrane type waves existing in various submerged (or in vacuo) plate and/or shell finite element models that are excited with steady state type harmonic loadings proportioned to e(i omega t) is discussed. Only thin walled plates and shells are treated wherein rotary inertia and shear correction factors are not included. More specifically, the issue of determining the shell or plate mesh size needed to represent the spatial distribution of the plate or shell response is of prime importance towards successfully representing the solution to the problem at hand. To this end, a procedure is presented for establishing guide lines for determining the mesh size based on a simple test model that can be used for a variety of plate and shell configurations such as, cylindrical shells with water loading, cylindrical shells in vacuo, plates with water loading, and plates in vacuo. The procedure for doing these four cases is given, with specific numerical examples present only for the cylindrical shell case.
Sound transmission through an infinite cylindrical sandwich shell is studied in the context of the transmission of airborne sound into aircraft interiors. The cylindrical shell is immersed in fluid media and excited by an oblique incident plane sound wave. The internal and external fluids are different and there is uniform airflow in the external fluid medium. An explicit expression of transmission loss is derived in terms of modal impedance of the fluids and the shell. The results show the effects of (a) the incident angles of the plane wave; (b) the flight conditions of Mach number and altitude of the aircraft; (c) the ratios between the core thickness and the total thickness of the shell; and (d) the structural loss factors on the transmission loss. Comparisons of the transmission loss are made among different shell constructions and different shell theories.
Semimomentless theory of cylindrical laminar shell
Longitudinal vibration of cylindrical membrane shells containing liquid, with liquid velocity potential expanded into matrix-eigenvalue problem
The force input mobility of an infinite elastic circular cylindrical shell filled with fluid is derived by using the spectral equations of motion. Mobilities are evaluated and their physical interpretations are discussed for a steel shell of thickness h/a = 0.05 filled with water and vibrating in the n = 0, 1 and 2 circumferential modes. The results are subsequently used to analyze the related situations of wave transmission through a radial ring constraint and the far field vibrational energy distributions between the contained fluid and the shell wall for line and point driving forces.
The natural frequencies and associated mode shapes for three thick open cantilevered cylindrical shells were determined both numerically and experimentally. The shells ranged in size from moderately to very thick with length to thickness ratios of 16, 8 and 5.6, the independent dimension being the shell thickness. The shell geometry is characterized by a circumferential angle of the 142 degrees and a ratio of length to inner radii arc length near 1.0. The finite element analysis was performed using NASTRAN's (COSMIC) triangular plate bending element CTRIA2, which includes membrane effects. The experimental results were obtained through holographic interferometry which enables one to determine the resonant frequencies as well as mode shapes from photographs of time-averaged holograms.
The radiation of sound from an infinite elastic cylindrical shell excited by an internal monopole source is investigated analytically. Coupled equations of motion are used. The modal mobility of the shell wall at the source plane is examined for differing source locations and the behavior is explained in terms of free wave propagation. The radiated pressure and line power from the shell surface is then evaluated for a similar range of source positions and frequencies. A real surface power flow, that circulates backwards and forward between the shell and fluid while propagating axially, but does not contribute to the radiated far field, is uncovered. Finally, the transmission loss of the shell wall is evaluated and found to be between 10 and 35 dB lower than predicted by existing simplified theories. The lower transmission losses predicted by the coupled analysis presented here are shown to be due to excitation of higher order 'shell' type waves at the source plane.
The vibrational characteristics and mechanical properties of shell structures are discussed. The subjects presented are: (1) fundamental equations of thin shell theory, (2) characteristics of thin circular cylindrical shells, (3) complicating effects in circular cylindrical shells, (4) noncircular cylindrical shell properties, (5) characteristics of spherical shells, and (6) solution of three-dimensional equations of motion for cylinders.