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The dependence between static instability and kinetic instability (flutter) on autoparameteric resonance is studied by taking compressibility into account in a model of a cantilever beam under the action of a follower force. It is shown that both instabilities are formally special cases of instabilities known as subharmonic and combination resonances.
An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.
The design of an infant weight scale is reported that fits into an isolette without disturbing its controlled atmosphere. The scale platform uses strain gages to measure electronically deflections of cantilever beams positioned at its four corners. The weight of the infant is proportional to the sum of the output voltages produced by the gauges on each beam of the scale.
An energy-balance analysis is presented for adhesive failure in end loaded cantilever beams. The analysis includes the effects of input work, stored strain energy, dissipated plastic energy, and specific adhesive surface energy. Experimental results obtained with 6061-T6 aluminum are presented as evidence for the validity of the approach.-
A thrust bearing consisting of pads mounted on resilient, metallic, cantilever beams is described and analyzed. Compliance and stiffness of the bearing assembly are discussed, and the effects of bearing design parameters on performance are shown. After the general analysis, a design example is presented for a flat sector-shaped gas bearing. A special case where zero axial movement of the runner can be obtained is pointed out.
The large deformation of a cantilevered beam under a gravity tip load was studied. The beam root is rotated so that the tip load is oriented at various angles with respect to the beam principal axes. Static twist and bending deflections of the tip and bending natural frequencies were measured as a function of tip load magnitude and orientation. The experimental data are compared with the results of a recently developed nonlinear structural theory and agreement is good for deflections that are small compared to the beam span with systematic deviations for larger deflections. These results support the validity and utility of the nonlinear structural theory for rotor blade applications.
This is an addendum to an experimental study of the large deformation of a cantilevered beam under a gravity tip load. It adds higher quality and new data on the static twist and bending deflections of the beam. The experimental data are compared with a recently developed nonlinear structural theory. Agreement is good for deflections that are small compared to the beam span and has systematic deviations for larger deflections.
Two methods for studying the free vibration characteristics of a large split blanket solar array in both a 0-g and a 1-g cantilevered configuration are presented. The 0-g configuration corresponds to an in-orbit configuration of the array; the 1-g configuration is a typical ground test configuration. The first method applies the equations of continuum mechanics to determine the mode shapes and frequencies of the array; the second method uses the Rayleigh-Ritz approach. In the Rayleigh-Ritz method the array displacements are represented by string modes and cantilevered beam modes. The results of this investigation are summarized by a series of graphs illustrating the effects of various array parameters on the mode shapes and frequencies of the system. The results of the two methods are also compared in tabular form.
A miniature drag-force anemometer is described which is capable of measuring dynamic velocity head and flow direction. The anemometer consists of a silicon cantilever beam 2.5 mm long, 1.5 mm wide, and 0.25 mm thick with an integrated diffused strain-gage bridge, located at the base of the beam, as the force measuring element. The dynamics of the beam are like those of a second-order system with a natural frequency of about 42 kHz and a damping coefficient of 0.007. The anemometer can be used in both forward and reversed flow. Measured flow characteristics up to Mach 0.6 are presented along with application examples including turbulence measurements.
The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the nonlinear transient responses of a beam with solid cross section and that of a thin-walled beam on elastic supports under impulsive loads are examined.
A comparison is made between fracture toughness KIc as measured by recommended ASTM procedures and crack arrest toughness KIa as measured on more than 100 bolt-loaded double-cantilever beam (DCB) specimens from 7075, 7050, and 7049 alloy plates. Close agreement was found between the two values, KIa being on the average less than KIc over a specified range. This indicates that a simplified test based on a bolt-loaded DCB specimen could be used for quality control, lot release, and screening purposes. Measurements of crack length and specimen deflection are all that are required. The specimens do not have to be fatigue precracked, nor is a tensile machine needed.
A miniature drag force anemometer is described which is capable of measuring dynamic velocity head and flow direction. The anemometer consists of a silicon cantilevered beam 2.5 mm long, 1.5 mm wide, and 0.25 mm thick with an integrated diffused strain gage bridge, located at the base of the beam, as the force measuring element. The dynamics of the beam are like that of a second order system with a natural frequency of about 42 kHz and a damping coefficient of 0.007. The anemometer can be used in both forward and reversed flow. Measured flow characteristics up to Mach 0.6 are presented along with application examples including turbulence measurements.
The design technology is described for manufacturing a 20 m or larger space erectable antenna with high thermal stability, high dynamic stiffness, and minimum stowed size. The selected approach includes a wrap rib design with a cantilever beam basic element and graphite-epoxy composite lenticular cross section ribs. The rib configuration and powered type operated deploying mechanism are described and illustrated. Other features of the parabolic reflector discussed include weight and stowed diameter characteristics, structural dynamics characteristics, orbit thermal aperture limitations, and equivalent element and secondary (on axis) patterns. A block diagram of the multiple beam pattern is also presented.
A gas-lubricated bearing is described, employing at least one pad mounted on a rectangular cantilever beam to produce a lubricating wedge between the face of the pad and a moving surface. The load-carrying and stiffness characteristics of the pad are related to the dimensions and modulus of elasticity of the beam. The bearing is applicable to a wide variety of types of hydrodynamic bearings.
A preliminary evaluation was conducted of the use of cast urethane as a possible material for low-cost blades for wind turbines. Specimen test data are presented for ultimate tensile strength, elastic modulus, flexural strain, creep, and fatigue properties of a number of urethane formulations. Data are also included for a large-scale urethane blade section composed of cast symmetrical half-profiles tested as a cantilever beam. Based on these results, an analysis was conducted of a full-scale blade design of cast urethane that meets the design specifications of the rotor blades for the NASA/DOE experimental 100-kW MOD-0 wind turbine. Because of the low value of elastic modulus for urethane (around 457 000 psi), the design loads would have to be carried by metal reinforcement. Considerations for further evaluation are noted.
A resilient-pad gas thrust bearing consisting of pads mounted on cantilever beams was tested to determine its operating characteristic. The bearing was run at a thrust load of 74 newtons to a speed of 17000 rpm. The pad film thickness and bearing friction torque were measured and compared with theory. The measured film thickness was less than that predicted by theory. The bearing friction torque was greater than that predicted by theory.
Modification of double-cantilever-beam resistance strain gage makes boiling of hydrogen on gage arms less of problem. Modified gages are encapsulated nickel/chromium alloy, and bridge-excitation voltage is reduced from 10 to 1.5 volts. Sensitivity is 1.0 millivolt per inch with 1.5 volt excitation.
A geometrical nonlinear analysis based on an alternative definition of strain is presented. Expressions for strain are obtained by computing the change in length of the base vectors in the curvilinear element coordinate system. The isoparametric element formulation is assumed in the global Cartesian coordinate system. The approach is based on the minimization of the strain energy, and the resulting nonlinear equations are solved by the modified Newton method. Integration of the first and second variation of the strain energy is performed numerically in the case of two and three dimensional elements. Application is made to a simple long cantilever beam.