Showing papers on "Cantilever published in 1973"

An augmented double cantilever beam model for studying crack propagation and arrest

Abstract: An improved analytical model for the double cantilever beam fracture specimen is developed by treating a finite length beam which is partly free and partly supported by an elastic foundation. The results obtained are shown to be in excellent agreement with established data for initial crack extension. Some preliminary computational results for unstable crack propagation are also presented.

Optimum design of vibrating cantilevers

Abstract: We determine the optimum tapering of a cantilever carrying an end mass, i.e., the shape which, for a given total mass, yields the highest possible value of the first fundamental frequency of harmonic bending vibrations in the vertical plane.

Effect of support flexibility on the fundamental frequency of vibrating beams

Abstract: The effect of rotational and translational support flexibility on the fundamental frequency of both an almost-clamped-clamped beam and a flexibly supported cantilever beam is considered. In each case the effect of a rotationally flexible support becomes more pronounced for decreasing values of the length-to-depth ratio. It is shown that the effect of end-fixity on the fundamental frequency can be of a magnitude equal to or greater than that due to the effect of shear deformation or rotatory inertia. Results using Bernoulli-Euler beam theory and Timoshenko beam theory are compared. Expressions are formulated that give the fundamental frequency as a function of the support flexibility, length to depth ratio and fundamental frequency for a rigid support.

Angular rate sensor

Abstract: A multiple axis angular rate inertial sensor measures the flexing of vibrating piezoelectric cantilevers induced by Coriolis forces, when the instrument is turned about an axis, in a mechanically resonant system excited by similar piezoelectric cantilever elements.

An approximate solution for the free vibrations of rotating uniform cantilever beams

Abstract: Approximate solutions are obtained for the uncoupled frequencies and modes of rotating uniform cantilever beams. The frequency approximations for flab bending, lead-lag bending, and torsion are simple expressions having errors of less than a few percent over the entire frequency range. These expressions provide a simple way of determining the relations between mass and stiffness parameters and the resultant frequencies and mode shapes of rotating uniform beams.

Stress Analysis of Group of Interconnect Thin-Walled Cantilevers

Abstract: The longitudinal axes of the cantilevers are assumed to be parallel while the main axes of the cross sections may have arbitrary directions. In addition to rigid diaphragms the flanges of the thin-walled cantilever may be rigidly connected by an elastic continuously distributed laminar system having bending stiffness in the direction parallel to the longitudinal axes. The analytical model may be an idealization of a group of thin-walled steel members interconnected by equidistant lammelas or a group of thin-walled stiffening elements interconnected by beams in a tall building. The basic static determinate scheme will be obtained by means of fictitious longitudinal cuts along the midpoints of the laminar system and along the ridges of the thin-walled element. The unknowns are the shear force functions along the cuts, which will be obtained from compatibility conditions along the fictive cut, expressed by a system of nonhomogeneous second-order differential equations with constant coefficients.

Characterization of p-n junctions under the influence of a time varying mechanical strain

Abstract: This paper is concerned with the influence of time varying mechanical stress on the electrical properties of p-n junctions. A strain generator based upon a vibrating cantilever beam is described. Data obtained on silicon junctions are presented and compared to a theoretical model for the effects. The results indicate that the major effect of mechanical strain is to change the energy band structure of the semiconductor.

Forced Vibration of Class of Nonlinear Dissipative Beams

Abstract: An “exact” solution employing a Galerkin-type approach is presented for the steady-state motion of a class of dissipative Bernoulli-Euler beams provided with nonlinear auxiliary mass dampers. The beams are viscously damped and the excitation is furnished in the form of distributed, or concentrated loads, or both, that vary sinusoidally. The nonlinear damper may be applied to any point in the system. Experimental studies with a mechanical model corroborate the theoretical results. Results of the analysis are applied to cantilever and simply-supported beams subjected to base excitation, uniform load, and discrete force excitation at various points along the beams. The effects of all system parameters and mass ratio are determined. It is found that the damper under consideration is an efficient device for reducing the vibration of continuous systems, particularly cantilevered structures.

Upper and Lower Bounds for Deflections of Laminated Cantilever Beams Including the Effect of Transverse Shear Deformation

Abstract: A previous paper (reference [3]) has formulated a version of the well-known plane stress problem of the end-loaded cantilever beam of narrow rectangular cross section in a way which allowed the statement of upper and lower bounds for the deflection of the beam, through use of the principles of minimum potential and complementary energy.

Dual extremum principles relating to optimum beam design

Abstract: Of concern is a cantilever beam resting on an elastic foundation and supporting a load at the free end. The beam is of rectangular cross section and of constant height but variable width. It is required to taper the beam for maximum strength. This means that the beam is to support a maximum vertical load W at the free end when the free end is given unit deflection. The constraint is that the weight of the beam should not exceed a given bound K. It is shown that the optimum taper should be so chosen that the curvature of the beam is constant. This yields the solution of the problem in terms of explicit formulas. For more general constraints, an inequality is found which gives upper and lower bounds for the maximum load W even though explicit formulas are not available.

Inelastic Shear Deflection of Steel Beams

Abstract: The effect of shear on the deflection response and on the redistribution of moments in beams is presented. Three types of beams are treated: simple, propped cantilever, and fixed. The fixed beam is...

Tapered Cantilevers with Varying Distributed Loads

Abstract: Many investigators have considered the problems of cantilever beams undergoing large deflections. Barton and Bisshopp and Drucker solved exactly a cantilever carrying a concentrated load at its free end. Hummell and Morton, Bickley, and Rhode presented an approximate treatment of a cantilever beam under uniformly distributed load. All of the above cases were for beams of constant section. Recently, Kemper solved the problems of tapered cantilevers subjected to a concentrated load at the free end by computer methods, considering both rectangular and round cross sections, and the results were checked by experimental verification. In the present note, a slender cantilever beam with a uniform taper of the rectangular cross section, carrying varying distributed loads, is considered, and the solution is obtained by the use of power series method. A general load distribution function is introduced and a set of coefficients are provide for various kinds of load distribution. Numerical results of load-deflection relationships are also presented for a cantilever with a uniformly distributed load.

The Random Vibration of a Nonuniform Cantilever Beam with Concentrated Mass

Abstract: SUMMARY The random vibration of a nonuniform cantilever beam with a concentrated mass at its end, is studied as a simple model of the suspension spring of a motor vehicle. The spectral response of the displacement of the concentrated mass is obtained when the beam is subjected to the random motion of the support. The conditions for the validity of the single degree approximation is also discussed.

An examination of the edge effect in a cantilever beam

Abstract: A solution of the plane elasticity problem for the cantilever beam is presented. The classical solution in the interior region of the beam is developed with the aid of a geometric parameter. The effect of local transverse deformations and distortions are accounted for in the solution near the clamped edge. Some numerical results are presented.

Optical Fiber Breaking Stress Distributions Obtained by a Cantilever Method

Abstract: A description is given of a cantilever apparatus to determine the mechanical strength and elastic modulus of optical fibers. This test method overcomes the problem of fiber breakage in the jaws of tensile machines. Young's modulus, the breaking stress distribution, and values of the breaking radius of curvature and strain are presented for fused quartz fibers.

On the problem concerned with the study of the effect of the ratios of the geometrical dimensions of a cantilever plate on the plate modes of vibration

Abstract: 1. It has been established that the relationship between the ordinal number of the natural frequency of the lowest plate mode of vibration and the ratio of the plate length to its width is linear; it does not depend on the form of the materials investigated and the dimensions of the cross section of the plate used. 2. An empirical expression has been obtained which allows us to determine the place of the lowest plate mode in the general spectrum of natural modes of vibration of a cantilever plate, dependent on the variation of the ratio of length to width.

Static and differential pressure transducers

Abstract: Apparatus for accurately producing a DC current or voltage directly proportional to the static pressure of a fluid or proportional to the difference between the pressures of the same or different fluids A mechanical connection is made between a pressure sensor and the free end of a cantilever beam having strain gages fixed thereto The strain gages are connected in a bridge across which a pressure analog is derived The mechanical connection includes a strip snap fit over ball bearings mounted on the beam and carrier means fixed to the sensor The ball bearings double the accuracy of the apparatus achieved with solder connections between the strip, carrier means and beam The disclosed apparatus also improves the stability of the transmitter output versus time

Transverse‐vibration responses of nonuniform, internally damped cantilever beams. I

Abstract: The Bernoulli‐Euler theory of transverse beam vibration, suitably extended to take into account internal beam damping, is used to derive closed‐form expressions for the mechanical driving‐point impedance and force transmissibility of two types of nonuniform cantilever beams that are driven at their free ends by a sinusoidally varying point force. The beams are truncated and of rectangular cross section; they have a linearly tapered depth and have either (1) constant breadth or (2) parabolically varying breadth. Representative computations of the frequency dependence of impedance and transmissibility are plotted for beams having the same length and mass as an equally long and equally massive uniform reference beam. Significant attenuation or amplification of force transmissibility is observed, depending on the proportions of the beams and on whether their depth tapers towards their fixed or free end. The measured resonance frequencies of a set of nonuniform aluminum (6061‐T651) cantilever beams agree close...

Dynamic behavior of cantilever bridges under moving loads

Abstract: THE DYNAMIC BEHAVIOR OF DOUBLE CANTILEVER BRIDGES IS STUDIED UNDER MOVING LOADS. THE BRIDGE IS TREATED AS A BEAM AND THE VEHICLE IS REPRESENTED BY TWO SIMPLE MODELS: (1) A MOVING CONSTANT FORCE, (2) A MOVING SPRUNG FORCE. DETAILED NUMERICAL RESULTS ARE PRESENTED FOR FOUR BRIDGES OF DIFFERENT ASPECT RATIOS FOR THE MOVING FORCE PROBLEM AND FOR A FEW TYPICAL CASES IN THE MOVING SPRUNG LOAD PROBLEM. THE RESULTS OF NUMERICAL STUDIES ARE PRESENTED IN TWO FORMS: (1) THE AMPLIFICATION SPECTRA, AND (2) THE "HISTORY CURVES". /AUTHOR/

Theoretical and experimental investigation of the state of stress of a cantilevered plate with low shear stiffness

Abstract: A general solution is obtained for the problem of a cantilevered, transversely isotropic plate in the form of an infinite strip with a clamped edge bent by a concentrated load applied at the free edge. The investigation relies on the equations of the generalized theory of plates [21–23] with allowance for interlaminar shears. In contrast with the Papkovich solution [1], the maximum theoretical bending moment at the clamped edge depends on the relative width of the strip and on the properties of the material. The classical result is asymptotically exact as h → 0 or GZ → ∞. The experimental results confirm the principal conclusions based on the theoretical solution.

Determination of mechanical properties of excised dog radii from lateral vibration experiments

Abstract: Experimental data which can be used as a guideline in developing a mathematical model for lateral vibrations of whole bone are reported. The study used wet and dry dog radii mounted in a cantilever configuration. Data are also given on the mechanical, geometric, and viscoelastic properties of bones.

Deformation behaviour of mild steel beams under alternating loads

Abstract: A method has been developed to predict the cyclic behaviour of simple structures subjected to reversed bending under load control conditions. Cyclic moment-curvature relations are developed from pure bending tests under moment control and are applied to predict deflection range and maximum deflection amplitude for a cantilever beam.