Geometric Eccentricity Research Articles

Effect of dropped plies on the strength of graphite-epoxy laminates

The reduction in the compressive and tensile strengths of graphite-epoxy laminates with thickness discontinuities due to dropped plies was studied by experiment and analysis. The specimens were fabricated with all the dropped plies lumped together in the center of a sixteen-ply quasi-isotropic layup, such that one surface was flat and the slope of the opposite surface changed abruptly at the dropped ply location to accommodate the thickness change. Even though the thick and thin sections are symmetrically laminated, there exists bending-extension coupling due to the geometric eccentricity of the middle planes of the thick and thin sections. Experiments were conducted on fifty-four specimens that differed in the configuration of the dropped plies only. The strength of a laminate with dropped plies is less than the strength of its thin section, and the compressive strength of a laminate with dropped plies is less than its tensile strength. The reduction in strength is directly related to the axial stiffness change between the thick and thin sections. To examine the mechanism of failure, the three-dimensional state of stress in the dropped ply region was evaluated by the finite element method. A tensile interlaminar criterion predicted the correct location of failure, but underestimated the failure load.

On Dynamic Gear Tooth Loading Due to Coupled Torsional-Lateral Vibrations in a Geared Rotor-Hydrodynamic Bearing System

This paper is an attempt to provide an estimation of dynamic gear tooth loading due to coupled torsional-lateral vibrations in a geared rotor-hydrodynamic bearing system. The effects of mass unbalance and geometrical eccentricity of the pinion and the combined effects of manufacturing errors and profile modifications of gear teeth have been considered. Gear mesh compliance and damping at gear teeth are also included in the analysis. Journal lateral motions in the oil film spaces of hydrodynamic bearings are shown to be associated with variations in the angular velocity ratio of meshing gears and with dynamic loading of gear teeth. The journal center is observed to trace trajectories of limited amplitudes under stable operating conditions.

Electric and optical anisotropy and their osmotically induced changes of photoreceptor disk membrane vesicles.

Electro-optical characterization of the photoreceptor disk membrane vesicle is performed by examining the electric field and concentration dependence of the study-state birefringence of aqueous suspensions of the vesicles. The electric polarizability anisotropy is found to be negative and of large magnitude: alpha 1 - alpha 2 = -(1-3) X 10 cm3. The optical anisotropy is determined to be also negative but of small magnitude: g 1 - g 2 = -1 X 10(-7). The specific Kerr constant deduced from the concentration dependence of the Kerr constant is found to be very large: Ksp = 7 X 10(-4) e.s.u. Upon deforming the vesicles osmotically from the spherical shell to the disk structure, the steady-state birefringence increases by an order of magnitude which is attributed solely to the increase in optical anisotropy attending the corresponding change in the geometric eccentricity of the vesicle. A plausible birefringence mechanism based on the known structural features of the vesicles is proposed, which would account for these findings.

Tortional Vibration of Along-Wind Excited Structures

A method for analyzing the torsional vibration of along-wind excited structures is presented. The method is based on random vibration concepts and yields the expected maximum translational and torsional responses of a single-mass structure. The approach is similar to the gust factor method. Aerodynamic admittance functions are derived which are used to estimate the spectral density function of the random torque and the cross-spectral density function of the force and torque acting on the structure. These are required for estimating the structure’s translational and torsional mean square responses. Results for several examples indicate that the dynamic torsional response increases as follows: as the width of the structure’s exposed face increases, as the structural or geometric eccentricity increases, and as torsional natural frequency decreases.

Coupled Torsional-flexural Vibration of a Shaft in a Geared System of Rotors : 1st Report

Coupled torsional-flexural vibration of a shaft in a spur geared system is investigated. Equation of motion which contain the terms of geometrical eccentricity of gears and mass unbalance are introduced. The coupling between torsional and flexural displacements is considered in the equations which assume that surfaces of tooth of meshed gears are always in contact during the rotation. By solving the equation, it is possible to get natural frequencies, mode shapes, and frequency response of the system. It is usual to ignore the effect of the coupling between torsional and flexural vibrations. But comparing the result with them, some new phenomena were revealed. They are: (1) shifts of the critical speeds (2) transformations of the mode shapes (3) a forced vibration which is caused by geometrical eccentricity of a gear.

Application of the Rayleigh Criterion to the Null Test of Dall-Kirkham Primary Mirrors

The Rayleigh tolerance on residual spherical aberration is utilized to predict the permitted error in geometrical surface figure eccentricity of the concave ellipsoidal primary mirror of a Dall-Kirkham objective system. The corresponding deviation from complete null when the conventional Foucault knife edge test at the conjugate foci is applied to this mirror is evaluated. This deviation is found to equal the Rayleigh limit of spherical aberration as computed for the particular mirror diameter and knife edge distance used.This equality is interpreted to mean that a mirror made to any criterion of perfection will function within that criterion in an otherwise perfect objective system even if the test procedure is completely foreign to the final use of the mirror.The effect of variation of secondary magnification as a means of improving the performance of the complete system is discussed. It is shown that primary surfaces slightly outside tolerance can be made to perform within tolerance by appropriate changes in system EFL whenever this EFL is not critical.