Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

SUMMARY Spline and generalized spline smoothing is shown to be equivalent to Bayesian estimation with a partially improper prior. This result supports the idea that spline smoothing is a natural solution to the regression problem when one is given a set of regression functions but one also wants to hedge against the possibility that the true model is not exactly in the span of the given regression functions. A natural measure of the deviation of the true model from the span of the regression functions comes out of the spline theory in a natural way. An appropriate value of this measure can be estimated from the data and used to constrain the estimated model to have the estimated deviation. Some convergence results and computational tricks are also discussed.

Improper Priors, Spline Smoothing and the Problem of Guarding Against Model Errors in Regression

A brief review is given of techniques which have been employed in attempts to determine the mechanical properties of composite materials under tensile impact loading. The difficulties encountered in the design of a satisfactory tensile impact testing machine for composite materials are discussed and a new method, using a modified version of the standard tensile split Hopkinson's pressure bar (SHPB), is described. Dynamic stress-strain curves for unidirectionally-reinforced carbon/epoxy composite, in which failure occurs in less than 30 μsec at a mean strain rate of about 400 sec−1, are presented and their validity is established. An extension of the technique to allow the testing of wovenroving reinforced glass/epoxy composites is described and dynamic stress-strain curves obtained for which the times to failure approach 100 μsec and the average strain rate is of the order of 1000 sec−. Comparative stress-strain curves at low and intermediate rates of strain are obtained and the effect of strain rate, over about 7 orders of magnitude, on the tensile modulus, and strength, fracture strain and energy absorbed in fracturing is determined. The limitations of the technique are discussed.

A tensile testing technique for fibre-reinforced composites at impact rates of strain

A review of the tensile, compressive, flexural and shear properties of hybrid fibre-reinforced plastics.

Recent Advances in Liquid Sloshing Dynamics

A method was developed for testing and characterizing composite materials at strain rates in the 100 to 500 s−1 regime. The method utilizes a thin ring specimen, 10.16 cm (4 in.) in diameter, 2.54 cm (1 in.) wide and 6–8 plies thick. This specimen is loaded by an internal pressure pulse applied explosively through a liquid. Pressure is measured by means of a calibrated steel ring instrumented with strain gages. Strains in the composite specimen are measured with strain gages. Strains in the calibration and specimen rings are recorded with a digital processing oscilloscope. The equation of motion is solved numerically and the data processed by the mini-computer attached to the oscilloscope. Results are obtained, and plotted by an X-Y plotter in the form of a dynamic stress-strain curve. Unidirectional 0-deg, 90-deg and 10-deg off-axis graphite/epoxy rings were tested at strain rates up to 690 s−1. Times to failure ranged between 30 and 60 μs. The 0-deg properties which are governed by the fibers do not vary much from the static ones with only small increases in modulus. The 90-deg properties show much higher than static modulus and strength. The dynamic in-plane shear properties, obtained from the 10-deg off-axis specimens, are noticeably higher than static ones. In all cases the dynamic ultimate strains do not vary much from the static values.

New method for testing composites at very high strain rates

The influence of ply-stacking sequence and ply orientation on the magnitude of lamination residual stresses in graphite/polyimide angle-ply laminates was investigated. The effect of stacking sequence was investigated with laminates of [02/±45]s, [±45/02]s, [0/+45/0/−45]s and [+45/02/−45]s layup. The effect of ply orientation was evaluated with additional specimens of [02/±15]s and [02/902]s layup. Thermal strains were measured using embedded-gage techniques. Residual strains were determined by comparing thermal strains in the angle-ply laminates with those of a unidirectional laminate. The ply-stacking sequence did not have an influence on the magnitude of residual strains. The highest residual strains occur in the [02/902]s laminate and the lowest, approximately one-fourth in magnitude, occur in the [02/±15]s laminate. The maximum residual strains in the [02/±45]s group are slightly lower than those in the [02/902]s laminate. Residual stress computations show that, at room temperature, the transverse-to-the-fibers stresses in all plies, except those of the [02/±15]s laminate, exceed the transverse tensile strength of the unidirectional material.

Effect of laminate construction on residual stresses in graphite/polyimide composites: The effects of ply-stacking sequence and ply orientation on the magnitude of residual stresses were investigated experimentally in graphite/polyimide angle-ply laminates using embedded-strain-gage techniques

Breathing vibrations of pressurized fluid-filled cylindrical shells analyzed, establishing characteristic equations

Breathing vibrations of pressurized partially filled tanks.

Cubic-spline and discrete-quadratic polynomial techniques are presented for reliably computing up to third-order derivatives of experimental information. The concept is demonstrated by stress analyzing from measured displacements a transversely loaded plate and a beam under four-point bending. The respective displacement fields were recorded using holography and moire. The accuracy of the employed numerical-differentiation techniques is indicated.

https://link.springer.com/content/pdf/10.1007/BF02323967.pdf

Higher-order numerical differentiation of experimental information - Cubic-spline and discrete-quadratic polynomials are described for numerically computing up through third-order derivatives. Concept is demonstrated by stress analyzing, from moiré and holographically recorded displacements, loaded plates and beams

Embedded-strain-gage techniques were developed and used for measuring strains in composite angle-ply laminates during curing and thermal cycling. The specimens were 2.54 by 22.9 cm eight-ply boron-epoxy and S-glass-epoxy laminates. Unidirectional specimens were used for control purposes. Strain readings were corrected for the purely thermal output of the gages obtained from an instrument quartz reference specimen. The strains measured during the cooling part of the curing cycle were in agreement with those recorded during subsequent thermal cycling, indicating that residual stresses induced during curing are primarily caused by differential thermal expansions of the various plies. Restraint strains were computed for the 0-deg and 45-deg plies of the angle-ply laminates tested, and the residual stresses obtained using the anisotropic constitutive relations and taking into account the temperature dependence of stiffnesses and strains.

T. Liber

Papers

New method for testing composites at very high strain rates

Effect of laminate construction on residual stresses in graphite/polyimide composites: The effects of ply-stacking sequence and ply orientation on the magnitude of residual stresses were investigated experimentally in graphite/polyimide angle-ply laminates using embedded-strain-gage techniques

Breathing vibrations of pressurized partially filled tanks.

Measurement of residual strains in boron-epoxy and glass-epoxy laminates