Damping ratio

Abstract: BASED ON NUMEROUS TESTS ON A SPECTRUM OF DISTURBED AND UNDISTURBED SOILS, THE SHEAR MODULUS DECREASES AND THE DAMPING RATIO INCREASES VERY RAPIDLY WITH INCREASING STRAIN AMPLITUDE. THE RATE OF INCREASE OR DECREASE DEPENDS ON MANY PARAMETERS: EFFECTIVE MEAN PRINCIPAL STRESS; DEGREE OF SATURATION; VOID RATIO; AND NUMBER OF CYCLES OF LOADING. AMBIENT STATES OF OCTAHEDRAL SHEAR STRESS, OVERCONSOLIDATION RATIO, EFFECTIVE STRENGTH ENVELOPE, FREQUENCY OF LOADING, AND TIME EFFECTS HAVE A LESS IMPORTANT INFLUENCE ON THESE PROPERTIES. COHESIVE SOILS ARE AFFECTED DIFFERENTLY THAN CLEAN SANDS. THE APPARATUS USED TO MEASURE SHEAR MODULUS AND DAMPING MUST BE CAPABLE OF MAKING ACCURATE MEASUREMENTS AT VERY SMALL SHEARING STRAINS, THE RANGE BEING DEFINED BY PRACTICAL PROBLEMS IN EARTHQUAKE AND FOUNDATION VIBRATIONS. A PSEUDO STATIC SIMPLE SHEAR APPARATUS AND TWO DIFFERENT RESONANT COLUMN APPARATUS WERE USED. /AUTHOR/

Abstract: A theory of solid friction damping of mechanical vibrations is presented that is based on a solid friction mathematical model previously proposed by the author. A summary and improved description of the general analytic features of the solid friction model are given as necessary background for the theory. The Coulomb friction damped oscillator is analyzed to establish an approach to the treatment of a simple friction damped oscillator. The approach then is generalized to treat a more general model of friction where the author's model is used to describe friction force primarily as a function of displacement. The solid friction damped oscillator studied is a wire pendulum where solid friction enters via inelastic flexing of the wire at the support. Theoretical results are generalized to be applicable to other types of oscillators and other sources of solid friction. An expression for the decay rate of the oscillation amplitude envelope of an unforced oscillator is derived. The decay rate and an equivalent linear damping ratio are determined for several values of an exponent parameter in the solid friction model.

Abstract: Available experimental data on dynamic shear moduli and damping ratios of various soils including non-plastic sands to highly plastic clays are collected. Those are reanalyzed and brought into simple unified formulas. The unified formulas express the dynamic shear moduli and the damping ratios in terms of maximum dynamic shear modulus, cyclic shear strain amplitude, mean effective confining pressure and soil’s plasticity index. Although the availability of experimental data on clay is still limited at this time, the formulas fit those data reasonably well and could be conveniently utilized in dynamic analyses such as seismic ground response and soil-structure interaction problems.

Abstract: Structural damping is frequently approximated in the frequency domain by the constant hysteretic damping model. Transient vibrations of a member with constant hysteretic damping leads to a non-causal precursor response. The non-causal response can be avoided by introducing actual measured frequency dependent stiffness and damping behaviour of the material, or by introducing constitutive equations of differential operator type with classical derivatives (integer order) or generalised type (fractional order). This paper uses and generalises constitutive equations of viscoelastic behaviour of materials and members in the time and frequency domain. Weak frequency dependence of actual viscoelastic material can be fitted using only a few parameters by adopting the fractional derivative concept. The impulse response function of an oscillator with a fractional derivative damping model is integrated in the present paper with a new efficient technique using the inverse Fourier transform, this requires a unique definition of the constitutive equation in the frequency domain. The response is shown to fulfill causality requirements. Amplitude decay of the considered damping models are compared after selection of equivalent damping properties.

Abstract: Polymer composites reinforced by carbon nanotubes have been extensively researched for their strength and stiffness properties. Unless the interface is carefully engineered, poor load transfer between nanotubes (in bundles) and between nanotubes and surrounding polymer chains may result in interfacial slippage and reduced performance. Interfacial shear, although detrimental to high stiffness and strength, could result in very high mechanical damping, which is an important attribute in many commercial applications. We previously reported evidence of damping in nanocomposites by measuring the modal response (at resonance) of cantilevered beams with embedded nanocomposite films. Here we carry out direct shear testing of epoxy thin films containing dense packing of multiwalled carbon nanotube fillers and report strong viscoelastic behaviour with up to 1,400% increase in loss factor (damping ratio) of the baseline epoxy. The great improvement in damping was achieved without sacrificing the mechanical strength and stiffness of the polymer, and with minimal weight penalty. Based on the interfacial shear stress (approximately 0.5 MPa) at which the loss modulus increases sharply for our system, we conclude that the damping is related to frictional energy dissipation during interfacial sliding at the large, spatially distributed, nanotube-nanotube interfaces.