This paper studies the interaction between non-viscous damping and nonlinearities for nonlinear oscillators with reflection symmetry. The non-viscous damping function is an exponential damping model which adds a decaying memory property to the damping term of the oscillator. We consider the case of softening and hardening behaviour in the frequency response of the system. Numerical simulations ...

It has long been a puzzle that the Raman optical modes shift to lower frequency or termed optical mode softening or redshift associated with the creation of Raman acoustic modes that shift to higher energy or called acoustic hardening or blueshift upon a nanosolid being formed and its size being reduced. Understandings of the mechanism behind the size-induced Raman shifts have been quite contro...

The deformation of metallic glasses involves two competing processes: a disordering process involving dilatation, free volume accumulation, and softening, and a relaxation process involving diffusional ordering and densification. For metallic glasses at room temperature and under uniaxial loading, disordering usually dominates, and the glass can fail catastrophically as the softening process ru...

Background: Physical wedges are still widely used as beam modifiers in external beam radiotherapy. However the presence of them in the beam trace may cause beam hardening which may not be considered in many treatment planning systems. The aim of this study is to investigate the beam hardening effect generated by physical wedges via different beam quality indexes as photon spectrum, half value l...

The goal of this contribution is the development of a plane stress orthotropic plasticity material model for clear spruce wood. Such a model has to consider an initially linear elastic domain as well as hardening and softening behaviour at higher states of stress and strain, respectively. Combining the advantage of a smooth single-surface plasticity model with the identification of distinct har...

The hardening hypothesis has intuitive and common sense appeal: in jurisdictions that have implemented evidence-based tobacco control policies, the smokers who have a relatively easy time quitting will quit, and as the future unfolds there will be an increasing proportion of remaining smokers who cannot quit and are more resistant to quitting than smokers in the past. In this context, ‘hardenin...

We show how to achieve large-amplitude oscillation and good frequency stability in a nonlinear NEMS oscillator by using a softening nonlinearity to locally balance the hardening behaviour of the Duffing nonlinearity for a given motion amplitude. The case when the softening behaviour is obtained via electrostatic biasing is theoretically investigated, under parallel-plate assumptions, for a full...

A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of ...

background: physical wedges are still widely used as beam modifiers in external beam radiotherapy. however the presence of them in the beam trace may cause beam hardening which may not be considered in many treatment planning systems. the aim of this study is to investigate the beam hardening effect generated by physical wedges via different beam quality indexes as photon spectrum, half value l...

Pravdo et al (1997) claimed that the phase resolved x-ray spectrum in Crab pulsar (PSR B0531+21) shows a spectral hardening at the leading edge of the first peak of its integrated profile (IP); this was a new and unexpected result. This article reanalyzes their data, as well as some other related data, and argues that the spectrum is as likely to be unvarying (i.e., neither hardening nor soften...