Related papers: Toward a Universal Model of Damping--Modified Coul…
The author's modified Coulomb damping model has been generalized to accommodate internal friction that derives from several dissipation mechanisms acting simultaneously. Because of its fundamental nonlinear nature, internal friction damping…
The force of dry friction is studied extensively in introductory physics but its effect on oscillations is hardly ever mentioned. Instead, to provide a mathematically tractable introduction to damping, virtually all authors adopt a viscous…
The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook…
Although "friction" is included in many models of oscillator damping, including viscous ones applied to the pendulum; they "miss the mark" with regard to a conceptual understanding of the mechanisms responsible for energy loss. The theory…
Contact problems with Coulomb friction in linear elasticity are notoriously difficult and their mathematical analysis is still largely incomplete. In this paper, a model problem with heterogeneous friction coefficient is considered in…
We introduce a model of friction between two contacting (stationary or co-sliding) rough surfaces, each comprising a random ensemble of polydisperse hemispherical bumps. In the simplest version of the model, the bumps experience on contact…
Non-linear equations of radial motion of a gas bubble in a compressible viscous liquid have been modified considering effects of viscosity and compressibility more complete than all previous works. A new set of equations has been derived…
Analytical and numerical modelling of the nonlinear interaction of shear wave with a frictional interface is presented. The system studied is composed of two homogeneous and isotropic elastic solids, brought into frictional contact by…
An elastic layer slides on a rigid flat governed by Coulomb's friction law. We demonstrate that if the coefficient of friction is high enough, the sliding localizes within stick-slip pulses, which transform into opening waves propagating at…
In this article, we extend the capstan equation to non-circular geometries. We derive a closed form solution for a membrane with a zero Poisson's ratio (or a string with an arbitrary Poisson's ratio) supported by a rigid prism (at…
We show how to adapt the approach introduced for viscous damping in [1] to derive the approximate amplitude decay in the case of damping by a force of constant magnitude (sliding friction) and in the case of damping by a force proportional…
If a contact of two purely elastic bodies with no sliding (infinite coefficient of friction) is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears, that is not dependent on…
The change of the friction law from a mesoscopic level to a macroscopic level is studied in the spring-block models introduced by Burridge-Knopoff. We find that the Coulomb law is always scale invariant. Other proposed scaling laws are only…
The change of the friction law from a mesoscopic level to a macroscopic level is studied in the spring-block models introduced by Burridge-Knopoff. We find that the Coulomb law is always scale invariant. Other proposed scaling laws are only…
Cementless implants are widely used in orthopedic and oral surgery. However, debonding-related failure still occurs at the bone-implant interface. It remains difficult to predict such implant failure since the underlying osseointegration…
An exact transformation method is introduced that reduces the governing equations of a continuum structure coupled to strong nonlinearities to a low dimensional equation with memory. The method is general and well suited to problems with…
The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…
This study shows that typical pendulum dynamics is far from the simple equation of motion presented in textbooks. A reasonably complete damping model must use nonlinear terms in addition to the common linear viscous expression. In some…
We establish a relationship between the normalized damping coefficients and the time that takes a nonlinear pendulum to complete one oscillation starting from an initial position with vanishing velocity. We establish some conditions on the…
A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation…