Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1706.04828

Restrictions on wave equations for passive media

Sverre Holm·Martin Blomhoff Holm
View original source ↗Read source document ↗Export metadata ↓

Abstract

Most derivations of acoustic wave equations involve ensuring that causality is satisfied. Here we explore the consequences of also requiring that the medium should be passive. This is a stricter criterion than causality for a linear system and implies that there are restrictions on the relaxation modulus and its first few derivatives. The viscous and relaxation models of acoustics satisfy passivity and have restrictions on not only a few, but all derivatives of the relaxation modulus. This is the important class of completely monotone systems. It is the only class where the medium is modeled as a system of springs and dampers with positive parameters. It is shown here that the attenuation as a function of frequency for such media has to increase slower than a linear function. Likewise the phase velocity has to increase monotonically. This gives criteria on which one may judge whether a proposed wave equation is passive or not, as illustrated by comparing two different versions of the viscous wave equation.

Explore related subjects

physics.class-phphysics.app-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Sverre Holm, Martin Blomhoff Holm. 2017-06-14. Restrictions on wave equations for passive media. https://doi.org/10.1121/1.5006059

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Contact mechanics and friction of soft materials: an apparatus combining multi-axes dynamical actuation/measurement and in situ/in operando visualisation

The mechanics and friction of contact interfaces involving soft materials like gel, rubber or human skin are of both fundamental and applied interest. Recent insights have been made into this field thanks to in situ observations of the contact interface. However, current soft-material-oriented tribometers enable only few degrees of freedom for the actuation of the contact, far from covering the richness of the loading conditions relevant to real tribological contacts. Here, we introduce an apparatus dedicated to the study of the contact mechanics and friction of soft materials which, in addition to in situ / in operando optical monitoring of the interface, enables simultaneous actuation along five degrees of freedom: three translations and two rotations. While all three translations feature large velocity/large stroke motion, the one responsible for normal contact loading can also apply high frequency/small amplitude vibrations. The contact's dynamical response is monitored using both a 6-axes force/torque sensor and a 6-axes displacement/rotation sensor. We first describe the structure of the apparatus, its implementation, alignment, calibration and resolutions. We then illustrate its capabilities through a series of experiments on elastomer contacts. Our apparatus will be useful to investigate the mechanics of a wide range of soft interfaces submitted to rich, tribology-relevant kinematic or dynamic stimuli.

physics.class-ph↗
arXiv2026

Sliding contact fraction in gravity-driven dense cohesionless granular flows

Using large-scale, three-dimensional discrete element simulations, we investigate the kinematic properties of granular chute flows of cohesionless grains, together with the evolution of the coordination number and the fraction of sliding contacts. Our results reveal that, under certain conditions, increasing the grain--grain friction coefficient leads to a decrease in the global dissipation of the system. This finding highlights that the overall dissipation is not solely governed by the energy lost during sliding contacts, but also by the probability that such contacts occur, a probability that decreases markedly as the friction coefficient increases. Together, these effects demonstrate the subtle and nontrivial interplay between grain-scale frictional interactions and macroscopic flow behavior in dense and cohesionless granular materials.

physics.class-ph↗
arXiv2026

Increase of the electromechanical coupling of piezoelectric vibration harvesters through lateral bars

To enhance the performance of vibration energy harvesters, it is essential to maximise the electromechanical coupling coefficient k${}^2$ of piezoelectric devices. This enables sufficient harvested power and tuning capability of the resonant frequency through electrical methods. While much literature treats the optimisation of piezoelectric cantilevers, the optimisation range is usually limited by the transverse coupling coefficient k31${}^2$ of the material. This work introduces an innovative solution to extend the optimisation range and increase the coupling coefficient of piezoelectric cantilevers. This is achieved by minimising lateral strain in the beam using lateral bars to maximise the equivalent material coupling coefficient. The theoretical basis of this innovation is demonstrated through the exploitation of the constitutive equations of piezoelectric materials. The interest of the addition of lateral bars to increase the coupling coefficient is demonstrated and studied with simulations based on the finite elements method. Finally, a proof of concept is realised using a aluminum cantilever prototype integrating a lead-free KNaNbO3 (KNN) piezoelectric material. It is tested under vibration at 0.1 m/s${}^2$ with variable resistive loads. The results show that the coupling coefficient increases by 30% and the relative frequency bandwidth by 32% with resistive tuning of the resonant frequency, by fixing eight steel bars to the cantilever. The designed prototype is a highly performant leadfree vibration energy harvester. It produces a maximum power of 49.9 $μ$W at resonance, and its normalised power density is equal to 16.5 mW/G${}^2$/cm${}^3$. Its relative frequency bandwidth is equal to 3.1%.

physics.class-ph↗