NDLI: Dynamics of a middle ear with fractional type of dissipation

Content Provider	Springer Nature Link
Author	Kovincic, Nemanja I. Spasic, Dragan T.
Copyright Year	2016
Abstract	In this paper, a model of spatial motion of the ossicular chain described as a system of two rigid bodies connected to the temporal bone through the system of particularly chosen massless viscoelastic rods was proposed. Several assumptions regarding the relative motion between incus and malleus, external loading force, distributed pressure of the perilymph on the stapes baseplate behind the oval window, and supporting ligaments were made. In order to avoid merging with fractional partial differential equations, the dissipation of energy due to the deformation of the eardrum is taken into account through deformation of its radial fibers while simple shear deformation pattern of the stapedial annular ligament was replaced by uniaxial deformation of viscoelastic rods. By use of the Gibbs–Appel approach and the complementary constitutive axioms corresponding to the fractional Kelvin–Zener model of viscoelastic body, the equations of motion were derived. The Cauchy problem given in terms of coupled fractional differential equations was transformed in the equivalent integer order form and solved numerically by standard numerical procedures. These results, obtained by means of the Atanackovic–Stankovic expansion formula, were compared with the ones received by use of Laplace’s transform and its numerical inversion. As a principal novelty, this model uses both fractional calculus and recently reported results on mechanical tests performed on human middle ear tissues. Thus, it can be used for either predicting of the middle ear behavior in normal and pathological conditions or simulations preceding implants design within restoration of the hearing function.
Starting Page	2369
Ending Page	2388
Page Count	20
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	85
Issue Number	4
e-ISSN	1573269X
Language	English
Publisher	Springer Netherlands
Publisher Date	2016-05-14
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Middle ear Gibbs–Appel equations Fractional calculus Energy dissipation Vibration, Dynamical Systems, Control Mechanics Mechanical Engineering Automotive Engineering
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Entropy analysis of integer and fractional dynamical systems

Partial fractional derivatives of Riesz type and nonlinear fractional differential equations

A fractional calculus interpretation of the fractional volatility model

On exact solutions of a class of fractional Euler–Lagrange equations

Fractional Euler–Lagrange equations revisited

Fractional-order Euler–Lagrange equations and formulation of Hamiltonian equations

Fractional diffusion equations for open quantum system

Relative fractional dynamics of stock markets

Discrete fractional diffusion equation

Dynamics of a middle ear with fractional type of dissipation

Similar Documents

Entropy analysis of integer and fractional dynamical systems

Partial fractional derivatives of Riesz type and nonlinear fractional differential equations

A fractional calculus interpretation of the fractional volatility model

On exact solutions of a class of fractional Euler–Lagrange equations

Fractional Euler–Lagrange equations revisited

Fractional-order Euler–Lagrange equations and formulation of Hamiltonian equations

Fractional diffusion equations for open quantum system

Relative fractional dynamics of stock markets

Discrete fractional diffusion equation

Dynamics of a middle ear with fractional type of dissipation