Biomechanics of the Human Middle Ear with Viscoelasticity of the Maxwell and the Kelvin–Voigt Type and Relaxation Effect

Abstract

The middle ear is one of the smallest biomechanical systems in the human body and is responsible for the hearing process. Hearing is modelled in different ways and by various methods. In this paper, three-degree-of-freedom models of the human middle ear with different viscoelastic properties are proposed. Model 1 uses the Maxwell type viscoelasticity, Model 2 is based on the Kelvin–Voigt viscoelasticity, and Model 3 uses the Kelvin–Voigt viscoelasticity with relaxation effect. The primary aim of the study is to compare the models and their dynamic responses to a voice excitation. The novelty of this study lies in using different models of viscoelasticity and relaxation effect that has been previously unstudied. First, mathematical models of the middle ear were built, then they were solved numerically by the Runge–Kutta procedure and finally, numerical results were compared with those obtained from experiments carried out on the temporal bone with the Laser Doppler Vibrometer. The models exhibit differences in the natural frequency and amplitudes near the second resonance. All analysed models can be used for modelling the rapidly changing processes that occur in the ear and to control active middle ear implants.

An analytical approach to the stress relaxation behavior of a low temperature shape-memory fabric based on viscoelastic models

“…The total axial force created in standard linear elements (F LS ) is zero at zero time. Thus, according to equation (13), the axial dynamic frictional force component (F d ) becomes zero at zero time. This means that the load extension curve starts from the origin at the loading stage.…”

“…Different combinations of spring and dashpot systems are typically considered to model the mechanical behavior of textile materials. Viscoelastic models are usually made of two elements, that is, springs that follow Hooke's law and viscous dashpots obeying Newton's law [9][10][11][12][13]. Maxwell and generalized Maxwell models can be used to study the viscoelastic properties of filament yarns and nonwoven textiles [14,15].…”