On Standing Waves in Tires

1977 ◽  
Vol 5 (2) ◽  
pp. 83-101 ◽  
Author(s):  
J. Padovan
Keyword(s):  
Standing Wave ◽  
Wave Phenomenon ◽  
Shell Theory ◽  
Constitutive Law ◽  
Integral Type ◽  
Nonlinear Version ◽  
Viscoelastic Effects ◽  
Hereditary Integral ◽  
Finite Element Procedure

Abstract By using a comprehensive rotating laminated shell model of the tire, the effects of viscoelastic damping on the standing wave phenomenon are investigated in more detail than was previously possible. The shell theory employed is a nonlinear version of Novoshilov's work and the onset of the standing wave is characterized as a small dynamic deformation superposed on a finite deformation. To expand the scope of the model, the viscoelastic constitutive law is treated as either of the differential or hereditary integral type. The solution for the stated model is obtained by the finite element procedure, and the results of several numerical experiments are presented. The substantial role of viscoelastic effects in the development of the standing wave phenomenon of tires is emphasized by the results.

A Multi-Mode Approach for the Nonlinear Vibrations of Circular Cylindrical Shells

2001 ◽  
Author(s):  
Francesco Pellicano ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Symbolic Manipulation ◽  
Comparison Functions ◽  
Circular Cylindrical Shells ◽  
Multi Mode

Abstract The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell’s nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

scholarly journals Using geometric algebra to represent curvature in shell theory with applications to Starling resistors

2017 ◽  
Vol 4 (11) ◽  
pp. 171212
Author(s):  
A. L. Gregory ◽  
A. Agarwal ◽  
J. Lasenby
Keyword(s):  
Curvature Tensor ◽  
Geometric Algebra ◽  
Shell Theory ◽  
Constitutive Law ◽  
Working Fluid ◽  
Scaling Analysis ◽  
Relative Importance ◽  
Bending Energy ◽  
Initial Curvature ◽  
Flexible Tubes

We present a novel application of rotors in geometric algebra to represent the change of curvature tensor that is used in shell theory as part of the constitutive law. We introduce a new decomposition of the change of curvature tensor, which has explicit terms for changes of curvature due to initial curvature combined with strain, and changes in rotation over the surface. We use this decomposition to perform a scaling analysis of the relative importance of bending and stretching in flexible tubes undergoing self-excited oscillations. These oscillations have relevance to the lung, in which it is believed that they are responsible for wheezing. The new analysis is necessitated by the fact that the working fluid is air, compared to water in most previous work. We use stereographic imaging to empirically measure the relative importance of bending and stretching energy in observed self-excited oscillations. This enables us to validate our scaling analysis. We show that bending energy is dominated by stretching energy, and the scaling analysis makes clear that this will remain true for tubes in the airways of the lung.

scholarly journals Absorption in ultrathin GaN-based membranes: The role of standing wave effects

2019 ◽  
Vol 126 (8) ◽  
pp. 083109 ◽  
Author(s):  
E. A. Amargianitakis ◽  
R. Jayaprakash ◽  
F. G. Kalaitzakis ◽  
E. Delamadeleine ◽  
E. Monroy ◽  
...  
Keyword(s):  
Standing Wave ◽  
Wave Effects

On Viscoelasticity and Standing Waves in Tires

1976 ◽  
Vol 4 (4) ◽  
pp. 233-246 ◽  
Author(s):  
J. Padovan
Keyword(s):  
Exact Solution ◽  
Standing Wave ◽  
Wave Phenomenon ◽  
Numerical Experiments ◽  
Standing Waves ◽  
Structural Damping ◽  
Resonance Response ◽  
Foundation Model ◽  
Stated Problem ◽  
Classical Ring

Abstract Based on the classical ring on foundation model for the tire, the effect which structural damping has on the development of the standing wave phenomenon is investigated. In particular, the model employed consists of a rotating ring on foundation where, in addition to including Coriolis effects, Kelvin-Voigt-type viscoelasticity is admitted in both the ring and foundation. Enforcing strict periodicity in space and time, the exact solution is obtained to the stated problem. Several parametric numerical experiments employing this solution are reported. These demonstrate that the standing wave phenomenon in tires is essentially a viscoelastic-type resonance response.

scholarly journals Thermal Bragg Shields for Thermal Waves.

2021 ◽  
Author(s):  
Angela Camacho de la Rosa ◽  
David Becerril ◽  
Guadalupe Gómez-Farfán ◽  
Raul Esquivel-Sir
Keyword(s):  
Heat Conduction ◽  
Dispersion Relation ◽  
Wave Phenomenon ◽  
Response Times ◽  
Thermal Response ◽  
Thermal Waves ◽  
Thin Metallic Film ◽  
Very High ◽  
High Reflectance

Abstract Ultrafast heating processes do not follow Fourier's heat conduction law, but rather the proposed Cattaneo-Vernotte equation (CVe) which has wave-like solutions that have some important differences from other wave phenomenon. In a periodic system made of materials with different thermal conductivities, solutions of the CVe lead to a band-like structure in the dispersion relation. In this work, we show that highly reflective Bragg mirrors for thermal waves can be designed. Even for a mirrors with a few layers a very high reflectance is achieved (>90%). The mirrors are made of materials with large thermal response times, where thermal waves have been measured. A second alternative consists of adding a thin metallic film which also leads to an efficient thermal Bragg mirror. Finally, the role of defects in opening new thermal-stop bands is demonstrated.

The role of the integral type II transmembrane protein BRI2 in health and disease

2021 ◽  
Author(s):  
Filipa Martins ◽  
Isabela Santos ◽  
Odete A. B. da Cruz e Silva ◽  
Simone Tambaro ◽  
Sandra Rebelo
Keyword(s):  
Transmembrane Protein ◽  
Type Ii ◽  
Integral Type ◽  
Health And Disease

scholarly journals Homogenization of the nonlinear Maxwell model of viscoelasticity and of the Prandtl—Reuss model of elastoplasticity

2008 ◽  
Vol 138 (6) ◽  
pp. 1363-1401 ◽  
Author(s):  
Augusto Visintin
Keyword(s):  
Strain Tensor ◽  
Mean Field ◽  
Maxwell Model ◽  
Constitutive Law ◽  
Scale Model ◽  
Single Scale ◽  
Linearized Strain ◽  
Nonlinear Version ◽  
Non Local ◽  
Image Position

This paper deals with processes in nonlinear inelastic materials whose constitutive behaviour is represented by the inclusionhere we denote by σ the stress tensor, by ε the linearized strain tensor, by B(x) the compliance tensor and by ∂ϕ(·, x) the subdifferential of a convex function ϕ(·, x). This relation accounts for elasto-viscoplasticity, including a nonlinear version of the classical Maxwell model of viscoelasticity and the Prandtl—Reuss model of elastoplasticity.The constitutive law is coupled with the equation of continuum dynamics, and well-posedness is proved for an initial- and boundary-value problem. The function ϕ and the tensor B are then assumed to oscillate periodically with respect to x and, as this period vanishes, a two-scale model of the asymptotic behaviour is derived via Nguetseng's notion of two-scale convergence. A fully homogenized single-scale model is also retrieved, and its equivalence with the two-scale problem is proved. This formulation is non-local in time and is at variance with that based on so-called analogical models that rest on a mean-field-type hypothesis.

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