scholarly journals On a Laminated Timoshenko Beam with Nonlinear Structural Damping

2020 ◽  
Vol 25 (2) ◽  
pp. 35
Author(s):  
Tijani A. Apalara ◽  
Aminu M. Nass ◽  
Hamdan Al Sulaimani
Keyword(s):  
Timoshenko Beam ◽  
Convex Functions ◽  
Nonlinear Term ◽  
Interfacial Slip ◽  
Structural Damping ◽  
Damping Term ◽  
Wave Speeds ◽  
Boundary Damping ◽  
One Dimensional ◽  
Nonlinear Structural

In the present work, we study a one-dimensional laminated Timoshenko beam with a single nonlinear structural damping due to interfacial slip. We use the multiplier method and some properties of convex functions to establish an explicit and general decay result. Interestingly, the result is established without any additional internal or boundary damping term and without imposing any restrictive growth assumption on the nonlinear term, provided the wave speeds of the first equations of the system are equal.

Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound

2019 ◽  
Vol 26 (1) ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad M. Al-Gharabli ◽  
Salim A. Messaoudi
Keyword(s):  
Decay Rate ◽  
Convex Functions ◽  
Semigroup Theory ◽  
General Decay ◽  
Well Posedness ◽  
Second Sound ◽  
Nonlinear Feedback ◽  
Damping Term ◽  
General Decay Rate ◽  
One Dimensional

Abstract In this paper, we consider a one-dimensional porous thermoelastic system with second sound and nonlinear feedback. We show the well-posedness, using the semigroup theory, and establish an explicit and general decay rate result, using some properties of convex functions and the multiplier method. Our result is obtained without imposing any restrictive growth assumption on the damping term.

scholarly journals Exponential and Polynomial Decay for a Laminated Beam with Fourier's Type Heat Conduction

2019 ◽  
Author(s):  
Wenjun Liu ◽  
Weifan Zhao
Keyword(s):  
Heat Conduction ◽  
Energy Method ◽  
Rotation Angle ◽  
Polynomial Decay ◽  
Structural Damping ◽  
Laminated Beam ◽  
Wave Speeds ◽  
One Dimensional ◽  
Exponentially Stable ◽  
Well Posed

In this paper, we study the well-posedness and asymptotics of a one-dimensional thermoelastic laminated beam system either with or without structural damping, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We show that the system is well-posed by using Lumer-Philips theorem, and prove that the system is exponentially stable if and only if the wave speeds are equal, by using the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem. Furthermore, we show that the system with structural damping is polynomially stable provided that the wave speeds are not equal, by using the second-order energy method.

scholarly journals Tornado-type stationary vortex with nonlinear term due to moisture transport

2010 ◽  
Vol 4 (1) ◽  
pp. 77-82 ◽  
Author(s):  
P. B. Rutkevich ◽  
P. P. Rutkevych
Keyword(s):  
Tropical Cyclones ◽  
Shooting Method ◽  
Nonlinear Term ◽  
Numerical Solutions ◽  
Variable Temperature ◽  
Slow Rotation ◽  
Nonlinear Phenomenon ◽  
One Dimensional ◽  
Stationary Vortex ◽  
General Possibility

Abstract. Tornado vortex is believed to be essentially nonlinear phenomenon; and the puzzle to choose the nonlinear term(s) responsible for its formation is still unresolved. In the present work we consider the nonlinear term associated with atmosphere humidity, by introducing variable temperature gradient depending on the vertical velocity of the fluid. Such term is able to yield energy to the system and is very suitable for such a problem. Other nonlinear terms are neglected, assuming slow rotation, or in other words a "weak" tornado approximation. We consider one-dimensional radial boundary problem, and use a modificaiton of shooting method to satisfy boundary conditions at large radii. Obtained numerical solutions of the nonlinear differential equation qualitatively agree with the observed atmosphere vortices (tornados, tropical cyclones). The obtained results show general possibility of existence of unstable motion even in convectively stable atmosphere stratification.

scholarly journals A Parameter Study of Localization

1996 ◽  
Vol 3 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Sandor Stephen Mester ◽  
Haym Benaroya
Keyword(s):  
Periodic Structures ◽  
Numerical Study ◽  
Vibration Characteristics ◽  
Periodic Pattern ◽  
Parameter Study ◽  
Structural Damping ◽  
One Dimensional

Extensive work has been done on the vibration characteristics of perfectly periodic structures. Disorder in the periodic pattern has been found to lead to localization in one-dimensional periodic structures. It is important to understand localization because it causes energy to be concentrated near the disorder and may cause an overestimation of structural damping. A numerical study is conducted to obtain a better understanding of localization. It is found that any mode, even the first, can localize due to the presence of small imperfections.

scholarly journals Periodic and Near-Periodic Structures

1995 ◽  
Vol 2 (1) ◽  
pp. 69-95 ◽  
Author(s):  
S. S. Mester ◽  
H. Benaroya
Keyword(s):  
State Physics ◽  
Solid State ◽  
Periodic Structures ◽  
Vibration Characteristics ◽  
Aerospace Engineering ◽  
Structural Damping ◽  
Solid State Physics ◽  
One Dimensional ◽  
Fields Of Study ◽  
Effects Of Disorder

Extensive work has been done on the vibration characteristics of perfectly periodic structures. This article reviews the different methods of analysis from several fields of study, for example solid-state physics and civil, mechanical, and aerospace engineering, used to determine the effects of disorder in one-dimensional (1-D) and 2-D periodic structures. In the work examined, disorder has been found to lead to localization in 1-D periodic structures. It is important to understand localization because it causes energy to be concentrated near the disorder and may cause an overestimation of structural damping. The implications of localization for control are also examined.

Complex Modal Extraction for Estimating Wave Parameters in One-Dimensional Media

2010 ◽  
Author(s):  
B. F. Feeny
Keyword(s):  
Group Velocity ◽  
Traveling Waves ◽  
Random Noise ◽  
Mode Shapes ◽  
Transient Wave ◽  
Wave Speeds ◽  
One Dimensional ◽  
Wave Numbers ◽  
Displacement Profile ◽  
Complex Modal

A method of complex orthogonal decomposition is applied to the extraction of modes from simulation data of multi-modal traveling waves in one-dimensional continua. The decomposition of a transient wave is performed on a nondispersive pulse. Complex wave modes are then extracted from a two-harmonic simulation of a dispersive medium. The wave frequencies and wave numbers are obtained by looking at the whirl of the complex modal coordinate, and the complex modal function, respectively, in the complex plane. From the frequencies and wave numbers, the wave speeds are then estimated, as well as the group velocity associated with the two waves. The group velocity is also extracted directly from a decomposition of the traveling envelope of the waveform. The observations from the first two examples are used to help interpret the decomposition of a simulation of the traveling waves produced by a Gaussian initial displacement profile in an Euler-Bernoulli beam. While such a disturbance produces a continuous spectrum of wave components, the sampling conditions limit the range of wave components (i.e. mode shapes and modal coordinates) to be extracted. Within this working range, the wave numbers and frequencies are obtained from the extraction, and compared to theory. The frequency distribution is then approximated. The results are robust to random noise.

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