Spectral analysis of Timoshenko beam with time delay in interior damping

2019 ◽  
Vol 70 (2) ◽  
Author(s):  
Xiaorui Wang ◽  
Zhongjie Han ◽  
Genqi Xu
Keyword(s):  
Spectral Analysis ◽  
Time Delay ◽  
Timoshenko Beam

scholarly journals On the use of ELF/VLF emissions triggered by HAARP to simulate PLHR and to study associated MLR events

2022 ◽  
Vol 74 (1) ◽  
Author(s):  
Michel Parrot ◽  
Frantisěk Němec ◽  
Morris B. Cohen ◽  
Mark Gołkowski
Keyword(s):  
Spectral Analysis ◽  
Time Delay ◽  
High Frequency ◽  
Conjugate Point ◽  
Physical Processes ◽  
Line Radiation ◽  
Harmonic Radiation ◽  
Frequency Spacing ◽  
Low Altitude ◽  
Vlf Emissions

AbstractA spectrogram of Power Line Harmonic Radiation (PLHR) consists of a set of lines with frequency spacing corresponding exactly to 50 or 60 Hz. It is distinct from a spectrogram of Magnetospheric Line Radiation (MLR) where the lines are not equidistant and drift in frequency. PLHR and MLR propagate in the ionosphere and the magnetosphere and are recorded by ground experiments and satellites. If the source of PLHR is evident, the origin of the MLR is still under debate and the purpose of this paper is to understand how MLR lines are formed. The ELF waves triggered by High-frequency Active Auroral Research Program (HAARP) in the ionosphere are used to simulate lines (pulses of different lengths and different frequencies). Several receivers are utilized to survey the propagation of these pulses. The resulting waves are simultaneously recorded by ground-based experiments close to HAARP in Alaska, and by the low-altitude satellite DEMETER either above HAARP or its magnetically conjugate point. Six cases are presented which show that 2-hop echoes (pulses going back and forth in the magnetosphere) are very often observed. The pulses emitted by HAARP return in the Northern hemisphere with a time delay. A detailed spectral analysis shows that sidebands can be triggered and create elements with superposed frequency lines which drift in frequency during the propagation. These elements acting like quasi-periodic emissions are subjected to equatorial amplification and can trigger hooks and falling tones. At the end all these known physical processes lead to the formation of the observed MLR by HAARP pulses. It is shown that there is a tendency for the MLR frequencies of occurrence to be around 2 kHz although the exciting waves have been emitted at lower and higher frequencies. Graphical Abstract

scholarly journals SPECTRAL ANALYSIS AND TIME-DEPENDENT SCATTERING THEORY ON MANIFOLDS WITH ASYMPTOTICALLY CYLINDRICAL ENDS

2013 ◽  
Vol 25 (02) ◽  
pp. 1350003 ◽  
Author(s):  
S. RICHARD ◽  
R. TIEDRA DE ALDECOA
Keyword(s):  
Spectral Analysis ◽  
Time Delay ◽  
Hilbert Spaces ◽  
Scattering Theory ◽  
Asymptotic Completeness ◽  
Time Dependent ◽  
Resolvent Estimates ◽  
Wave Operators ◽  
Use Of Time ◽  
Stationary Scattering

We review the spectral analysis and the time-dependent approach of scattering theory for manifolds with asymptotically cylindrical ends. For the spectral analysis, higher order resolvent estimates are obtained via Mourre theory for both short-range and long-range behaviors of the metric and the perturbation at infinity. For the scattering theory, the existence and asymptotic completeness of the wave operators is proved in a two-Hilbert spaces setting. A stationary formula as well as mapping properties for the scattering operator are derived. The existence of time delay and its equality with the Eisenbud–Wigner time delay is finally presented. Our analysis mainly differs from the existing literature on the choice of a simpler comparison dynamics as well as on the complementary use of time-dependent and stationary scattering theories.

The hypothesis of equal wave speeds for stabilization of Timoshenko beam is not necessary anymore: the time delay cases†

2019 ◽  
Vol 84 (4) ◽  
pp. 763-796 ◽  
Author(s):  
D S Almeida Júnior ◽  
I Elishakoff ◽  
A J A Ramos ◽  
L G Rosário Miranda
Keyword(s):  
Time Delay ◽  
Timoshenko Beam ◽  
Solid Mechanics ◽  
Type Systems ◽  
Recent Contribution ◽  
Wave Speeds ◽  
Delay Effects ◽  
Timoshenko Systems ◽  
Stability Results ◽  
Second Spectrum

AbstractIn the current study, we consider the Bresse–Timoshenko type systems and we prove some stability results for time delay cases into setting of so called simplified Bresse–Timoshenko equations (or truncated version of Bresse–Timoshenko equations) according to contributions of Elishakoff et al. (2010, Advances in Mathematical Modeling and Experimental Methods for Materials and Structures. Solid Mechanics and Its Applications. Springer: Berlin, 249–254.; 2015, Celebrating the Centenary of Timoshenko’s study of effects of shear deformation and rotary inertia. Appl. Mech. Rev.67, 1–11.; 2017, Critical contrasting of three versions of vibrating Bresse-Timoshenko beam with a crack. Int. J. Solids Struct. 109, 143–151.). These equations are free of the so-called ‘second spectrum’ phenomenon, and they have important consequences on stabilization setting. Specifically, following Almeida Júnior and Ramos (2017, On the nature of dissipative Timoshenko systems at light of the second spectrum. Z. Angew. Math. Phys.68, 31.) in a recent contribution that shows that damping effects eliminate the consequences of this spectrum for equal wave propagation velocities, we prove that time delay effects are able of stabilizing the truncated version regardless of any relationship between coefficients of system. It is concluded that dissipative truncated versions of Bresse–Timoshenko equations are advantageous over the classical Bresse–Timoshenko equations in stabilization context.

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