Heinrich Hertz | EPFL Graph Search

Heinrich Rudolf Hertz (hɜrts ; ˈhaɪnʁɪç ˈhɛʁts; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's equations of electromagnetism. The unit of frequency, cycle per second, was named the "hertz" in his honor. Biography Heinrich Rudolf Hertz was born in 1857 in Hamburg, then a sovereign state of the German Confederation, into a prosperous and cultured Hanseatic family. His father was Gustav Ferdinand Hertz. His mother was Anna Elisabeth Pfefferkorn. While studying at the Gelehrtenschule des Johanneums in Hamburg, Hertz showed an aptitude for sciences as well as languages, learning Arabic. He studied sciences and engineering in the German cities of Dresden, Munich and Berlin, where he studied under Gustav R. Kirchhoff and Hermann von Helmholtz. In 1880, Hertz obtained his PhD from the University of Berlin, and for the next three years remained for post-doctoral

Radial elasticity of multiwalled carbon nanotubes

Harald Brune, Stephan Fedrigo, Ismaël Palaci

We report an experimental and a theoretical study of the radial elasticity of multiwalled carbon nanotubes as a function of external radius. We use atomic force microscopy and apply small indentation amplitudes in order to stay in the linear elasticity regime. The number of layers for a given tube radius is inferred from transmission electron microscopy, revealing constant ratios of external to internal radii. This enables a comparison with molecular dynamics results, which also shed some light onto the applicability of Hertz theory in this context. Using this theory, we find a radial Young modulus strongly decreasing with increasing radius and reaching an asymptotic value of 30&PLUSMN; 10 GPa.

2005

Analysis and Design of Ultra-Wideband Antennas in the Spectral and Temporal Domains

Gabriela Quintero Diaz De Leon

Formal research on Ultra-wideband (UWB) technology started in the U.S. in 2002; where its definition was formulated and the frequency allocation in that country established. However, the first ultra-wideband transmission was done during the confirmation of Maxwell's equations by Heinrich Hertz in 1886, the first ever reported radio transmission. Sparks or very short pulses were sent and received at a distance away from its source. UWB antennas have existed since those times, but technology has been mostly focused on the transmission of continuous wave narrowband signals. The largest problematic encountered in today's UWB antennas is that characterization methods were, since the beginning, meant to describe narrowband antennas. The frequency characteristics of these antennas are constant over their operational bandwidth, hence they can be fully characterized in the frequency domain. UWB antennas, on the other hand, are meant to transmit pulsed signals. Analyzing them only in the frequency domain is not enough to fully evaluate their performance, as pulse distortion is an important parameter that should be controlled. An extended literature review is included in the first part of this thesis, where the available UWB antenna characterization methods are evaluated. Many limitations were encountered, showing that the available techniques do not analyze simultaneously the most important parameters of an UWB antenna. A new characterization method is proposed: the System Fidelity Factor (SFF). Its main purpose is to incorporate frequency, time and space characteristics of a two-antennas system to compare UWB antennas in an efficient way. This is achieved with the correlation between the received and the input pulses, quantifying the distortion produced by the system. The SFF is an interesting tool because both simulations and measurements can be done in a simple and straight-forward manner, using tools that are commonly available in any antenna lab. Any combination of antennas can be analyzed and the free-space channel can be easily replaced with any other environment. Several UWB antennas were designed and used to prove the efficiency of the SFF. A good agreement between the proposed simulation techniques and the measurements was achieved. The antennas are novel designs specially developed for UWB applications under the American or European regulations. The last part of the thesis presents these antennas and analyzes them using the SFF to compare their performance.

EPFL2010

Wave propagation in periodic buckled beams

Florian Paul Robert Maurin

Folding of the earth's crust, wrinkling of the skin, rippling of fruits, vegetables and leaves are all examples of natural structures that can have periodic buckling. Periodic buckling is also present in engineering structures such as compressed lattices, cylinders, thin films, stretchable electronics, tissues, etc., and the question is to understand how wave propagation is affected by such media. These structures possess geometrical nonlinearities and intrinsic dispersive sources, two conditions which are necessary to the formation of stable, nonlinear waves called solitary waves. These waves are particular since dispersive effects are balanced by nonlinear ones, such that the wave characteristics remain constant during the propagation, without any decay or modification in the shape. It is the goal of this thesis to demonstrate that solitary waves can propagate in periodic buckled structures. This manuscript focuses specifically on periodically buckled beams that require either guided or pinned supports for stability purposes. Buckling is initially considered statically and investigations are made on stability, role played by imperfections, shape of the deflection, etc. Linear dispersion is analyzed employing the semi-analytical dispersion equation, a new method that relates the frequency explicitly to the propagation constant of the acoustic branch. This allows the quantification of the different dispersive sources and it is found that in addition to periodicity, transverse inertial and coupling effects are playing a dominant role. Modeling the system by a mass-spring chain that accounts for additional dispersive sources, homogenization and asymptotic procedures lead to the double-dispersion Boussinesq equation. Varying the pre-compression level and the support type, the main result of this thesis is to show that four different waves are possible, namely compressive supersonic, rarefaction (tension) supersonic, compressive subsonic and rarefaction subsonic solitary waves. For high-amplitude waves, models based on strongly-nonlinear PDEs as the one modeling wave propagation in granular media (Hertz power law) are more appropriate and adaptation of existing work is done. Analytical model results are then compared to finite-element simulations of the structure and experiments, and are found in excellent agreement. In this thesis, in addition to the semi-analytical dispersion equation, two other new methods are proposed. For periodic structures by translation with additional glide symmetries (e.g. buckled beams), Bloch theorem is revisited and allows the use of a smaller unit cell. Advantages are dispersion curves easier to interpret and computational cost reduced. Finally, the last contribution of this thesis is the use of NURBS-based isogeometric analysis (IGA) to solve the extensible-elastica problem requiring at least C1-continuous basis functions, which was not possible before with classical finite-element methods. The formulation is found efficient to solve dynamic problems involving slender beams as buckling.