Vibration Energy Propagation Research Articles

A method for determining the contribution of an individual source to the vibrational and acoustic field of complex mechanical structures

A calculation-experimental method is presented for determining the contribution of individual mechanisms to the vibrational and acoustic field of complex structures. The method is based on measuring vibrations in a set of points on the vibration energy propagation path from an operating mechanism, as well as on the subsequent calculation of the dynamic forces and external field using a numerical model of the structure. Experimental implementation of the method has shown that the contribution of an individual mechanism can be evaluated with high accuracy, including in the presence of vibrations at its base induced by external sources, the magnitude of which may significantly exceed the eigenvibrations of the mechanism.

Method of Assessing the Impact of Material Properties on the Propagation of Vibrations Excited with a Single Force Impulse

Method of Assessing the Impact of Material Properties on the Propagation of Vibrations Excited with a Single Force Impulse The article provides a discussion on the studies comprising active experiments conducted on selected structural components, the purpose of which was to analyse the impact of properties of the material used on the dynamic state form. The vibration excitation was achieved by applying a force impulse of a specific value. The studies were conducted on excitations acting perpendicularly to the surface of the component being examined in strictly established geometric arrangements. Consequently, signals were obtained to be subsequently applied for the sake of analysis of the impact of material properties on the manner of the vibration energy propagation in the machine components examined. The signal processing method used was based on application of a time and frequency transformation which enables obtaining the information the signals carry in two domains simultaneously, namely those of time and frequency. The results provided and discussed evidence the applicability of the method described in the analysis of the material impact on dynamic properties of the given structural component.

The modeling of energy transport for life goes on: Comment on “The theory of bio-energy transport in the protein molecules and its properties” by Xiao-feng Pang

There is absolutely no doubt that bio-energy transport in protein molecules plays a key role in understanding various basic problems in life science. This topic, regarded as a “crisis in bioenergetics”, was discussed in depth in a symposium of the New York Academy of Sciences in 1973. Since the first quantum mechanical model for vibrational energy propagation down the α helix of a protein proposed by Davydov and Kislukha [1], various models have been developed to unwind this mystery in biological systems. A soliton, a localized and dynamically self-sufficient solitary wave, is believed to be the energy carrier through the α-helical protein structures. Started from the discovery of the “wave of translation” by John Scott Russell in 1834, this interesting phenomenon is also observed in other fluid-like systems such as plasmas and flowing sand, and in many other areas of physics involving nonlinear partial differential equations, for example, the FitzHugh–Nagumo equations of nerve impulse propagation [2], and the sine–Gordon equation in solid state physics and nonlinear optics [3]. Recently, great interest in this research area has been further strengthened because of its applications in nanotechnologies, microelectronics, information storage devices, and biosensors. The significance of this scientific topic has stretched beyond fundamental science into practical utilizations. One of the critical questions to ask about these energy transport models for protein is whether a soliton has a sufficiently long lifetime to carry out the energy transfer along the polypeptide chains of the protein structure. Are solitons really too delicate to survive in biology? Like other nonlinear scientific phenomenon, the system behavior is relatively unpredictable and the solution is relatively hard to obtain. Yet scientists spared no effort in solving the energy transport mechanism based on the soliton model. While biological solitons remain an abstruse concept and their observation in protein is experimentally difficult (if not impossible), the theoretical framework may enable us to gradually unveil the mysterious process of energy transport in life. Proteins are the major workers within the cells and carrying out the functions described by the genetic codes: providing structural support, transmitting signals, catalyzing reactions, and transporting molecules. Thus the fundamental understanding on the energy transport mechanism in protein will also have great values to protein folding, conformational changes, and misfolding disease research. Experimental data are needed to verify the mathematical modeling of the energy transport [4,5]. The first evidence for the soliton-like state was obtained in the crystal of acetanilide [6,7]. Further evidence for self-trapped states was observed in the organic crystal of N-methylacetamide (NMA) [8] and even in a small polypeptide

Alwyn C. Scott, a subversive character in Biological Physics

Modern nonlinear science got started when Enrico Fermi, John Pasta, Stan Ulam, and Mary Tsingou Menzel discovered a remarkable effect about nonlinear system dynamics while exploring the dynamics of a chain of masses connected by anharmonic springs via a computer simulation (in 1952!) [1, 2]. To their great surprise, the system was not ergodic under certain initial conditions, but periodically returned to its original conditions. The Fermi–Pasta–Ulam–Tsingou discovery of what could be called nonthermalization took a while to get into the public domain, and during this time the mathematician Martin Kruskal at Princeton, with Norman Zabusky at Bell Labs, discovered that there were integrable solutions to a nonlinear differential equation called the Korteweg de Vries (KdV) equation that came out of studies of nonlinear dispersive waves [3]. These solutions had remarkably robust properties and Kruskal coined the term “soliton” to describe them, a wonderful term that immediately entered the public domain. Of course, these kinds of self-sustaining structures in anharmonic systems had been seen before, most notably in the case of John Scott Russell in 1834 who discovered what he called a “wave of translation” due to the abrupt stopping of a canal barge [4]. Solitons are particularly interesting phenomena and important to physics at many different levels because they act as “particles” with an identity as they move through an anharmonic region. An excellent introduction to solitons can be found in the book by Drazin and Johnson [5]. A remarkable surge in the interest in solitons in biology occurred in the early 1970s because of two people: Alwyn C. Scott, a powerful theoretical physicist with a strong interest in nonlinear phenomena and biology, and Alexander Davydov, an eminent theoretical solid state theorist. Davydov constructed in 1973 a fully quantum mechanical model for vibrational energy propagation down the alpha helix of a protein, but it was not a very accessible article to either find (in the Western literature) or read [6]. Al Scott became fascinated with the subject and wrote several masterful reviews of the subject [7, 8] and helped popularize the idea that these quantum nonlinear entities might be important in biology. Among his efforts were the unearthing of Scott Russell’s original “wave of translation” observation and the tenacious recreation of this event in spite of being a card-carrying theorist. Yesterday, a temporary lack of concentration sprawled me on the pavement and hopefully just hurt my knee. Today, I am limping around cursing my temporary immobility, and realizing how extraordinarily brave Alwyn C. Scott was, in addition to his prodigious skills as a theoretical physicist and expositor of nonlinear science. Shortly after moving to Tucson in 1985, he was struck while riding a bike by a pick-up truck which ran a red light. He was left partially paralyzed and in constant pain the rest of his life, but this did not slow down Al Scott. I have found this wonderful picture (Fig. ​(Fig.1,1, from http://www.ma.hw.ac.uk/~chris/kruskal/scott_kr_95.jpg) of Scott, Kruskal, and Chris Eilbeck of Heriot-Watt University on 12 July 1995 when they witnessed a re-creation of the Scott Russell wave of translation. Fig. 1 Chris Eilbeck, Alwyn C. Scott, and Martin Kruskal (left to right) waiting for a Scott Russell soliton water wave (reproduced with kind permission of Chris Eilbeck, Heriot-Watt University, Edinburgh, UK) Solitons do indeed exist, of course, and are very important. Although the emphasis of this memorial issue is on the possible biological role of Davydov’s soliton (see the articles by Shyamsunder Erramilli, Peter Hamm, Leonor Cruzeiro, Alan Bishop, and myself), we also included some more condensed matter articles by Peter Christiansen and Al Sievers to provide a solid background. Biological solitons remain an elusive concept, and we still do not know if indeed they play a major role in biology. We leave it to the reader to decide for him- or herself and read the sad and cautionary tale written by Luca Turin about Colin McClare who tried, as Martin Kruskal’s tee-shirt says, to “Subvert the Dominant Paradigm!” Alwyn C. Scott did that in many ways.

A diffusion model for a one-dimensional structure, coupled with an auxiliary system

This paper extends the concept of a local energy approach to homogeneous structures which are coupled with an auxiliary resonant system. The case of a one-dimensional homogeneous master structure (bar, beam) coupled over its length with a homogeneous auxiliary system composed of resonant arbitrary subsystems is analyzed. It is shown that under specific assumptions, the vibrational energy density of the coupled master structure can be predicted by solving a simple energetic boundary value problem that accounts for the mechanical coupling with the auxiliary subsystem. In the context of vibrational energy propagation, an important question is whether heterogeneity introduced by the auxiliary system enhances the diffusive behavior of the master structure. Numerical results for various types of auxiliary systems show that the effective diffusion coefficient of the coupled system is generally increased compared to the uncoupled master structure.

Heat flow in proteins: Computation of thermal transport coefficients

The rate of vibrational energy transfer and thermal transport coefficients are computed for two structurally distinct proteins, green fluorescent protein (GFP) and myoglobin. The computation of thermal transport coefficients exploits the scaling of the energy diffusion coefficient with the vibrational mode frequency of a protein. Near 300 K we find that vibrational energy transfer due to anharmonicity contributes substantially to thermal transport because of the localization of many thermally accessible normal modes. The thermal diffusivity for the beta-barrel GFP is larger than that for myoglobin, particularly at low temperature due to a mean free path for vibrational energy propagation that is twice as large at low frequency. Vibrational energy transfer is also faster in GFP than in myoglobin for most vibrational modes.

Numerical calculations of solitary waves in Davydov's equations

Families of numerically very accurate bright and dark lattice solitary waves in Davydov's equations, which have been proposed to describe propagation of vibrational energy in α-helix protein are calculated using spectral collocation and path-following methods. Travelling solitary waves are found to exist only when the nonlinear coupling is less than some critical value which depends on the velocity of the solitary wave.