Nonlinear normal modes in mechanical systems: concept and computation with numerical continuation

The purpose of this Project is, first and foremost, to disclose the topic of nonlinear vibrations and oscillations in mechanical systems and, namely, nonlinear normal modes NNMs to a greater audience of researchers and technicians. To do so, first of all, the dynamical behavior and properties of nonlinear mechanical systems is outlined from the analysis of a pair of exemplary models with the harmonic balanced method. The conclusions drawn are contrasted with the Linear Vibration Theory. Then, it is argued how the nonlinear normal modes could, in spite of their limitations, predict the frequency response of a mechanical system. After discussing those introductory concepts, I present a Matlab package called 'NNMcont' developed by a group of researchers from the University of Liege. This package allows the analysis of nonlinear normal modes of vibration in a range of mechanical systems as extensions of the linear modes. This package relies on numerical methods and a 'continuation algorithm' for the computation of the nonlinear normal modes of a conservative mechanical system. In order to prove its functionality, a two degrees of freedom mechanical system with elastic nonlinearities is analized. This model comprises a mass suspended on a foundation by means of a spring-viscous damper mechanism -analogous to a very simplified model of most suspended structures and machines- that has attached a mass damper as a passive vibration control system. The results of the computation are displayed on frequency energy plots showing the NNMs branches along with modal curves and time-series plots for each normal mode. Finally, a critical analysis of the results obtained is carried out with an eye on devising what they can tell the researcher about the dynamical properties of the system.

Computation, prediction, and experimental tests of fitness for bacteriophage T7 mutants with permuted genomes

We created a simulation based on experimental data from bacteriophage T7 that computes the developmental cycle of the wild-type phage and also of mutants that have an altered genome order. We used the simulation to compute the fitness of more than 105 mutants. We tested these computations by constructing and experimentally characterizing T7 mutants in which we repositioned gene 1, coding for T7 RNA polymerase. Computed protein synthesis rates for ectopic gene 1 strains were in moderate agreement with observed rates. Computed phage-doubling rates were close to observations for two of four strains, but significantly overestimated those of the other two. Computations indicate that the genome organization of wild-type T7 is nearly optimal for growth: only 2.8% of random genome permutations were computed to grow faster, the highest 31% faster, than wild type. Specific discrepancies between computations and observations suggest that a better understanding of the translation efficiency of individual mRNAs and the functions of qualitatively “nonessential” genes will be needed to improve the T7 simulation. In silico representations of biological systems can serve to assess and advance our understanding of the underlying biology. Iteration between computation, prediction, and observation should increase the rate at which biological hypotheses are formulated and tested.

Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons.

The collective behavior of interconnected spiking nerve cells is investigated. It is shown that a variety of model systems exhibit the same short-time behavior and rapidly converge to (approximately) periodic firing patterns with locally synchronized action potentials. The dynamics of one model can be described by a downhill motion on an abstract energy landscape. Since an energy landscape makes it possible to understand and program computation done by an attractor network, the results will extend our understanding of collective computation from models based on a firing-rate description to biologically more realistic systems with integrate-and-fire neurons.

Scheduling and simulation of computation graphs for multiple resource computers /

"UILU Eng 79 1709."

A procedure for computation of the total river sand discharge and detailed distribution bed to surface /

"November 1968."

Flood-hydrograph analyses and computation.

Cover title.

New techniques and equipment for correlation and computation

"Technical memorandum 7668-TM-2"

Computation of inflows and outflows of eight regulated lakes in the Oswego River basin, New York, 1930-79 /

Mode of access: Internet.

The steam fitters' computation and price book; consisting of tables giving the cubical contents of rooms of various sizes, tables giving the number of square feet of wall surface, tables giving the number of square feet of window surface. Tables giving radiation required for rooms of any size at various proportions. Also tables showing the cost of radiation ... Tables giving size, price, weight etc., of pipe, fittings, valves, etc. In addition ... some general information on points of interest to steam and hot water fitters.

At foot of t.-p.: Copyrighted 1893 by Mark Dean; on verso of t.-p. copyright date given 1895.

Tables for the computation of railway and other earthwork,

Mode of access: Internet.

Methods of mathematical analysis and computation.

Mode of access: Internet.

Blair's chronological and historical tables : from the creation to the present time, with additions and corrections from the most authentic writers, including the computation of St. Paul, as connecting the period from the exode to the temple.

"The present volume has been reconstructed from the folio edition by a literary friend [John Sharpe] ... the ... revision of the manuscript ... having been intrusted to myself."--Sir Henry Ellis, in preface (dated 1844) cf. also Lowndes.

Graphical and mechanical computation,

"Embodies a course given by the writer for a number of years in the mathematical laboratory of the Massachusetts Institute of Technology."

Basin rainfall and snowmelt computation : Hydrologic Engineering Center computer program 23-J2-L226.

At head of cover title: Generalized computer program.

Tables for the computation of railway and other earthwork,

Mode of access: Internet.