Aetiology of ergot disease of male sterile wheat

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An invariant manifold approach to nonlinear normal modes of oscillation

International audienceA method for determining the amplitude-dependent mode shapes and the corresponding modal dynamics of weakly nonlinear vibratory systems is de· scribed. The method is a combination of a Galerkin projection and invariant manifold techniques and is applied to a class of distributed parameter vibratory systems. In this paper the general theory for a class of conservative systems is outlined and applied to determine the nonlinear mode shapes and modal dynamics of a linear Euler-Bernoulli team attached to a nonlinear elastic foundation

H2O contents in olivine-hosted melt inclusions from primitive magmas in the Northern Cascade arc

The subducting Juan de Fuca plate is the hot endmember of slabs worldwide, and its unique thermal character prompts debate about the role of fluid-flux melting versus decompression melting in the Cascade arc. While slow subduction of this hot slab is expected to result in strong dehydration prior to reaching sub-arc depths, there is no consensus on whether the slab is entirely dehydrated at this point, or whether volcanism is the result of water-poor, decompression melting, or fluid-flux melting. I provide the first measurements of pre-eruptive volatile contents in olivine-hosted melt inclusions from primitive magmas in the northern region of the arc, at Mount Baker and Glacier Peak. These volatile contents and melt inclusion compositions are used to model mantle melting processes. Low-K olivine tholeiite (LKT) and calc-alkaline basalt (CAB) melt inclusions at Glacier Peak have minimum H2O concentrations of 2.0 and 2.2 wt. % and fO2 of ΔQFM +1.1 and +1.5, respectively. The evolved compositions of these melt inclusions in both lava types (host olivine: Fo85-89) are corrected to mantle values by addition of ≤15 wt. % olivine, and the results suggest that the minimum water contents in the parental magmas are 1.7 wt. % and 2.0 wt. %. Measured values themselves may be low due to degassing at crustal depths. The Mount Baker Schreiber\u27s Meadow cinder cone (CAB) has minimum H2O concentrations of 2.3 wt. %, though these contents cannot be adequately disentangled from potential crustal involvement and/or magma mixing/mingling to be corrected to mantle values. Results of modeling indicate that both LKT and CAB magmas at Glacier Peak are the result of 13-15% fluid-fluxed melting of a compositionally heterogeneous mantle source, last equilibrated near the base of the crust. Source regions are interpreted to contain both an ocean island basalt (OIB)-like component and a mid-ocean ridge basalt (MORB)-like component. Minimum H2O contents suggested in the source region are between 0.21 and 0.28 wt %. This is in contrast to southern regions of the Cascade arc, where LKT magmas are considered to be the result of dry decompression melting of a MORB-like source

A periodically forced piecewise linear oscillator

International audienceA single-degree of freedom non-linear oscillator is considered. The non-linearity is in the restoring force and is piecewise linear with a single change in slope. Such oscillators provide models for mechanical systems in which components make intermittent contact. A limiting case in which one slope approaches infinity, an impact oscillator, is also considered. Harmonic, subharmonic, and chaotic motions are found to exist and the bifurcations leading to them are analyzed

Normal modes for piecewise linear vibratory systems

International audienceA method to construct the normal modes for a class of piecewise linear vibratory systems is developed in this study. The approach utilizes the concepts of Poincare maps and invariant manifolds from the theory of dynamical systems. In contrast to conventional methods for smooth systems, which expand normal modes in a series form around an equilibrium point of interest, the present method expands the normal modes in a series form of polar coordinates in a neighborhood of an in variant disk of the system. It is found thal the normal modes, modal dynamics and frequency-amplitude dependence relationship are all of piecewise type. A two degree of freedom example is used to demonstrate the method

The impact of nonlinearity on degenerate parametric amplifiers

This work investigates the effects of system nonlinearities on degenerate parametric amplifiers. A simple, Duffing-type nonlinearity is appended to a representative equation of motion for a mechanical or electromechanical parametric amplifier, and classical perturbation methods are used to characterize the resulting effects on the amplifier\u27s frequency response and performance. Ultimately, the work demonstrates that parametric amplification can be realized in nonlinear, dynamic-range limited systems, such as resonant micro-or nanosystems, but at the expense of performance degradation. Additionally, it is shown that nonlinear amplifiers can be operated above their linear instability threshold but that doing so results in bistable amplified responses

The construction of non-linear normal modes for systems with internal resonance

International audienceA numerical method, based on the invariant manifold approach, is presented for constructing non-linear normal modes for systems with internal resonances. In order to parameterize the non-linear normal modes of interest, multiple pairs of system state variables involved in the internal resonance are kept as 'seeds' for the construction of the multi-mode invariant manifold. All the remaining degrees of freedom are then constrained to these 'seed', or master, variables, resulting in a system of non-linear partial differential equations that govern the constraint relationships, and these are solved numerically. The computationally-intensive solution procedure uses a combination of finite difference schemes and Galerkin-based expansion approaches. It is illustrated using two examples, both of which focus on the construction of two-mode models. The first example is based on the analysis of a simple three-degree-of-freedom example system, and is used to demonstrate the approach. An invariant manifold that captures two non-linear normal modes is constructed, resulting in a reduced order model that accurately captures the system dynamics. The methodology is then applied to a larger order system, specifically, an 18-degree-of-freedom rotating beam model that features a three-to-one internal resonance between the first two flapping modes. The accuracy of the non-linear two-mode reduced order model is verified by comparing time-domain simulations of the two DOF model and the full system equations of motion

Large-amplitude non-linear normal modes of piecewise linear systems

International audienceA numerical method for constructing non-linear normal modes (NNMs) for piecewise linear autonomous systems is presented. These NNMs are based on the concept of invariant manifolds, and are obtained using a Galerkin-based solution of the invariant manifold's non-linear partial differential equations. The accuracy of the constructed non-linear modes is checked by the comparison of the motion on the invariant manifold to the exact solution, in both time and frequency domains. It is found that thisconstruction approach can accurately capture the NNMs over a wide range of amplitudes, including those with strong non-linear effects. Several interesting dynamic characteristics of the non-linear modal motion are found and compared to those of linear modes. A two-degree-of-freedom example is used to illustrate the technique. The existence, stability and bifurcations of the NNMs for this example are investigated

Non-linear modal analysis of structural systems using multi-mode invariant manifolds

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76304/1/AIAA-1994-1672-138.pd