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

Nonlinear Normal Modes of a Rotating Shaft Based on the Invariant Manifold Method

International audienceThe nonlinear normal mode methodology is generalized to the study of a rotating shaft supported by two short journal bearings. For rotating shafts, nonlinearities are generated by forces arising from the supporting hydraulic bearings. In this study, the rotating shaft is represented by a linear beam, while a simplified bearing model is employed so that the nonlinear supporting forces can be expressed analytically. The equations of motion of the coupled shaft-bearings system are constructed using the Craig-Bampton method of component mode synthesis, producing a model with as few as six degrees of freedom (d.o.f.). Using an invariant manifold approach, the individual nonlinear normal modes of the shaft-bearings system are then constructed, yielding a single d.o.f. reduced-order model for each nonlinear mode. This requires a generalized formulation for the manifolds, since the system features damping as well as gyroscopic and non-conservative circulatory terms. The nonlinear modes are calculated numerically using a nonlinear Galerkin method that is able to capture large amplitude motions. The shaft response from the nonlinear mode model is shown to match extremely well the simulations from the reference Craig-Bampton model

Nonlinear normal modes and their application in structural dynamics

Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced-order models that accurately describe the vibrations of large-scale nonlinear engineering structures. The general approach makes use of nonlinear normal modes that are defined in terms of invariant manifolds in the phase space of the system model. An efficient Galerkin projection method is developed, which allows for the construction of nonlinear modes that are accurate out to large amplitudes of vibration. This approach is successfully extended to the generation of nonlinear modes for systems that are internally resonant and for systems subject to external excitation. The effectiveness of the Galerkin-based construction of the nonlinear normal modes is also demonstrated for a realistic model of a rotating beam

Bidirectional association between handgrip strength and ADLs disability: a prospective cohort study

BackgroundDecreased handgrip strength (HGS) and activities of daily living (ADL) disability are common in aging populations. No studies have evaluated the bidirectional associations between HGS and ADL disability. This study aimed to explore the bidirectional effects of HGS and ADL disability.MethodsThis study analyzed data from two waves (2011 and 2015) of China Health and Retirement Longitudinal Study (CHARLS). Low HGS is defined by the Asian Working Group for Sarcopenia criteria. Meanwhile, disability was assessed by ADLs scale. The prospective bidirectional association between HGS and ADL disability was examined using binary logistic regression. Subgroup analysis were performed according to age and gender.ResultsA total of 4,902 and 5,243 participants were included in the Stage I and Stage II analyses, respectively. On the one hand, low HGS was significantly associated with subsequent ADL disability. The odds ratio (OR) value of developing BADL disability and IADL disability were 1.60 (95% confidence interval (CI): 1.23–2.08) and 1.40 (95% CI: 1.15–1.70), respectively, in participants with low HGS. On the other hand, baseline ADL disability was associated with an increased risk of developing low HGS. The OR value of developing low HGS were 1.84 (95% CI: 1.34–2.51) and 1.46 (95% CI: 1.19–1.79) for participants with BADL disability and participants with IADL disability, respectively. Lastly, the strength of the bidirectional associations varied among subgroups.ConclusionsA significant bidirectional associations were identified between HGS and ADL disability. Interventions should be developed to prevent the development or progression of both low HGS and ADL disability

Whole-genome sequencing of <em>Oryza brachyantha</em> reveals mechanisms underlying <em>Oryza</em> genome evolution

The wild species of the genus Oryza contain a largely untapped reservoir of agronomically important genes for rice improvement. Here we report the 261-Mb de novo assembled genome sequence of Oryza brachyantha. Low activity of long-terminal repeat retrotransposons and massive internal deletions of ancient long-terminal repeat elements lead to the compact genome of Oryza brachyantha. We model 32,038 protein-coding genes in the Oryza brachyantha genome, of which only 70% are located in collinear positions in comparison with the rice genome. Analysing breakpoints of non-collinear genes suggests that double-strand break repair through non-homologous end joining has an important role in gene movement and erosion of collinearity in the Oryza genomes. Transition of euchromatin to heterochromatin in the rice genome is accompanied by segmental and tandem duplications, further expanded by transposable element insertions. The high-quality reference genome sequence of Oryza brachyantha provides an important resource for functional and evolutionary studies in the genus Oryza

A Highly Conserved, Small LTR Retrotransposon that Preferentially Targets Genes in Grass Genomes

LTR retrotransposons are often the most abundant components of plant genomes and can impact gene and genome evolution. Most reported LTR retrotransposons are large elements (>4 kb) and are most often found in heterochromatic (gene poor) regions. We report the smallest LTR retrotransposon found to date, only 292 bp. The element is found in rice, maize, sorghum and other grass genomes, which indicates that it was present in the ancestor of grass species, at least 50–80 MYA. Estimated insertion times, comparisons between sequenced rice lines, and mRNA data indicate that this element may still be active in some genomes. Unlike other LTR retrotransposons, the small LTR retrotransposons (SMARTs) are distributed throughout the genomes and are often located within or near genes with insertion patterns similar to MITEs (miniature inverted repeat transposable elements). Our data suggests that insertions of SMARTs into or near genes can, in a few instances, alter both gene structures and gene expression. Further evidence for a role in regulating gene expression, SMART-specific small RNAs (sRNAs) were identified that may be involved in gene regulation. Thus, SMARTs may have played an important role in genome evolution and genic innovation and may provide a valuable tool for gene tagging systems in grass

Modeling-Dependent Protein Characterization of the Rice Aldehyde Dehydrogenase (ALDH) Superfamily Reveals Distinct Functional and Structural Features

The completion of the rice genome sequence has made it possible to identify and characterize new genes and to perform comparative genomics studies across taxa. The aldehyde dehydrogenase (ALDH) gene superfamily encoding for NAD(P)+-dependent enzymes is found in all major plant and animal taxa. However, the characterization of plant ALDHs has lagged behind their animal- and prokaryotic-ALDH homologs. In plants, ALDHs are involved in abiotic stress tolerance, male sterility restoration, embryo development and seed viability and maturation. However, there is still no structural property-dependent functional characterization of ALDH protein superfamily in plants. In this paper, we identify members of the rice ALDH gene superfamily and use the evolutionary nesting events of retrotransposons and protein-modeling–based structural reconstitution to report the genetic and molecular and structural features of each member of the rice ALDH superfamily in abiotic/biotic stress responses and developmental processes. Our results indicate that rice-ALDHs are the most expanded plant ALDHs ever characterized. This work represents the first report of specific structural features mediating functionality of the whole families of ALDHs in an organism ever characterized