M. R. M. Crespo da Silva

Bio: M. R. M. Crespo da Silva is an academic researcher from University of Cincinnati. The author has contributed to research in topics: Nonlinear system & Differential equation. The author has an hindex of 6, co-authored 9 publications receiving 619 citations.

Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. I. Equations of Motion

Abstract: This paper is divided into two parts. The authors’ purpose in Part I is to formulate a set of mathematically consistent governing differential equations of motion describing the nonplanar, nonlinear dynamics of an inextensional beam. The beam is assumed to undergo flexure about two principal axes and torsion. The equations are developed with the objective of retaining contributions due to nonlinear curvature as well as nonlinear inertia. A priori ordering assumptions are avoided as much as possible in the process. The equations are expanded to contain nonlinearities up to order three to facilitate comparison with analogous equations in the literature, and to render them amenable to the study of moderately large amplitude flexural-torsional oscillations by perturbation techniques. The utilization of the order-three equations in the analysis of nonlinear beam oscillations is the subject of Part II.

Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. II. Forced Motions

Abstract: The nonplanar, nonlinear, resonant forced oscillations of a fixed-free beam are analyzed by a perturbation technique with the objective of determining quantitative and qualitative information about the response. The analysis is based on the differential equations of motion developed in Part I of this paper which retain not only the nonlinear inertia but also nonlinear curvature effects. It is shown that the latter play a significant role in the nonlinear flexural response of the beam.

Nonlinear Flexural-Flexural-Torsional Dynamics of Inextensional Beams. I. Equations of Motion

Abstract: This paper is divided into two parts. The authors’ purpose in Part I is to formulate a set of mathematically consistent governing differential equations of motion describing the nonplanar, nonlinear dynamics of an inextensional beam. The beam is assumed to undergo flexure about two principal axes and torsion. The equations are developed with the objective of retaining contributions due to nonlinear curvature as well as nonlinear inertia. A priori ordering assumptions are avoided as much as possible in the process. The equations are expanded to contain nonlinearities up to order three to facilitate comparison with analogous equations in the literature, and to render them amenable to the study of moderately large amplitude flexural-torsional oscillations by perturbation techniques. The utilization of the order-three equations in the analysis of nonlinear beam oscillations is the subject of Part II.

Tuning nonlinearity, dynamic range, and frequency of nanomechanical resonators

Abstract: We explore an electrostatic mechanism for tuning the nonlinearity of nanomechanical resonators and increasing their dynamic range for sensor applications. We also demonstrate tuning the resonant frequency of resonators both upward and downward. A theoretical model is developed that qualitatively explains the experimental results and serves as a simple guide for design of tunable nanomechanical devices.

Colloquium: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays

Abstract: It has been known for some time that nonlinearity and discreteness play important roles in many branches of condensed-matter physics as evidenced by the appearance of domain walls, kinks, and solitons. A recent discovery is that localized dynamical energy in a perfect nonlinear lattice can be stabilized by the lattice discreteness. Intrinsic localized modes (ILMs) are the resulting signature. Their energy profiles resemble those of localized modes at defects in a harmonic lattice but, like solitons, they can move. ILMs have been observed in macroscopic arrays as diverse as coupled Josephson junctions, optical waveguides, two-dimensional nonlinear photonic crystals, and micromechanical cantilevers. Such dynamically driven localized modes are providing a new window into the underlying simplicity of nonequilibrium dynamics. This Colloquium surveys the studies of ILMs in micromechanical cantilever arrays. Because of the ease of sample fabrication with silicon technology and the intuitive optical visualization techniques, these experiments are able to demonstrate the general nature and properties of dynamical energy localization while at the same time providing new information on ILM generation, locking, pinning, and interaction with impurities.

Modal Interactions in Dynamical and Structural Systems

Abstract: The authors review theoretical and experimental studies of the influence of modal interactions on the nonlinear response of harmonically excited structural and dynamical systems. In particular, they discuss the response of pendulums, ships, rings, shells, arches, beam structures, surface waves, and the similarities in the qualitative behavior of these systems. The systems are characterized by quadratic nonlinearities which may lead to two-to-one and combination autoparametric resonances. These resonances give rise to a coupling between the modes involved in the resonance leading to nonlinear periodic, quasi-periodic, and chaotic motions.

Rather than resonance, flapping wing flyers may play on aerodynamics to improve performance

Abstract: Saving energy and enhancing performance are secular preoccupations shared by both nature and human beings. In animal locomotion, flapping flyers or swimmers rely on the flexibility of their wings or body to passively increase their efficiency using an appropriate cycle of storing and releasing elastic energy. Despite the convergence of many observations pointing out this feature, the underlying mechanisms explaining how the elastic nature of the wings is related to propulsive efficiency remain unclear. Here we use an experiment with a self-propelled simplified insect model allowing to show how wing compliance governs the performance of flapping flyers. Reducing the description of the flapping wing to a forced oscillator model, we pinpoint different nonlinear effects that can account for the observed behavior—in particular a set of cubic nonlinearities coming from the clamped-free beam equation used to model the wing and a quadratic damping term representing the fluid drag associated to the fast flapping motion. In contrast to what has been repeatedly suggested in the literature, we show that flapping flyers optimize their performance not by especially looking for resonance to achieve larger flapping amplitudes with less effort, but by tuning the temporal evolution of the wing shape (i.e., the phase dynamics in the oscillator model) to optimize the aerodynamics.