453 research outputs found

    Vibration analysis of composite circular and annular membranes

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    Mechanical mode engineering with orthotropic metamaterial membranes

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    Metamaterials are structures engineered at a small scale with respect to the wavelength of the excitations they interact with. These structures behave as artificial materials whose properties can be chosen by design, mocking and even outperforming natural materials and making them the quintessential tool for manipulation of wave systems. In this Letter we show how the acoustic properties of a silicon nitride membrane can be affected by nanopatterning. The degree of asymmetry in the pattern geometry induces an artificial anisotropic elasticity, resulting in the splitting of otherwise degenerate mechanical modes. The artificial material we introduce has a maximum Ledbetter-Migliori anisotropy of 1.568, favorably comparing to most bulk natural crystals. With an additional freedom in defining arbitrary asymmetry axes by pattern rotation, our approach can be useful for fundamental investigation of material properties as well as for devising improved sensors of light, mass or acceleration based on micromechanical resonators

    Wind-structure interaction simulations for the prediction of ovalling vibrations in silo groups

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    Wind-induced ovalling vibrations were observed during a storm in October 2002 on several empty silos of a closely spaced group consisting of 8 by 5 thin-walled silos in the port of Antwerp (Belgium). The purpose of the present research is to investigate if such ovalling vibrations can be predicted by means of numerical simulations. More specifically, the necessity of performing computationally demanding wind-structure interaction (WSI) simulations is assessed. For this purpose, both one-way and two-way coupled simulations are performed. Before considering the entire silo group, a single silo in crosswind is simulated. The simulation results are in reasonably good agreement with observations and WSI simulations seem to be required for a correct prediction of the observed ovalling vibrations

    Proceedings of the Twenty Second Nordic Seminar on Computational Mechanics

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    Low-frequency vibrations of strongly inhomogeneous multicomponent elastic structures

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    The thesis deals with 1D and 2D scalar equations governing dynamic behaviour of strongly inhomogeneous layered structures. Harmonic vibrations of a composite rod and antiplane shear motions of a cylindrical body consisting of several components are studied paying particular attention to the lowest frequencies. The main focus is on a strong contrast between the parameters characterising structure components, including their sizes, material stiffness, and densities. We start with a multi-parametric analysis of the near-rigid body motions of rods and cylindrical bodies with piecewise uniform properties. The listed problems allow exact analytical solutions demonstrating that the values of all lowest eigenfrequencies tend to zero at large/small ratios of material and geometric parameters. The low-frequency behaviour is considered for so-called global and local regimes, and simple explicit conditions on the problem parameters, underlying each of the regimes, are derived. Further, we present a perturbation procedure for a more general setup based on the evaluation of the almost rigid body motions of “stronger” components assuming a high contrast of material parameters. The proposed approach is extended to structures of arbitrary shape, with variable material parameters, as well as to multi-component structures. We obtain asymptotic formulae for the lowest natural frequencies and also present illustrative examples for each of the studied problems. Many of asymptotic estimations are compared with exact solutions. The results of the thesis are applicable to a mathematical justification of shear deformation theories for multi-layered plates and shells with a strong transverse inhomogeneity

    Mechanical systems in the quantum regime

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    Mechanical systems are ideal candidates for studying quantumbehavior of macroscopic objects. To this end, a mechanical resonator has to be cooled to its ground state and its position has to be measured with great accuracy. Currently, various routes to reach these goals are being explored. In this review, we discuss different techniques for sensitive position detection and we give an overview of the cooling techniques that are being employed. The latter include sideband cooling and active feedback cooling. The basic concepts that are important when measuring on mechanical systems with high accuracy and/or at very low temperatures, such as thermal and quantum noise, linear response theory, and backaction, are explained. From this, the quantum limit on linear position detection is obtained and the sensitivities that have been achieved in recent opto and nanoelectromechanical experiments are compared to this limit. The mechanical resonators that are used in the experiments range from meter-sized gravitational wave detectors to nanomechanical systems that can only be read out using mesoscopic devices such as single-electron transistors or superconducting quantum interference devices. A special class of nanomechanical systems are bottom-up fabricated carbon-based devices, which have very high frequencies and yet a large zero-point motion, making them ideal for reaching the quantum regime. The mechanics of some of the different mechanical systems at the nanoscale is studied. We conclude this review with an outlook of how state-of-the-art mechanical resonators can be improved to study quantum {\it mechanics}.Comment: To appear in Phys. Re
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