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Quantum Euler beam—QUEB: modeling nanobeams vibration

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Abstract

The theory of vibration of engineering structures belongs to a known chapter of mechanics. Nevertheless, new emerging technologies operating at the smallest scales open a completely new landscape in the field of nanodevices, nanostructured materials as well as biological systems. Nanoscale structures are always involved and characterized by extremely high-frequency vibrations and very small energy, implying quantum effects. This approach, even for simple oscillators, implies both conceptual and mathematical difficulties. It is a matter of fact that the analysis of complex structures, as for example beams and shells, has never been considered in the physical and engineering recent literature in a complete quantum-mechanical context using directly the Schrodinger’s equation. The present paper proposes an attempt in this direction, introducing a quantum Euler beam, the QUEB model at the ground state energy. The idea is to shape a new model for flexural structures that is mathematically similar to those used in classical mechanics, but mimicking the peculiarity of the quantum motion.

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Authors and Affiliations

  1. Center for Nanotechnology in Engineering Sapienza, CNIS, Rome, Italy

    A. Carcaterra

  2. Department of Mechanical and Aerospace Engineering, University of Rome Sapienza, Via Eudossiana 18, Rome, Italy

    A. Carcaterra

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Communicated by Andreas Öchsner.

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Carcaterra, A. Quantum Euler beam—QUEB: modeling nanobeams vibration. Continuum Mech. Thermodyn. 27, 145–156 (2015). https://doi.org/10.1007/s00161-014-0341-1

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