Nano Vibrations of Flexural Structures: Quantum Mechanics Approach

The theory of vibration of engineering structures belongs to a well established chapter of mechanics. Nevertheless, new emerging technologies operating at the smallest scales open a completely new landscape in the field. The presence of small scale structures leads to extreme high-frequency vibrations with very small energy, involving 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, have never been considered in the physical and engineering recent literature in a complete quantum-mechanical context using directly the Schrodinger equation. The present paper proposes an attempt in this direction, introducing a Euler-beam model that accounts for quantum effects. The idea is two shape a new model for flexural structures that is mathematically similar to those used in classical mechanics, but mimicking characteristics of the quantum motion. This could be a route sounding on the engineering ground.