Toroidal Phononic Crystal Isolator for Low-Frequency Band Gaps
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Solution Overview
Problem
Existing materials struggle to achieve broadband wave attenuation at low frequencies below 20 kHz with a combination of high stiffness and low mass density, as natural crystals cannot produce band gaps in the THz range, and previous metamaterial designs face limitations in band gap frequency and width due to mass constraints and energy dissipation mechanisms.
Innovation Solution
The proposed unit cell for artificial phononic crystals incorporates a toroidal building block with mechanical connections that exploit rotational inertia in the x-y plane, allowing for inertia amplification and decoupling of rotational inertia from the wave propagation direction, resulting in a phononic metamaterial with broader band gaps and a more favorable mass density relation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If heavy resonators are used to obtain wide band gaps at low frequencies, then the attenuation band width increases, but the mass density increases significantly
Solution Approach 1:
The patent changes the geometric parameters of the unit cell structure, specifically using a toroidal building block with strategically positioned mechanical connections (struts) to create an inertia amplification mechanism. This geometric parameter optimization allows achieving wide band gaps without increasing mass density, as the inertial effect is amplified through the mechanical connection arrangement rather than by simply increasing resonator mass.
Solution Approach 2:
The patent employs a composite structural design combining a toroidal building block with mechanical connections (struts) arranged in a specific pattern. This composite structure creates an effective medium with tailored inertial properties, where the combination of the toroidal mass and the mechanical connections produces inertia amplification that achieves wide band gaps without requiring heavy resonators.
2Weight of stationary object
If point masses are used as resonators, then the structure remains lightweight, but the band gap width is limited
Solution Approach 1:
The patent introduces dynamic mechanical connections (struts) that can rotate and deform, creating a dynamic inertia amplification mechanism. The struts are designed with specific inclination angles and lengths that enable them to amplify the inertial effect of the toroidal building block during vibration, thereby widening the band gap without increasing the static mass of the system.
Solution Approach 2:
The patent utilizes the spatial arrangement of mechanical connections in three-dimensional space, with struts inclined at specific angles relative to the wave propagation direction. This dimensional arrangement allows the system to exploit rotational inertia and mechanical leverage effects that amplify the inertial response, achieving wider band gaps without proportionally increasing mass.
3Object-affected harmful factors
If energy dissipation mechanisms are used for vibration attenuation, then vibration reduction is achieved, but the material loses stiffness
Solution Approach 1:
The patent exploits mechanical vibration and resonance principles by designing a structure with specific natural frequencies that create band gaps. The toroidal building block with mechanical connections forms a resonant system where the inertial amplification creates frequency ranges where wave propagation is inhibited, achieving vibration attenuation through resonant interference rather than energy dissipation, thereby preserving material stiffness.
4Speed
If the characteristic length of the lattice is increased to achieve rotational inertia, then the band gap frequency decreases, but the unit cell size increases
Solution Approach 1:
The patent optimizes the geometric parameters of the unit cell, specifically the length and inclination angle of mechanical connections (struts), to achieve inertia amplification within a compact size. By carefully selecting these parameters, the system achieves rotational inertia effects without proportionally increasing the characteristic length, thereby maintaining lower band gap frequencies with smaller unit cells.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This design achieves strong vibration attenuation at low acoustic frequencies below 5 kHz with high quasi-static stiffness and low mass density, enabling broader band gaps and improved mechanical properties, suitable for various applications requiring vibration isolation.
Implementation Method 1
utilizing rotational inertia to achieve broad band gaps and high quasi-static stiffness while maintaining a small characteristic length
Implementation Method 2
showing reduced mechanical vibrations in a defined frequency range with at least one band gap in the band structure dispersion relation of the unit cell respectively the metamaterial
Data Source
AI summary
A unit cell of an artificial phononic crystal for building of an artificial phononic metamaterial, showing reduced mechanical vibrations in a defined frequency range with at least one band gap in the band structure dispersion relation of the unit cell. The unit cell includes at least one building block and at least one mechanical connection connected to the building block, showing reduced mechanical vibrations in a defined frequency range with tailored dispersion properties with at least one band gap is sought. This is accomplished by forming the building block as a toroid, with a central opening and a front surface from which a first multiplicity of struts, which are tiltable relatively to the principal direction, is extending from the front surface. More than one strut is inclined with respect to the principal direction so that a rotation of the toroid around the principal direction is possible.