Phononic band gaps and vibrations in one- and two-dimensional mass–spring structures

Jensen, Jakob Søndergaard

doi:10.1016/s0022-460x(02)01629-2

Cited by 362 publications

(163 citation statements)

References 17 publications

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“…Additionally, there has several studies into the use of materials with negative refractive index at optical wavelengths, where examples include the superlenses proposed by Pendry (2000) and the invisibility properties demonstrated by Kundtz and Smith (2010) and Urzhumov et al (2011). This has influenced the development of acoustic metamaterials, and there has been considerable attention placed on the design of sonic or phononic crystals (Kushwaha et al, 1993;Klironomos and Economou, 1998;Psarobas et al, 2000;Goffaux and Sánchez-Dehesa, 2003;Jensen, 2003;Hirsekorn, 2004;Wang et al, 2004a, b,c). Simple phononic crystals involving periodic arrays of cylinders have been shown to exhibit wave filtering behavior.…”

Section: Introductionmentioning

confidence: 99%

Investigation of elastic wave transmission in a metaconcrete slab

Mitchell

Pandolfi

Ortiz

2015

Mechanics of Materials

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a b s t r a c tA new type of modified concrete, termed metaconcrete, has been shown to exhibit trapping of wave energy and a reduction in mortar stress when subjected to dynamic loading. Metaconcrete replaces the standard stone and gravel aggregates of regular concrete with spherical inclusions consisting of a heavy core coated with a compliant outer layer. These new layered aggregates resonate at designed frequencies by allowing for relative motion between the heavy core and the mortar matrix, which causes the aggregate to absorb energy and therefore reduce stress within the mortar phase of the composite material. The transmission of wave energy through a metaconcrete slab can be used to visualize the effect of resonant behavior within the metaconcrete aggregates. To quantify this behavior we compute a transmission coefficient, which is a method of measuring the absorption of wave energy as an applied forcing of known frequency travels through the material. The transmission coefficient is plotted against forcing frequency for four different aggregate material and geometry configurations. A reduction in transmission ratio is observed at or near the computed natural modes of the aggregate, indicating the activation of resonance within the inclusions. This behavior is consistent with observations from studies on sonic metamaterials containing resonant inclusions with a similar layered structure. The frequency location and width of the dip in transmission coefficient will aid in the design of metaconcrete aggregates for specific forcing applications.

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Section: Introductionmentioning

confidence: 99%

Investigation of elastic wave transmission in a metaconcrete slab

Mitchell

Pandolfi

Ortiz

2015

Mechanics of Materials

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“…3(b), where the frequency gap It has been demonstrated in many papers, see e.g. [5,45], that a structure with a finite number of repeated unit cells may significantly suppress propagation of waves with frequencies in the stop band. Fig.…”

Section: Free Wave Propagation and Forced Vibration In The Optimized mentioning

confidence: 99%

“…The phenomenon may occur for elastic, acoustic or electromagnetic waves, see Refs. [1][2][3][4][5][6]. Except for regions close to the boundaries, a band-gap structure usually consists of a periodic distribution of different elastic materials, or repeated identical segments if a single elastic material is prescribed for the structure.…”

Section: Introductionmentioning

confidence: 99%

“…Due to a wealth of potential applications in vibration protection, noise isolation, waveguiding, etc., the study and development of bandgap rod, mass-spring, beam, grillage, disk and plate structures, in most cases by topology optimization, have attracted increasing attention in recent years, see e.g. [5,[7][8][9][10][11][12][13][14][15][16][17][18]. Elastodynamics of finite or infinite periodic 1D rod or beam structures has been studied in [6,[19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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On Optimum Design and Periodicity of Band-Gap Structures

Olhoff¹,

Niu²,

Cheng³

2014

Proceedings of the 4th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. A band-gap structure usually consists of a periodic distribution of elastic materials or segments, where the propagation of waves is impeded or This paper extends earlier optimum shape design results for transversely vibrating Bernoulli-Euler beams by determining new optimum band-gap beam structures for (i) different combinations of classical boundary conditions, (ii) much larger values of the orders n (n>1) and n-1 of adjacent upper and lower eigenfrequencies of maximized band-gaps, and (iii) different values of a minimum beam cross-sectional area constraint. In the present paper, instead of maximizing band-gaps between frequencies of propagating waves or forced vibrations excited by external time-harmonic loads, the closely relatedproblem of maximizing the gap between two adjacent eigenfrequencies ω n and ω n-1 of any given consecutive orders n (n>1) and n-1, is considered. This is justified by the fact that external time-harmonic dynamic loads cannot excite resonance with high vibration levels of standing waves, if the eigenfrequencies of the structure are moved outside the range of the external excitation frequencies by the optimization.Finally, the present study shows that if an infinite beam structure is constructed by repeated translation of an inner beam segment obtained by the aforementioned frequency gap optimization, then a band-gap of traveling waves in this infinite beam is found to correlate almost perfectly with the maximized frequency gap in the finite structure.

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“…Theoretical calculations of LRPC behavior mainly use multiple-scattering (MS) methods [19,20], plane-waveexpansion (PWE) methods [21], the finite-difference timedomain (FDTD) methods [22], transfer-matrix methods [23], and lumped-mass methods [24,25]. Lumped-mass methods are simple and effective for studying the performance of various LRSMs [24,25].…”

Section: Introductionmentioning

confidence: 99%

Investigation of locally resonant absorption and factors affecting the absorption band of a phononic glass

et al. 2014

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We experimentally and theoretically investigated the mechanisms of acoustic absorption in phononic glass to optimize its properties. First, we experimentally studied its locally resonant absorption mechanism. From these results, we attributed its strong sound attenuation to its locally resonant units and its broadband absorption to its networked structure. These experiments also indicated that the porosity and thickness of the phononic glass must be tuned to achieve the best sound absorption at given frequencies. Then, using lumped-mass methods, we studied how the absorption bandgaps of the phononic glass were affected by various factors, including the porosity and the properties of the coating materials. These calculations gave optimal ranges for selecting the porosity, modulus of the coating material, and ratio of the compliant coating to the stiff matrix to achieve absorption bandgaps in the range of 6-30 kHz. This paper provides guidelines for designing phononic glasses with proper structures and component materials to work in specific frequency ranges.

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Phononic band gaps and vibrations in one- and two-dimensional mass–spring structures

Cited by 362 publications

References 17 publications

Investigation of elastic wave transmission in a metaconcrete slab

Investigation of elastic wave transmission in a metaconcrete slab

On Optimum Design and Periodicity of Band-Gap Structures

Investigation of locally resonant absorption and factors affecting the absorption band of a phononic glass

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