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Designing low frequency bandgaps in additively manufactured parts using internal resonators
... [2][3][4]) and developing lattice structures for specific applications, such as biomedical implants [5][6][7], heat exchangers [8,9] and sandwich structures for lightweighting of structural engineering components [10,11]. The utility of lattice structures extends to precision engineering applications, where vibration isolating lattice structures have been designed for some low frequency bandwidths [12,13]. Such designs could be incorporated into machine frames in an attempt to reduce the noise in a measurement system. ...
... This work aims to provide a framework for efficient generation of tetrahedral meshes of lattice structures suitable for parametric studies of a wide range of manufacturing defects. Although the authors' main objective is to support the development of machine frames [12,13], this framework can be generally applied to FE studies of strut-based lattice structures. [15] (b) radius variation [15] (c) Left: original unit cell design, Right: texture bias in the manufactured part [16]. ...
Strut-based lattice structures produced by powder bed fusion are prone to characteristic manufacturing defects that alter both their form and surface texture. Most studies in the literature focus on a subset of commonly observed defects, typically radius variation and strut waviness; surface defects remain relatively unexplored. Furthermore, there remains a need for the development of a general finite element modelling framework that can implement a range of defects into any strut-based lattice design. This paper presents a modelling framework for implementing a range of both form and surface defects into finite element meshes of strut-based lattices. A signed distance function forms the foundation for this framework, upon which surface meshes can be modified and converted into tetrahedral meshes via open-source software. The paper demonstrates how radius variation, strut waviness, elliptical cross sections and localised surface defects can be modelled in lattice struts, for which intuitive mathematical definitions are provided. A parametric study is performed to assess the sensitivity of the compressive Young’s modulus of BCCZ and octet-truss lattices to upskin and downskin surface defects. The results showed higher sensitivity in the octet-truss than in BCCZ; both designs were more sensitive to downskin than to upskin defects.
... The results for WP1 can be seen in Chapter 5, results for WP2 are presented in Chapter 6, and the results of WP3 are available in Chapter 7 and Chapter 8. The methodology presented in this chapter formed part of these publications[54,56,[159][160][161][162][163]. ...
Advancements in additive manufacturing technology have allowed the realisation of geometrically complex structures with enhanced capabilities in comparison to solid structures. One of these capabilities is vibration attenuation which is of paramount importance for the precision and accuracy of metrology and machining instruments. In this project, new additively manufactured lattice structures are proposed for achieving vibration attenuation. The ability of these lattices to provide vibration attenuation at frequencies greater than their natural frequency was studied first. This is referred to as vibration isolation. For the vibration isolation study, a combination of finite element modelling and an experimental setup comprising a dynamic shaker and laser vibrometer was used. The natural frequencies obtained from the experimental results were 93 % in agreement with the simulated results. However, vibration attenuation was demonstrated only along one dimension and vibration waves were allowed to propagate, meaning the transmissibility was allowed to be greater than 0 dB. To achieve lower transmissibility, the project demonstrated that lattice structures can develop Bragg-scattering and internal resonance bandgaps. The bandgaps were identified from the lattices' dispersion curves calculated using a finite element based wave propagation modelling technique. Triply periodic minimal surface lattices and strut-based lattices developed Bragg-scattering bandgaps with a normalised bandgap frequency (wavelength divided by cell size) of ~ 0.2. The bandgap of the tested lattices was demonstrated to be tunable with the volume fraction of the lattice unit cell, thus, providing a tool to design lattice structures with bandgaps at required frequencies. An internal resonance mechanism in the form of a solid cube or sphere with struts was designed into the inner core of the unit cell of strut-based lattices. These new internal resonance lattices can provide (a) lower frequency bandgaps than Bragg-scattering lattices within the same design volume, and/or (b) comparable bandgaps frequencies with reduced unit cell dimensions. In comparison to lattices of higher normalised bandgap frequencies, lattices with lower normalised bandgap frequencies have cell sizes that are more suitable for manufacturing with the current additive manufacturing technologies and have higher periodicity within a constrained design volume, resulting in higher attenuation within the bandgaps and more homogenous structures. Similar to the Bragg-scattering lattices, the bandgaps of the internal resonance lattices were demonstrated to be tunable through modification of the geometry of the lattice unit cell. The internal resonance lattice experimentally demonstrated a bandgap of normalised frequency between 0.039 to 0.067 and an attenuation of up to -77 dB. These results are essential for engineering vibration attenuation capabilities within the macro-scale of materials for complete elimination of all mechanical vibration waves at tailorable frequencies. Future work will include further reduction of the bandgap frequencies and increasing the bandgap width by exploring new unit cell designs and new materials for additive manufacturing.
... The user has less design control with TPMS unit cells, however they are currently studied for applications such as biomedical implants [12]. Additionally, there are custom designs outside of strut-based and surface-based forms, for example those produced using topology optimisation [31] and with internal resonators for vibration isolation [32]. ...
Additively manufactured lattice structures are popular due to their desirable properties, such as high specific stiffness and high surface area, and are being explored for several applications including aerospace components, heat exchangers and biomedical implants. The complexity of lattices challenges the fabrication limits of additive manufacturing processes and thus, lattices are particularly prone to manufacturing defects. This paper presents a review of defects in lattice structures produced by powder bed fusion processes. The review focuses on the effects of lattice design on dimensional inaccuracies, surface texture and porosity. The design constraints on lattice structures are also reviewed, as these can help to discourage defect formation. Appropriate process parameters, post-processing techniques and measurement methods are also discussed. The information presented in this paper contributes towards a deeper understanding of defects in lattice structures, aiming to improve the quality and performance of future designs.
A number of strategies that enable lattice structures to be derived from Topology Optimisation (TO) results suitable for Additive Manufacturing (AM) are presented. The proposed strategies are evaluated for mechanical performance and assessed for AM specific design related manufacturing considerations. From a manufacturing stand-point, support structure requirement decreases with increased extent of latticing, whereas the design-to-manufacture discrepancies and the processing efforts, both in terms of memory requirements and time, increase. Results from Finite Element (FE) analysis for the two loading scenarios considered: intended loading, and variability in loading, provide insight into the solution optimality and robustness of the design strategies. Lattice strategies that capitalised on TO results were found to be considerably (∼40-50%) superior in terms of specific stiffness when compared to the structures where this was not the case. The Graded strategy was found to be the most desirable from both the design and manufacturing perspective. The presented pros-and-cons for the various proposed design strategies aim to provide insight into their suitability in meeting the challenges faced by the AM design community.
Architected materials that control elastic wave propagation are essential in
vibration mitigation and sound attenuation. Phononic crystals and acoustic
metamaterials use band gap engineering to forbid certain frequencies from
propagating through a material. However, existing solutions are limited in the
low frequency regimes and in their bandwidth of operation because they require
impractical sizes and masses. Here, we present a class of materials (labeled
elastic meta-structures) that supports the formation of wide and low frequency
band gaps, while simultaneously reducing their global mass. To achieve these
properties, the meta-structures combine local resonances with structural modes
of a periodic architected lattice. While the band gaps in these meta-structures
are induced by Bragg scattering mechanisms, their key feature is that the band
gap size and frequency range can be controlled and broadened through local
resonances, which is linked to changes in the lattice geometry. We demonstrate
these principles experimentally, using novel additive manufacturing methods,
and inform our designs using finite element simulations. This design strategy
has a broad range of applications, including control of structural vibrations,
noise and shock mitigation.
In this paper, band gaps tunned by material parameters in three-dimensional fluid-fluid sonic crystals are studied. From the basic wave equation, it is found that the material parameters directly determining the three-dimensional sonic band gaps are the mass density ratio and bulk modulus ratio. The calculation of the sonic band gaps is completed by the plane-wave expansion method. The effects of these parameters on sonic band gaps are discussed in details for the simple-cubic (sc), face-centered cubic (fcc) and body-centered cubic (bcc) lattices. The results show that the first potential sonic band gap easily appears at both small mass density ratio and bulk modulus ratio, and becomes wider with both of these two parameters decreasing. The bulk modulus ratio plays a more important role than the mass density ratio in tuning the sonic band gaps. The present analysis can be applied to artificially design band gaps.
We study the elastic wave propagation in phononic-crystal strip waveguides cut from a silicon phononic-crystal plate with square-lattice vacuum holes through analyzing the band structure and transmission spectra. We show the influence of different cutting ways is crucial to the band-gap formation, and four types of native strip modes are deserved to be fully taken into account. The results show that though there is no band gap existing in the phononic-crystal plates with a low filling fraction, band gaps are created in their corresponding cut strip waveguide because the derivative traction-free boundaries strongly modulate the shear-horizontal bands.
Three-dimensional pentamode metamaterials are artificial solids that
approximately behave like liquids, which have vanishing shear modulus.
Pentamodes have recently become experimental reality. Here, we calculate their
phonon band structures for various parameters. Consistent with static continuum
mechanics, we find that compression and shear waves exhibit phase velocities
that can realistically be different by more than one order of magnitude.
Interestingly, we also find frequency intervals with more than two octaves
bandwidth in which pure single-mode behavior is obtained. Herein, exclusively
compression waves exist due to a complete three-dimensional band gap for shear
waves and, hence, no coupling to shear modes is possible. Such single-mode
behavior might, e.g., be interesting for transformation-elastodynamics
architectures.
We report on the experimental observation of a one-octave-large omnidirectional elastic band gap for longitudinal waves in a three-dimensional phononic crystal consisting of face-centered-cubic arrays of close-packed steel beads in a solid epoxy matrix. The 60% relative width of the band gap is larger than expected based on the contrast in material properties, and is confirmed by band structure diagram and transmission spectra computations. The coupling between shear and longitudinal polarizations is pointed out as a mechanism for enlarging the band gap by comparing with the steel beads in water matrix case.
We have fabricated sonic crystals, based on the idea of localized resonant structures, that exhibit spectral gaps with a lattice constant two orders of magnitude smaller than the relevant wavelength. Disordered composites made from such localized resonant structures behave as a material with effective negative elastic constants and a total wave reflector within certain tunable sonic frequency ranges. A 2-centimeter slab of this composite material is shown to break the conventional mass-density law of sound transmission by one or more orders of magnitude at 400 hertz.
In this paper, the phonon dispersion curves of several surface-based lattices are examined, and their energy transmission spectra, along with the corresponding bandgaps are identified. We demonstrate that these bandgaps may be controlled, or tuned, through the choice of cell type, cell size and volume fraction. Our results include two findings of high relevance to the designers of lattice structures: (i) network and matrix phase gyroid lattice structures develop bandgaps below 15 kHz while network diamond and matrix diamond lattices do not, and (ii) the bandwidth of a bandgap in the network phase gyroid lattice can be tuned by adjusting its volume fraction and cell size.
In this work, the banded behaviour of composite one-dimensional structures with an additive manufactured stiffener is examined. A finite element method is used to calculate the stiffness, mass and damping matrices, and periodic structure theory is used to obtain the wave propagation of one-dimensional structures. A multi-disciplinary design optimisation scheme is developed to achieve optimal banded behaviour and structural characteristics of the structures under investigation. Having acquired the optimal solution of the case study, a representative specimen is manufactured using a carbon fibre cured plate and additive manufactured nylon-based material structure. Experimental measurements of the dynamic performance of the hybrid composite structure are conducted using a laser vibrometer and electrodynamic shaker setup to validate the finite element model.
Information-rich metrology (IRM) is a term that we introduce to refer to an approach where the conventional paradigm of measurement is enhanced, thanks to the introduction and active role of multiple novel sources of information. The overarching goal of IRM is to encompass and homogenise all those measurement scenarios where information available from heterogeneous sources, e.g. from the product being measured, the manufacturing process that was used to fabricate it, the internals of the measurement instrument itself, as well as from any previous measurement carried with any other instrument, is gathered and somehow incorporated with an active role into the measurement pipeline, in order to ultimately achieve a higher-quality measurement result (e.g. better metrological performance, shorter measurement times, smaller consumption of resources). A comprehensive investigation into the aspects, issues and opportunities of IRM requires a large number of test cases, and a research effort involving hardware (sensors, instrument architectures, communication networks, etc.) and software (data communication, instrument control and synchronisation, data analysis and processing), as well as significant research into mathematical and statistical modelling. As part of such an undertaking, we present here the design of an original, flexible and open-architecture, all-optical dimensional measuring system (AODMS) for measuring the geometry and surface topography of micro-scale components. The system is designed to operate in a cube of 100 mm sides, with micrometre or sub-micrometre measurement uncertainties. The key aspects of AODMS are a flexibility and open-architecture. The system is designed to accommodate a wide array of heterogeneous optical sensors, ranging from 3D measurement to 2D imaging, from prototype to commercial sensors, and is being designed to be particularly suitable to support the investigation of multi-sensor data fusion solutions [1]. The open nature of the architecture allows full flexibility in the design and configuration of the instrument control and communication software, as well as of the data analysis and processing software, thus presenting itself as an ideal platform to investigate IRM through the support to the development of solutions to enable knowledge-driven measurement, e.g. through the interaction with CAD/CAM systems, product data-management systems and any other IT-based knowledge-management solutions. The schema of the prototype AODMS are shown in Figure 1. The AODMS prototype includes a moving stage, a support and interface to a photogrammetric system dedicated to
This paper presents the design, analysis and experimental verification of strut-based lattice structures to enhance the mechanical vibration isolation properties of a machine frame, whilst also conserving its structural integrity. In addition, design parameters that correlate lattices, with fixed volume and similar material, to natural frequency and structural integrity are also presented. To achieve high efficiency of vibration isolation and to conserve the structural integrity, a trade-off needs to be made between the frame’s natural frequency and its compressive strength. The total area moment of inertia and the mass (at fixed volume and with similar material) are proposed design parameters to compare and select the lattice structures; these parameters are computationally efficient and straight-forward to compute, as opposed to the use of finite element modelling to estimate both natural frequency and compressive strength. However, to validate the design parameters, finite element modelling has been used to determine the theoretical static and dynamic mechanical properties of the lattice structures. The lattices have been fabricated by laser powder bed fusion and experimentally tested to compare their static and dynamic properties to the theoretical model. Correlations between the proposed design parameters, and the natural frequency and strength of the lattices are presented.
The classical distinction between a structure and a material is increasingly blurred in lattice materials made from beam and shell-like structures. This chapter is concerned with the elastodynamic response of 1D and 2D lattice materials. Of particular interest is to understand elastic wave propagation and related phenomena unique to periodic structures. Starting from 1D structures, the chapter ends with 2D lattice materials, establishing relevant connections between the solid-state physics and structural dynamics literature along the way. The Floquet–Bloch theory from solid-state physics is applied in combination with the finite-element (FE) formulations that are widely used in structural dynamics and other engineering disciplines. Emphasis is given to the synthesis of existing knowledge on wave transmission in periodic materials, from the classical discrete atomic lattices to the rapidly emerging multifunctional lattice materials, and avenues for future development are indicated.
Mechanical Vibrations: Modeling and Measurement describes essential concepts in vibration analysis of mechanical systems. It incorporates the required mathematics, experimental techniques, fundamentals of model analysis, and beam theory into a unified framework that is written to be accessible to undergraduate students, researchers, and practicing engineers. To unify the various concepts, a single experimental platform is used throughout the text. Engineering drawings for the platform are included in an appendix. Additionally, MATLAB programming solutions are integrated into the content throughout the text. © 2012 Springer Science+Business Media, LLC. All rights reserved.
The band structure and sound attenuation of the triply periodic co-continuous composite materials with simple cubic lattice, body-centered cubic lattice, and face-centered cubic lattice consisting of PMMA and air are investigated using finite element method. Complete band gaps are found in these structures and the width of band gaps is depending on volume fraction. It is shown that the width of band gaps along different directions in the first irreducible Brillouin zone enlarges as the volume fraction increases from 0.2 to 0.7. The largest complete band gap widths of the three types of co-continuous structures are 0.29, 0.54, and 0.55, respectively. As the complete band gaps appear in audible range of frequencies, these triply periodic co-continuous composite materials can be utilized to control noise.
Three-dimensional periodic structures have many applications in acoustics and their properties are strongly related to structural details. Here we demonstrate through simulations the ability to tune the phononic band gaps of 3D periodic elastomeric structures using deformation. The elastomeric nature of the material makes the transformation of the band gaps a reversible and repeatable process, providing avenues for the design of tunable 3D phononic crystals such as sonic switches.
Based on the variational theory, a wavelet-based numerical method is developed to calculate the defect states of acoustic waves in two-dimensional phononic crystals with point and line defects. The supercell technique is applied. By expanding the displacement field and the material constants (mass density and elastic stiffness) in periodic wavelets, the explicit formulations of an eigenvalue problem for the plane harmonic bulk waves in such a phononic structure are derived. The point and line defect states in solid-liquid and solid-solid systems are calculated. Comparisons of the present results with those measured experimentally or those from the plane wave expansion method show that the present method can yield accurate results with faster convergence and less computing time.
This work presents results on finite-difference time-domain (FDTD) integration of the full three dimensional elastic wave equation in nonhomogenous periodic media, for understanding the propagation and gap existence in these media. Extensive calculations are compared with plane wave expansion (PWE) data for different three dimensional systems consisting of Pb spheres in epoxy matrix forming an fcc lattice. The method of solving the wave equation provides good convergence and the agreement with the PWE method is excellent. The FDTD method, however, can handle cases such as fluids in solids which cannot be treated with the PWE method. Transmission results are presented for the case of Hg spheres in Al with fcc lattice, in order to prove the general use of the FDTD method. © 2000 American Institute of Physics.