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Li, J., Chen, B. & Mao, H. (2024). Exact closed-form solution for vibration characteristics of multi-span beams on an elastic foundation subjected to axial force. Structures, 60, Article ID 105884.
Open this publication in new window or tab >>Exact closed-form solution for vibration characteristics of multi-span beams on an elastic foundation subjected to axial force
2024 (English)In: Structures, E-ISSN 2352-0124, Vol. 60, article id 105884Article in journal (Refereed) Published
Abstract [en]

This paper investigates the vibration characteristics of multi-span beams resting on an elastic foundation and subjected to axial forces. A comprehensive analytical expression of the dynamic response of multi-span beams on an elastic foundation that is developed to address various boundary conditions. The vibration equation is derived by employing Newton's second law. By Laplace transformations and the Green's function method, the solution of this governing equation can be obtained. Subsequently, a unified description is implemented for distinct types of boundary conditions using matrix representations. The correctness is verified through reference results and finite element methods (FEM). The effects of different parameters such as support stiffness, foundation elastic and shear layer stiffness, and axial force on the vibration characteristics are analyzed. This study demonstrates two findings: First, there are two thresholds for support stiffness, and the stiffness value is divided into three intervals. In the same interval, multi-span beams show the same properties. Second, for a rigidly supported multi-span beam, the critical axial force with a natural frequency of zero is just the corresponding Euler's buckling load; for elastically supported multi-span beams, the critical axial force falls between the Euler's buckling load corresponding to single-span and multi-span beams.

Place, publisher, year, edition, pages
Elsevier BV, 2024
Keywords
Elastic foundation, Green's function, Multi-span beam, Steady-state dynamic responses
National Category
Applied Mechanics Other Civil Engineering
Identifiers
urn:nbn:se:kth:diva-342833 (URN)10.1016/j.istruc.2024.105884 (DOI)001163935400001 ()2-s2.0-85182888689 (Scopus ID)
Note

QC 20240301

Available from: 2024-01-31 Created: 2024-01-31 Last updated: 2024-03-01Bibliographically approved
Gaborit, M., Lundberg, E., Mao, H. & Göransson, P. (2022). Controlled anisotropy materials and 3D printing: experimentations and analyses. In: Proceedings of ISMA 2022 - International Conference on Noise and Vibration Engineering and USD 2022 - International Conference on Uncertainty in Structural Dynamics: . Paper presented at 30th International Conference on Noise and Vibration Engineering, ISMA 2022 and 9th International Conference on Uncertainty in Structural Dynamics, USD 2022, Leuven, Belgium, Sep 12 2022 - Sep 14 2022 (pp. 477-481). KU Leuven, Departement Werktuigkunde
Open this publication in new window or tab >>Controlled anisotropy materials and 3D printing: experimentations and analyses
2022 (English)In: Proceedings of ISMA 2022 - International Conference on Noise and Vibration Engineering and USD 2022 - International Conference on Uncertainty in Structural Dynamics, KU Leuven, Departement Werktuigkunde , 2022, p. 477-481Conference paper, Published paper (Refereed)
Abstract [en]

Novel computational tools and optimisation strategies offer an unprecedented framework to explore large design spaces within a short time frame. In the scope of material design, these new possibilities have completely revolutionized the research horizon, leading amongst other things to controlled anisotropy media with a finer granularity than ever seen before. However, a question arises regarding the manufacturability of such media which most of the time relies on 3D printing and the agreement between modelled and printed geometry. In the recent years, the authors published several articles on the properties of Kelvin Cell packings and the possibility to control their anisotropy. In the last few months, an effort towards printing the designed media has been made in search for experimental validation of the numerical results. This contribution describes the printing process for kelvin cell packing samples with controlled anisotropy and analyses their agreement with the model both from a geometric and from a physical response standpoint. Depending on the advances of current research, information on the dynamic behaviour of such systems will be discussed.

Place, publisher, year, edition, pages
KU Leuven, Departement Werktuigkunde, 2022
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-348779 (URN)2-s2.0-85195907888 (Scopus ID)
Conference
30th International Conference on Noise and Vibration Engineering, ISMA 2022 and 9th International Conference on Uncertainty in Structural Dynamics, USD 2022, Leuven, Belgium, Sep 12 2022 - Sep 14 2022
Note

Part of ISBN 9789082893151

QC 20240627

Available from: 2024-06-27 Created: 2024-06-27 Last updated: 2024-06-27Bibliographically approved
Matija, M., Mao, H., Tibert, G. & Dadbakhsh, S. (2022). Design and Development of Damping SandwichPanels for Satellite Housing Using AdditiveManufacturing. In: : . Paper presented at International Conference on Design for 3D Printing.
Open this publication in new window or tab >>Design and Development of Damping SandwichPanels for Satellite Housing Using AdditiveManufacturing
2022 (English)Conference paper, Published paper (Refereed)
Abstract [en]

The present work investigates the performance of additively-manufactured sandwich structures with the goal of reducing the effect of vibrations on a spacecraft during launch, whilst minimizing mass. Additive manufacturing allows designers to implement custom and complex geometries, such as the sheet gyroid structures, inside sandwich panels. Accordingly, this work details the development of gyroid-based sandwich structures for damping. Several test specimens are designed, additively manufactured using ABS plastic, and their damping performances are evaluated based on both simulation and experiments. Damping values are identified using frequency response transfer functions. The results show that as theory predicts, adding more mass, through the added thickness of the gyroid reduces the amplitude of vibrations. However, on a damping-per-unit-mass basis, the experimental results are inconclusive mainly due to the measurements of vibrations in the center of the sandwich panels instead of the sides where the vibrations can be maximum. Therefore, simulations better illustrate the changes of the damping behavior at different applied frequencies. Lessons and experiences are summarized for future work, particularly in exploring the effects of varying other 3D printed composite meta-lattice sandwich structures for satellites. 

National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-323991 (URN)
Conference
International Conference on Design for 3D Printing
Note

QC 20230220

Available from: 2023-02-17 Created: 2023-02-17 Last updated: 2023-02-27Bibliographically approved
Mao, H., Gaborit, M., Lundberg, E., Rumpler, R., Yin, B. & Göransson, P. (2022). Dynamic behaviour of low- to high-density anisotropic cellular materials. Journal of Sound and Vibration, 536, Article ID 117137.
Open this publication in new window or tab >>Dynamic behaviour of low- to high-density anisotropic cellular materials
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2022 (English)In: Journal of Sound and Vibration, ISSN 0022-460X, E-ISSN 1095-8568, Vol. 536, article id 117137Article in journal (Refereed) Published
Abstract [en]

The dynamic behaviour of a novel anisotropic cellular micro-structural geometry derived from the basic symmetric Kelvin cell is discussed for varying relative density. The cells are arranged in a cubic array and the dynamic response is studied in a classical seismic mass setup using beam elements to represent the ligaments of the cell. The eigenfrequencies and the eigenmodes of the cellular array are computed together with forced response simulations where a proportional damping model of the Young's modulus for the cell ligaments is assumed. The frequency dependence of the damping is based on a fractional derivative representation. Using a recently developed inversion method, equivalent, homogenised solid material models of the cellular array are discussed with the associated equivalent elastic properties given in terms of the 21 elastic constants of the Hooke's tensor. For the equivalent solid material models, the eigenfrequencies and eigenmodes are computed, and forced response simulations are performed assuming the same type of proportionality in the damping as the cellular array, for the same seismic mass setup. The correlation, between the eigenfrequencies and the eigenmodes, shows an overall interesting agreement between the cellular and the equivalent solid model for the quite complex deformation shapes observed. The forced response results indicate that the equivalent solid modelling accurately represents the global dynamics of the anisotropic cellular array, but needs to be further refined when local shearing deformation within the individual cells starts to be dominating.

Place, publisher, year, edition, pages
Elsevier BV, 2022
Keywords
Kelvincell, Microstructure, Low-tohigh-density, Anisotropic, Inverseestimation, Auxetic, Viscoelastic, Localshear
National Category
Medical Laboratory and Measurements Technologies
Identifiers
urn:nbn:se:kth:diva-320305 (URN)10.1016/j.jsv.2022.117137 (DOI)000861564300004 ()2-s2.0-85132929832 (Scopus ID)
Note

QC 20221024

Available from: 2022-10-24 Created: 2022-10-24 Last updated: 2022-10-24Bibliographically approved
Kleine-Wächter, L., Rumpler, R., Mao, H. & Müller, G. (2022). Numerical study of Kelvin cells for the design of periodic lattice metamaterials. In: Proceedings of ISMA 2022 - International Conference on Noise and Vibration Engineering and USD 2022 - International Conference on Uncertainty in Structural Dynamics: . Paper presented at 30th International Conference on Noise and Vibration Engineering, ISMA 2022 and 9th International Conference on Uncertainty in Structural Dynamics, USD 2022, Leuven, Belgium, Sep 12 2022 - Sep 14 2022 (pp. 2960-2974). KU Leuven, Departement Werktuigkunde
Open this publication in new window or tab >>Numerical study of Kelvin cells for the design of periodic lattice metamaterials
2022 (English)In: Proceedings of ISMA 2022 - International Conference on Noise and Vibration Engineering and USD 2022 - International Conference on Uncertainty in Structural Dynamics, KU Leuven, Departement Werktuigkunde , 2022, p. 2960-2974Conference paper, Published paper (Refereed)
Abstract [en]

Artificially-composed materials, often called metamaterials, are an increasingly considered measure for vibration control. By carefully arranging the material micro-structure, significant vibration attenuation is achievable in targeted frequency bands from resonant and wave scattering effects. An approach in designing materials for vibration control are micro-structures assembled from periodic cellular lattices. Such architectures result from the spatial repetition of cellular units that can be dynamically tuned by controlling the lattice characteristics. This contribution investigates the prospects of a three-dimensional lattice structure for application in vibration control. A unit cell design strategy is proposed based on the isometric Kelvin cell. By imposing twists on the faces of the Kelvin cell, a potential tuning mechanism for the cell's dispersive properties is introduced. Selected unit cell designs obtained from this approach are investigated in terms of the dispersion characteristics of 1D-infinite structures.

Place, publisher, year, edition, pages
KU Leuven, Departement Werktuigkunde, 2022
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-348787 (URN)2-s2.0-85195981652 (Scopus ID)
Conference
30th International Conference on Noise and Vibration Engineering, ISMA 2022 and 9th International Conference on Uncertainty in Structural Dynamics, USD 2022, Leuven, Belgium, Sep 12 2022 - Sep 14 2022
Note

QC 20240701

Part of ISBN 978-908289315-1

Available from: 2024-06-27 Created: 2024-06-27 Last updated: 2024-07-01Bibliographically approved
Lundberg, E., Mao, H., Gaborit, M., Rumpler, R., Semeniuk, B. & Göransson, P. (2022). Tuning sound transmission loss for multi-layer panels with anisotropic foams. Paper presented at ISMA 2022, International Conference on Noise and Vibration Engineering, Leuven, Belgium. , Article ID ID399.
Open this publication in new window or tab >>Tuning sound transmission loss for multi-layer panels with anisotropic foams
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2022 (English)Manuscript (preprint) (Other academic)
Abstract [en]

Multilayer panels consisting of a load carrying structure, a porous material for thermal and acoustic insulation and an interior trim panel is a very common type of design for vehicles. Weight as well as total build height are usually limiting constraints on the design. The idea of using an anisotropic porous material instead of an isotropic one to improve the sound transmission loss without adding a lot of weight or thickness is explored in the paper. By using a state space formulation of the transfer matrix method transmission loss it is possible to include anisotropic material properties in the calculation. The anisotropic material is modelled by a combination of a simplified analytical model for the acoustic losses and inverse estimation of the 21 independent elastic constants of the Hooke’s tensor. The porous material, which has typical dimensions possible to 3D print, is based on a Kelvin cell micro model that has a controlled degree of anisotropy. 

Keywords
Transmission loss, anisotropic, foam, micro-structure, analytical, open-cell
National Category
Fluid Mechanics and Acoustics Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-317065 (URN)
Conference
ISMA 2022, International Conference on Noise and Vibration Engineering, Leuven, Belgium
Funder
Vinnova, 2016-05195
Note

Proceedings will be published after the conference taking part 12th-14th September 2022. The conference paper has been submitted.

QC 20220909

Available from: 2022-09-05 Created: 2022-09-05 Last updated: 2022-10-12Bibliographically approved
Lundberg, E., Mao, H., Gaborit, M., Rumpler, R., Semeniuk, B. & Göransson, P. (2022). Tuning sound transmission loss for multi-layer panels with aniso-tropic foams. In: Proceedings of ISMA 2022 - International Conference on Noise and Vibration Engineering and USD 2022 - International Conference on Uncertainty in Structural Dynamics: . Paper presented at 30th International Conference on Noise and Vibration Engineering, ISMA 2022 and 9th International Conference on Uncertainty in Structural Dynamics, USD 2022, Leuven, Belgium, Sep 12 2022 - Sep 14 2022 (pp. 429-441). KU Leuven, Departement Werktuigkunde
Open this publication in new window or tab >>Tuning sound transmission loss for multi-layer panels with aniso-tropic foams
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2022 (English)In: Proceedings of ISMA 2022 - International Conference on Noise and Vibration Engineering and USD 2022 - International Conference on Uncertainty in Structural Dynamics, KU Leuven, Departement Werktuigkunde , 2022, p. 429-441Conference paper, Published paper (Refereed)
Abstract [en]

Multilayer panels consisting of a load carrying structure, a porous material for thermal and acoustic insulation and an interior trim panel is a very common type of design for vehicles. Weight as well as total build height are usually limiting constraints on the design. The idea of using an anisotropic porous material instead of an isotropic one to improve the sound transmission loss without adding a lot of weight or thickness is explored in the paper. By using a state space formulation of the transfer matrix method transmission loss it is possible to include anisotropic material properties in the calculation. The anisotropic material is modelled by a combination of a simplified analytical model for the acoustic losses and inverse estimation of the 21 independent elastic constants of the Hooke's tensor. The porous material, which has typical dimensions possible to 3D print, is based on a Kelvin cell micro model that has a controlled degree of anisotropy.

Place, publisher, year, edition, pages
KU Leuven, Departement Werktuigkunde, 2022
National Category
Fluid Mechanics and Acoustics Vehicle Engineering
Identifiers
urn:nbn:se:kth:diva-348785 (URN)2-s2.0-85195894747 (Scopus ID)
Conference
30th International Conference on Noise and Vibration Engineering, ISMA 2022 and 9th International Conference on Uncertainty in Structural Dynamics, USD 2022, Leuven, Belgium, Sep 12 2022 - Sep 14 2022
Note

Part of ISBN 9789082893151

QC 20240701

Available from: 2024-06-27 Created: 2024-06-27 Last updated: 2024-07-01Bibliographically approved
Mao, H., Rumpler, R. & Göransson, P. (2021). 3D tunable anisotropic metamaterial for low-frequency vibration absorption. In: Proceeding of Resource Efficient Vehicles 2021: . Paper presented at Resource Efficient Vehicles Conference 14 – 16 June 2021.
Open this publication in new window or tab >>3D tunable anisotropic metamaterial for low-frequency vibration absorption
2021 (English)In: Proceeding of Resource Efficient Vehicles 2021, 2021Conference paper, Published paper (Other academic)
Abstract [en]

In the well-known conflict between design space and performance requirements e.g. in termsof noise and vibration insulation, the emergence of new materials exhibiting exceptional insula-tion properties for a reduced weight or volume increase has received much attention in the lastdecade. Metamaterials with artificially designed architectures are increasingly considered as newfunctional materials with unusual properties. This paper presents a group of novel 3D latticemetamaterials for low-frequency vibration absorption. The novel lightweight cellular microstruc-tures for vibro-acoustic metamaterials are designed by modification of the Kelvin cell. Interestinganisotropic material properties are generated by controlling the geometries, e.g., high-stiffness,auxetic, and strong compression-torsional coupling properties. The interesting meta-propertiesenable to tune the cellular resonators of the structures at a low-frequency range. Previous researchis mostly focused on metamaterials for vibration absorption along only one or two directions. Inthis paper, wide-band high sound absorption properties of energy transfer coupling in all threedirections are achieved by tunning the frequency-dependent meta-structures in controlling the ge-ometry and material properties. Additive manufacturing technologies are used for making the 3Dcomplex tunable metamaterials.

National Category
Applied Mechanics Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-309384 (URN)
Conference
Resource Efficient Vehicles Conference 14 – 16 June 2021
Funder
Vinnova, 2016-05195),
Note

QC 20220309

Available from: 2022-03-01 Created: 2022-03-01 Last updated: 2022-06-25
Mao, H., Rumpler, R. & Göransson, P. (2021). A note on the linear deformations close to the boundaries of a cellular material. Mechanics research communications, 111, Article ID 103657.
Open this publication in new window or tab >>A note on the linear deformations close to the boundaries of a cellular material
2021 (English)In: Mechanics research communications, ISSN 0093-6413, E-ISSN 1873-3972, Vol. 111, article id 103657Article in journal (Refereed) Published
Abstract [en]

Previously reported measurements of uniaxial compression of cellular acoustic materials have shown an intriguing loss of stiffness in the regions close to the boundaries. The present contribution attempts to further investigate if these effects may be modelled by assuming a local alteration of the microstructure in these regions close to the boundaries resulting from cutting a block of material into smaller samples. Assuming that fewer struts contribute locally to the mechanical behaviour, implies a reduced equivalent porosity, or relative density, in the boundary region. The approach explored here consists in randomly removing a portion of the struts constituting the microstructure of the cells because of damage incurred in the cutting process. The analysis is performed using a linear elastic deformation behaviour at the boundary of cellular acoustic materials. For the modelling of the microstructure, the Kelvin cell geometry is chosen. Applying the assumption that struts are damaged in the process of cutting a block of material into smaller samples, as an explanation for the observed high-strain boundary regions, it is shown that the experimental observations may be qualitatively reproduced. It is also shown that the equivalent density in the boundary regions may be estimated from the ratio of the boundary compressive modulus to that of the interior region of the sample. Through the presented results, the approximation errors in compression stiffness measurements performed for a real material may be estimated. Although providing a viable explanation of the experimentally observed behaviour of the boundary regions, it should be understood that the proposed approach primarily offers a simple, accurate equivalent description of this phenomenon.

Place, publisher, year, edition, pages
Elsevier BV, 2021
Keywords
Cellular materials, Weak boundary region, Compressive modulus, Relative density, Porosity
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-292607 (URN)10.1016/j.mechrescom.2021.103657 (DOI)000624316500006 ()2-s2.0-85099372699 (Scopus ID)
Note

QC 20210409

Available from: 2021-04-09 Created: 2021-04-09 Last updated: 2022-06-25Bibliographically approved
Lundberg, E., Semeniuk, B., Mao, H., Rumpler, R. & Göransson, P. (2021). Analytical method for predicting micro-geometry based flow resistivity in anisotropic foams to improve sound absorption of vehicle panels. In: O'Reilly, Ciarán J. et al. (Ed.), Proceedings of the Resource Efficient Vehicles Conference - 2021 (rev2021): . Paper presented at Resource Efficient Vehicles Conference, 14-16 June 2021. Stockholm, Sweden
Open this publication in new window or tab >>Analytical method for predicting micro-geometry based flow resistivity in anisotropic foams to improve sound absorption of vehicle panels
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2021 (English)In: Proceedings of the Resource Efficient Vehicles Conference - 2021 (rev2021) / [ed] O'Reilly, Ciarán J. et al., Stockholm, Sweden, 2021Conference paper, Published paper (Other academic)
Abstract [en]

Vehicle structures such as train floors or car roofs are usually built as multi-layer panels, where a foam is placed between a load-carrying structure and an interior panel. The foam adds acoustical and thermal performance, but very little weight. In most contributions introducing foams for acoustic treatment, these have been considered isotropic, with acoustic losses mainly dependingon properties in the thickness direction. Another mechanism investigated here is the possibilityfor the acoustic flow in the foam to change from acting only in the thickness direction but rather to be re-directed to also travel in-plane, where dimensions are substantially larger than in the thickness direction, permitting more losses as the wave travels through the material. That kind of effect would result in higher acoustic losses without increasing the thickness of the vehicle panel and better use of the allowable space to achieve acoustic and functional requirements, i.e. a better functional density. A first step is to investigate how the absorption properties of an anisotropic foam differs from an isotropic foam. The chosen approach is to use an analytical micro-modelto calculate the dynamic drag impedance (flow resistivity on micro-scale) for an anisotropic opencell foam material. Based on a simple micro-scale geometry of Kelvin cells, it has been shown that  simple cell alterations to the micro-geometry, such as stretching, twisting and tilting results in an anisotropic foam structure. The anisotropic flow resistivity tensor is not diagonal and uniform, but different directions can have different magnitudes and it can display off-diagonal coupling terms. The influence of such micro-scale distortions on the flow resistivity, and on the resulting sound absorption is investigated with the purpose of improving the acoustic performance without adding volume. Future steps include to modify the functional density and tailor the sound transmission loss to a specific application.

Place, publisher, year, edition, pages
Stockholm, Sweden: , 2021
Keywords
sound absorption, Vehicle, anisotropic, foam, micro-geometry, resource efficient
National Category
Mechanical Engineering Vehicle Engineering
Research subject
Vehicle and Maritime Engineering
Identifiers
urn:nbn:se:kth:diva-309380 (URN)
Conference
Resource Efficient Vehicles Conference, 14-16 June 2021
Funder
Vinnova, 2016-05195
Note

QC 20220315

Available from: 2022-03-01 Created: 2022-03-01 Last updated: 2022-06-25Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0001-9980-0144

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