journal article·2026-02-11Open access

Tunable Cellular Structures with Damping for Industry-Ready Dynamic Load Management in Bus Applications

Tiago Cunha, Nuno A. T. C. Fernandes, Delfim Soares, Óscar Carvalho

Applied Sciences· Volume 16· Issue 4

Abstract

Sustainable mobility has been an emerging topic in recent years, and in this regard, investing heavily in public transport seems to be the best solution. For people to embrace this form of mobility, services must meet expectations, and one of the parameters to be considered is the comfort offered by vehicles. This is directly affected by the vibrations that affect vehicles. This work was developed to create a proof of concept for a support structure for bus seats that mitigates the vibrations felt by passengers, making these vehicles more comfortable and appealing to use. Current systems are expensive and complex, and the proposed solution presented here is based on the field of metamaterials. This study investigated vehicle dynamic loads and comfort standards from ISO 2631 to design a metamaterial-based seat support with optimized stiffness and damping. Using MATLAB (R2024b), ideal parameters were defined (k = 13,422.66 N/m, c = 534.07 Ns/m), with stiffness provided by the cell geometry and damping provided by a viscoelastic material. Parametric modeling and simulations in ANSYS (2025 R2) assessed stiffness, damping, and strength, followed by prototype fabrication and testing. The best structure showed 2.23 m/s2 at 4.5 Hz, achieving the target transmissibility above 8 Hz. While most designs effectively attenuate vibrations beyond 5 Hz, resonance peaks remain high, suggesting future work should focus on improved resonance reduction strategies.
Source: crossref · Quality: baseline

Research context

OpenAlex topics: Cellular and Composite Structures · Vibration Control and Rheological Fluids · Vehicle Noise and Vibration Control

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Mechanical Engineering, University of Minho, 4800-058 Guimarães, Portugal

Center for Microelectromechanical Systems (CMEMS), University of Minho, 4800-058 Guimarães, Portugal

Associate Laboratory in Biotechnology and Bioengineering and Microelectromechanical Systems (LABBELS), University of Minho, 4800-058 Guimarães, Portugal

Funding

Ministério da Ciência, Tecnologia e Ensino Superior, FCT, Portugal · individual PhD · LABBELS–Associate Laboratory in Biotechnology, Bioengineering and Microelectromechanical Systems · BrainStimMap—Mapping and modeling the transmission profile of optomechanical waves in the brain to optimize transcranial stimulation against brain disorders

References (81)

Show source-provided references
1. (2025, October 30). Directorate-General for Communication Transport and Tourism. Available online: https://commission.europa.eu/topics/transport-and-tourism_en.
2. de Portugal, G. (2024). Governo Anuncia 240 Milhões de Euros de Financiamento Para Transportes Públicos 2024, XXV Governo Constitucional de Portugal.
3. de Portugal, G. (2023). Sustentável 2030: Programa Temático Para a Ação Climática e Sustentabilidade.
4. de Portugal, G. (2020). Plano Nacional de Investimentos 2030.
5. Comission, E. (2007). Green Paper: Towards a New Culture of Urban Mobility, European Commission.
6. Agência Europeia do (2022). Transport and Environment Report 2021: Decarbonising Road Transport—The Role of Vehicles, Fuels and Transport Demand, Agência Europeia do Ambiente.
7. Determinants of Customer Satisfaction and Loyalty in Public Transport: A PLS-SEM Approach10.25115/eea.v39i8.4507 ↗
8. Passengers Comfort Perception and Demands on Railway Vehicles: A Review
9. Interference in Writing Performance under Whole-Body Vibration Exposure Together with Subject Posture10.1504/IJVNV.2016.079055 ↗
10. Effects of Vibration on Sedentary Activities in Passenger Trains10.1260/026309207781487448 ↗
11. A Python FDTD Method Algorithm for 1D Planar Acoustic Wave Propagation: Simulating High-Frequency Ultrasound in the Brain and Beyond10.1007/978-3-032-13225-3_39 ↗
12. Sharma, S., Fernandes, N.A.T.C., and Carvalho, Ó. (2025). A Frequency-Dependent and Nonlinear, Time-Explicit Five-Layer Human Head Numerical Model for Realistic Estimation of Focused Acoustic Transmission Through the Human Skull for Noninvasive High-Intensity and High-Frequency Transcranial Ultrasound Stimulation: An Application to Neurological and Psychiatric Disorders. Bioengineering, 12.10.3390/bioengineering12111161 ↗
13. Fernandes, N.A.T.C., Alves, D.I., Ferreira, D.P., Monteiro, M., Arieira, A., Silva, F., Hinckel, B., Leal, A., and Carvalho, Ó. (2025). Sustainable Tunable Anisotropic Ultrasound Medical Phantoms for Skin, Skeletal Muscle, and Other Fibrous Biological Tissues Using Natural Fibers and a Bio-Elastomeric Matrix. J. Compos. Sci., 9.10.3390/jcs9070370 ↗
14. Santos, A.Z., Rocha, S., Fernandes, N.A.T.C., Alves, D.I., Ferreira, D.P., Costa, S.M., Padrão, J., and Carvalho, Ó. (2026). Sustainable Shear Wave Elastography Medical Phantoms: Waste-Based Fibrous Structures for Medical Applications. Textiles, 6.10.3390/textiles6010006 ↗
15. Current State of Elastography Research in Multiple Anatomical Structures and Respective Phantoms10.1016/j.ejmp.2025.105192 ↗
16. Fernandes, N.A.T.C., Sharma, S., Arieira, A., Hinckel, B., Silva, F., Leal, A., and Carvalho, Ó. (2025). Experimental Validation of Time-Explicit Ultrasound Propagation Models with Sound Diffusivity or Viscous Attenuation in Biological Tissues Using COMSOL Multiphysics. Bioengineering, 12.10.3390/bioengineering12090946 ↗
17. The Effect That Lower Limb Orthoses Have on Cartilage on Patients with Knee Osteoarthritis: A Narrative Review10.1097/PXR.0000000000000128 ↗
18. European Commission (2008). Directorate-General for Employment, Social Affaires and Equal Opportunities Non-Binding Guide to Good Practice with a View to Implementation of Directive 2002/44/EC on the Minimum Health and Safety Requirements Regarding the Exposure of Workers to the Risks Arising from Physical Agents (Vibrations), Publications Office.
19. (1997). Mechanical Vibration and Shock—Evaluation of Human Exposure to Whole-Body Vibration (Standard No. ISO 2631).
20. Análise de Níveis de Vibração Em Usuários de Trens Urbanos
21. Zhao, Y., and Wang, X. (2019). A Review of Low-Frequency Active Vibration Control of Seat Suspension Systems. Appl. Sci., 9.10.3390/app9163326 ↗
22. Health Effects Associated with Occupational Exposure to Hand-Arm or Whole Body Vibration10.1080/10937404.2018.1557576 ↗
23. Additive Manufacturing of Composite Foam Metamaterial Springs for Vibration Isolation10.1002/adem.202300356 ↗
24. A Combined Review of Vibration Control Strategies for High-Speed Trains and Railway Infrastructures: Challenges and Solutions10.1177/14613484221128682 ↗
25. The Evolution of Vehicle Pneumatic Vibration Isolation: A Systematic Review
26. Comparison of Whole-Body Vibration Exposures When Operating a City Bus with an Active, Passive and Static Suspension Bus Seat10.1177/1071181319631472 ↗
27. Papaioannou, G., Sekulic, D., Velenis, E., and Antoniadis, I. (2021). Investigation of Seat Suspensions with Embedded Negative Stiffness Elements for Isolating Bus Users’ Whole-Body Vibrations, SAE International.10.4271/2021-01-5019 ↗
28. Phase Deviation of Semi-Active Suspension Control and Its Compensation with Inertial Suspension10.1007/s10409-023-23367-x ↗
29. Suresh Kumar, N., Naidu, K.C.B., Banerjee, P., Anil Babu, T., and Venkata Shiva Reddy, B. (2021). A Review on Metamaterials for Device Applications. Crystals, 11.10.3390/cryst11050518 ↗
30. Additive Manufacturing of Metamaterials: A Review
31. Metamaterials: A Comprehensive Review of Design and Applications10.29294/IJASE.11.1.2024.3816-3835 ↗
32. Wang, H., Lyu, Y., Bosiakov, S., Zhu, H., and Ren, Y. (2023). A Review on the Mechanical Metamaterials and Their Applications in the Field of Biomedical Engineering. Front. Mater., 10.10.3389/fmats.2023.1273961 ↗
33. Progress in Auxetic Mechanical Metamaterials: Structures, Characteristics, Manufacturing Methods, and Applications10.1002/adem.202000312 ↗
34. Mechanical Metamaterials Associated with Stiffness, Rigidity and Compressibility: A Brief Review10.1016/j.pmatsci.2017.12.003 ↗
35. A Review on Application of Mechanical Metamaterials for Vibration Control10.1080/15376494.2021.1892244 ↗
36. 3D-Printed Micro/Nano-Scaled Mechanical Metamaterials: Fundamentals, Technologies, Progress, Applications, and Challenges10.1002/smll.202206391 ↗
37. Bashmal, S., Nazir, A., Khan, S., and Alofi, A. (2025). Damping Optimization and Energy Absorption of Mechanical Metamaterials for Enhanced Vibration Control Applications: A Critical Review. Polymers, 17.10.3390/polym17020237 ↗
38. Advances in Mechanical Metamaterials for Vibration Isolation: A Review10.1177/16878132221082872 ↗
39. Mastering the Art of Designing Mechanical Metamaterials with Quasi-Zero Stiffness for Passive Vibration Isolation: A Review10.1088/1361-665X/ad5bcc ↗
40. Rao, S. (2017). Mechanical Vibrations, Pearson. [6th ed.].
41. Analysis and Optimization of Damping Properties of Constrained Layer Damping Structures with Multilayers10.1155/2021/6740696 ↗
42. Recent Applications of Viscoelastic Damping for Noise Control in Automobiles and Commercial Airplanes10.1016/S0022-460X(03)00106-8 ↗
43. Constrained Layer Damper Modelling and Performance Evaluation for Eliminating Squeal Noise in Trams
44. Development of a Single-Layer Finite Element and a Simplified Finite Element Modeling Approach for Constrained Layer Damped Structures10.1016/j.finel.2009.03.001 ↗
45. Viscoelastic Materials for Structural Dampers: A Review10.1016/j.conbuildmat.2022.127955 ↗
46. Zhou, J., Yang, Z., Feng, X., and Zhao, X. (2021, January 5). Dynamic Viscoelastic Analysis and Experiment of an Aerospace Silicone Rubber Damper Based on DMA Test. Proceedings of the 2021 the 5th International Conference on Robotics, Control and Automation, Seoul, Republic of Korea.10.1145/3471985.3472374 ↗
47. Prony Series Calculation for Viscoelastic Behavior Modeling of Structural Adhesives from DMA Data
48. (2019). Plastics—Determination of Dynamic Mechanical Properties—Part 1: General Principles (Standard No. ISO 6721-1).
49. Gallimore, C. (2008). Passive Viscoelastic Constrained Layer Damping Application for a Small Aircraft Landing Gear System. [Master’s Thesis, Virginia Polytechnic Institute and State University].
50. Ibrulj, J., Dzaferovic, E., Obucina, M., and Kuzman, M.K. (2021). Numerical and Experimental Investigations of Polymer Viscoelastic Materials Obtained by 3D Printing. Polymers, 13.10.3390/polym13193276 ↗
51. Melo, R.M. (2006). Exposição Ocupacional a Vibrações Transmitidas Ao Corpo Inteiro: Factores Condicionantes Na Condução de Autocarros Urbanos, Universidade Técnica de Lisboa, Faculdade de Motricidade Humana.
52. Effect of Seating on Exposures to Whole-Body Vibration in Vehicles10.1006/jsvi.2001.4257 ↗
53. Evaluation of Whole-Body Vibration in Vehicles10.1006/jsvi.2001.4256 ↗
54. Design of Half-Car Active Suspension System for Passenger Riding Comfort10.1088/1742-6596/1075/1/012030 ↗
55. Establishing Inspection Criteria to Verify the Dynamic Behaviour of the Vehicle Suspension System by a Platform Vibrating Test Bench10.1504/IJVD.2005.007623 ↗
56. Analysis of Bus Passenger Comfort Perception Based on Passenger Load Factor and In-Vehicle Time10.1186/s40064-016-1694-7 ↗
57. Study on the Influence of Bus Suspension Parameters on Ride Comfort10.21595/vp.2018.20271 ↗
58. Sun, R., Wang, J., and Liu, Y. (2023). Dynamic Analysis and Seat Selection of Bus Driving Comfort under Different Road Conditions. Appl. Sci., 13.10.3390/app13074639 ↗
59. Optimizing 3D Printing Process Parameters for the Tensile Strength of Thermoplastic Polyurethane Plastic10.1007/s11665-023-07892-8 ↗
60. Orthotropic Mechanical Properties of PLA Materials Fabricated by Fused Deposition Modeling10.1016/j.tws.2024.111800 ↗
61. Failure Analysis of Acrylonitrile Butadiene Styrene (ABS) Materials and Damage Modeling by Fracture
62. Dimic, A., Mišković, Ž., Jelovac, D., and Mitrović, R. (2016, January 21–23). Application of Rapid Prototyping in Maxillofacial Surgery. Proceedings of the Recent Advances in Medicine and Health Sciences (RAMHS 2016), Dubai, United Arab Emirates.
63. Mechanical Properties of 3D Printed Polymers
64. Performance of Multilayer Constrained Layer Damping Structures: A Comprehensive Study Using RKU, FEM, and Experimental Approaches10.1007/s42417-024-01538-2 ↗
65. Zhang, J., Zhou, W., Cao, D., and Zhang, J. (2023). A Study on the Genetic Algorithm Optimization of an Asphalt Mixture’s Viscoelastic Parameters Based on a Wheel Tracking Test. Infrastructures, 8.10.3390/infrastructures8120169 ↗
66. Dynamic Mechanical Analysis of Epoxy Composites: Master Curve Construction and Prony Series Fitting to Investigate Filler Shape Effects on Viscoelastic Properties10.1007/s42247-024-00992-8 ↗
67. Ferry, J.D. (1980). Viscoelastic Properties of Polymers, John Wiley & Sons. [3rd ed.].
68. (2015). Standard Test Method for Glass Transition Temperature (DMA Tg) of Polymer Matrix Composites by Dynamic Mechanical Analysis (DMA) (Standard No. ASTM D7028-07).
69. Apparent Mass and Seat-to-Head Transmissibility Responses of Seated Occupants under Single and Dual Axis Horizontal Vibration10.2486/indhealth.MSWBVI-15 ↗
70. Yan, L., and Gong, X. (2017). Experimental Study of Vibration Isolation Characteristics of a Geometric Anti-Spring Isolator. Appl. Sci., 7.10.3390/app7070711 ↗
71. Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook10.1115/1.4026911 ↗
72. Design and Optimization of Three-Resonator Locally Resonant Metamaterial for Impact Force Mitigation10.1088/1361-665X/aad479 ↗
73. A Brief Review of Metamaterials for Opening Low-Frequency Band Gaps10.1007/s10483-022-2870-9 ↗
74. Locally Resonant Sonic Materials10.1126/science.289.5485.1734 ↗
75. Ultralight, Ultrastiff Mechanical Metamaterials10.1126/science.1252291 ↗
76. Mechanical Properties and Failure Behaviour of Architected Alumina Microlattices Fabricated by Stereolithography 3D Printing10.1016/j.ijmecsci.2021.106285 ↗
77. Ma, T., Li, T., Jing, G., Liu, H., and Bi, F. (2022). Development of a Novel Seat Suspension Based on the Cubic Stewart Parallel Mechanism and Magnetorheological Fluid Damper. Appl. Sci., 12.10.3390/app122211437 ↗
78. Knap, L., Makowski, M., Siczek, K., Kubiak, P., and Mrowicki, A. (2023). Hydraulic Vehicle Damper Controlled by Piezoelectric Valve. Sensors, 23.10.3390/s23042007 ↗
79. Heidarian, A., and Wang, X. (2019). Review on Seat Suspension System Technology Development. Appl. Sci., 9.10.3390/app9142834 ↗
80. (2026, January 08). Zetarmold Moldagem Por Injeção: Como Calcular o Tempo de Ciclo 2024. Available online: https://hitopindustrial.com/pt/calcular-tempo-de-ciclo-em-moldagem-por-injecao/.
81. A Review on Machine Learning Models in Injection Molding Machines10.1155/2022/1949061 ↗