{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T16:18:19Z","timestamp":1771258699834,"version":"3.50.1"},"reference-count":13,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2018,6,27]],"date-time":"2018-06-27T00:00:00Z","timestamp":1530057600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/EMS\/00481\/2013-FCT"],"award-info":[{"award-number":["UID\/EMS\/00481\/2013-FCT"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"FEDER-Centro 2020","award":["CENTRO-01-0145-FEDER-022083"],"award-info":[{"award-number":["CENTRO-01-0145-FEDER-022083"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>This paper describes a numerical solution to characterize the deformation of a bellows-type air spring for automotive suspensions. In a first step, the shell structure is modeled as a practically inextensible membrane that has virtually no bending stiffness; the structure has only a pneumatic-elastic deformation due to the compressibility of the pressurized air. In a second step, a finite element modeling of the device using a commercial code is carried out in order to validate the first model. Complementing this work, an experimental procedure based on a pseudo-dynamic technique was implemented to simulate the behavior of the pneumatic suspension bellows subjected to dynamic loads. The method consists of a combined numeric\/experimental procedure simulating a suddenly applied load.<\/jats:p>","DOI":"10.3390\/app8071049","type":"journal-article","created":{"date-parts":[[2018,6,27]],"date-time":"2018-06-27T11:02:05Z","timestamp":1530097325000},"page":"1049","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["The Simulation of an Automotive Air Spring Suspension Using a Pseudo-Dynamic Procedure"],"prefix":"10.3390","volume":"8","author":[{"given":"Francisco J. M. Q.","family":"De Melo","sequence":"first","affiliation":[{"name":"Centre for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8342-5116","authenticated-orcid":false,"given":"Ant\u00f3nio B.","family":"Pereira","sequence":"additional","affiliation":[{"name":"Centre for Mechanical Technology and Automation, Department of Mechanical Engineering, University of Aveiro, 3810-193 Aveiro, Portugal"}]},{"given":"Alfredo B.","family":"Morais","sequence":"additional","affiliation":[{"name":"Aveiro Research Centre of Risks and Sustainability in Construction, University of Aveiro, 3810-193 Aveiro, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2018,6,27]]},"reference":[{"key":"ref_1","unstructured":"Humphreys, W. (1901). Pneumatic Spring for Vehicles. (673,682), U.S. Patent."},{"key":"ref_2","first-page":"75","article-title":"Air Suspension for Road Vehicles","volume":"11","author":"Sainsbury","year":"1957","journal-title":"Proc. Inst. Mech. Eng. Automob. Div."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1076\/vesd.35.6.443.2040","article-title":"Air Suspension Dimensionless Analysis and Design Procedure","volume":"35","author":"Quaglia","year":"2010","journal-title":"Veh. Syst. Dyn."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1515\/ijame-2015-0009","article-title":"The Dynamic Characteristic and Hysteresis Effect of an Air Spring","volume":"20","author":"Welsch","year":"2015","journal-title":"Int. J. Appl. Mech. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Huang, H., Chen, R., and He, M. (2015, January 25\u201326). Studies on Modeling a Single-Bellows Air Spring and Simulating its Inherent Characteristics. Proceedings of the 5th International Conference on Information Engineering for Mechanics and Materials, Huhhot, China.","DOI":"10.2991\/icimm-15.2015.284"},{"key":"ref_6","unstructured":"Apostol, M. (1969). Calculus Volume II, John Wiley & Sons. [2nd ed.]."},{"key":"ref_7","unstructured":"Ugural, A. (1999). Stresses in Plates and Shells, McGraw-Hill Co.. [2nd ed.]."},{"key":"ref_8","unstructured":"Reddy, J. (2004). An Introduction to Non-Linear Finite Element Analysis, Oxford University Press. [2nd ed.]."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1061\/JMCEA3.0000098","article-title":"A method of computation for structural dynamics","volume":"85","author":"Newmark","year":"1959","journal-title":"ASCE J. Eng. Mech. Div."},{"key":"ref_10","unstructured":"Pinto, A., Verzeletti, G., Molina, J., Varum, H., Pinho, R., and Coelho, E. (2002). Pseudo-Dynamic Tests of Non-Seismic Resisting RC Frames (Bare and Selective Retrofit Frames), Joint Research Centre. JRC-EUR 20244 EN Report."},{"key":"ref_11","first-page":"1125","article-title":"Pseudo-dynamic testing of bridges using non-linear substructuring, Earthquake Engineering Structural Dynamics","volume":"33","author":"Pinto","year":"2004","journal-title":"J. Int. Assoc. Earthq. Eng."},{"key":"ref_12","first-page":"337","article-title":"Pseudo-Dynamic Method for Structural Analysis of Automobile Seats","volume":"219","author":"Carneiro","year":"2005","journal-title":"Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Malmedahl, G. (2005). Analysis of Automotive Damper Data and Design of a Portable Measurement System. [Bachelor\u2019s Thesis, Department of Mechanical Engineering, Center for Automotive Research, The Ohio State University].","DOI":"10.4271\/2005-01-1043"}],"container-title":["Applied Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2076-3417\/8\/7\/1049\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:10:25Z","timestamp":1760195425000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2076-3417\/8\/7\/1049"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,27]]},"references-count":13,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2018,7]]}},"alternative-id":["app8071049"],"URL":"https:\/\/doi.org\/10.3390\/app8071049","relation":{},"ISSN":["2076-3417"],"issn-type":[{"value":"2076-3417","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6,27]]}}}