{"data":{"id":"10.17862/cranfield.rd.4288874.v2","type":"dois","attributes":{"doi":"10.17862/cranfield.rd.4288874.v2","prefix":"10.17862","suffix":"cranfield.rd.4288874.v2","identifiers":[],"alternateIdentifiers":[],"creators":[{"name":"Cooper, Samson","nameType":"Personal","givenName":"Samson","familyName":"Cooper","affiliation":[],"nameIdentifiers":[]}],"titles":[{"title":"Nonlinear vibration analysis of a complex aerospace structure"}],"publisher":"Cranfield University","container":{},"publicationYear":2016,"subjects":[{"subject":"90101 Aerodynamics (excl. Hypersonic Aerodynamics)","subjectScheme":"FOR"},{"subject":"FOS: Mechanical engineering","schemeUri":"http://www.oecd.org/science/inno/38235147.pdf","subjectScheme":"Fields of Science and Technology (FOS)"}],"contributors":[],"dates":[{"date":"2016-12-08","dateType":"Created"},{"date":"2016-12-08","dateType":"Updated"},{"date":"2016","dateType":"Issued"}],"language":null,"types":{"ris":"GEN","bibtex":"misc","citeproc":"article","schemaOrg":"Collection","resourceType":"Fileset","resourceTypeGeneral":"Collection"},"relatedIdentifiers":[{"relationType":"IsIdenticalTo","relatedIdentifier":"10.17862/cranfield.rd.4288874","relatedIdentifierType":"DOI"}],"relatedItems":[],"sizes":["10185999 Bytes"],"formats":[],"version":null,"rightsList":[{"rights":"CC BY-NC","rightsUri":"https://creativecommons.org/licenses/by-nc/4.0"}],"descriptions":[{"description":"Technical paper presented at the 2016 Defence and Security Doctoral Symposium.\u003cbr\u003eComplex\nshaped aerodynamic structures such as deployable missiles are prone to exhibit\nsome level of nonlinear phenomena due to their aerodynamic tailored design and\napplication. Aside from the aeroelastic control challenges experienced by a\nmissile, a fundamental challenge encountered by a deployable missile is the\ninevitable concentrated structural nonlinearities which are observed around the\nhinge of its fins. Due to the current design and manufacturing process, the\nhinge of the fin of a missile often consist of complex configurations, such as\njoints, friction and other nonlinear features which may lead to concentrated\nstructural nonlinearities. Some of the nonlinearities encountered includes\npiecewise linearity, bilinear nonlinearity, hysteresis, coulomb friction and\nnonlinear damping mechanisms. These nonlinearities are frequently triggered at\nlarge vibration amplitudes, caused by high pressure loads during operational\nflight. Activation of these nonlinearities often affect the dynamic response of\nthe missile and in some cases lead to structural failures in the major\ncomponents of the air vehicle. In this context, identifying and predicting the\nvibration response of such aerodynamic structures with nonlinearities, may be\nof great advantage to the present structural dynamic community. \n\nIn this paper, the nonlinear\ndynamic behaviour of a B61 prototype missile has been examined. A two-step\nmethodology for integrating nonlinear system identification for estimating\nnonlinear stiffness and damping mechanism and nonlinear finite element\nmodelling has been adopted in this investigation. The first step made use of\nacquired input and output data from random and sine sweep vibration test to\nderive a nonlinear experimental model for the missile, where the nonlinear\nexperimental model was developed using a white box identification process,\nnamely (detection, characterisation and parameter estimation). The second step\nimplements the parameters of the identified nonlinear system into a finite\nelement model (FEM) of the missile to develop a nonlinear FEM. The nonlinear\ndynamic response of the FEM was computed using the Harmonic balance method (HB)\nand pseudo-arclength continuation in the frequency domain. In addition, Force\ncontrolled stepped sine experiments at several excitation levels were conducted\nto validate the numerical solution obtained from the nonlinear FEM computation.\nThe results obtained were used to understand the amplitude dependant behaviour\nof the missile under a vibration controlled environment and in addition predict\nthe dynamic response of the missile in the existence of deployable hinge\nnonlinearity.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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