Here we consider the ro le of rotational inertia in the process of phase t ransition in a one-dimensional flexural system\, t hat may represent a simplified model of the \; failure of a bridge exposed to hazardous vibratio ns. The phase transition process is assumed to occ ur with a uniform speed that is driven by feeding waves carrying energy produced by an applied oscil lating moment and force. We show that the problem can be reduced to a functional equation via the Fo urier transform which is solved using the Wiener-H opf technique. From the solution we identify the d ynamic behaviour of the system during the transiti on process. The minimum energy required to initiat e the phase transition process with a given speed is determined and it is shown there exist paramete r domains defined by the force and moment amplitud es where the phase transition can occur. The influ ence of the rotational inertia of the system on th e wave radiation phenomenon connected with the pha se transition is also discussed. All results are s upplied with numerical illustrations confirming th e analytical predictions.

Acknowledgement : M.J.N. and M.B. gratefully acknowledge the suppo rt of the EU H2020 grant MSCA-IF-2016-747334-CAT-F FLAP.

References

[1] Slepyan\, L.I.: Models and Phenomena in Fracture Mechanics\, Found ations of Engineering Mechanics\, Springer\, (2002 ).

[2] Brun\, M.\, Movchan\, A.B. and Slepyan\ , L.I.: Transition wave in a supported heavy beam\ , J. Mech. Phys. Solids 61\, no. 10\, pages 2067&n dash\;2085\, (2013).

[3] Brun\, M.\, Giaccu\, G.F.\, Movchan\, A.\, B.\, and Slepyan\, L. I.. Tr ansition wave in the collapse of the San Saba Brid ge. Front. Mater. 1:12\, (2014). doi: 10.3389/fmat s.2014.00012.

[4] Nieves\, M.J.\, Mishuris\, G .S.\, Slepyan\, L.I.: Analysis of dynamic damage p ropagation in discrete beam structures\, Int. J. S olids Struct. 97-98\, pages 699&ndash\;713\, (2016 ).

[5] Garau\, M.\, Nieves\, M.J. and Jones\, I.S. (2019): Alternating strain regimes for failur e propagation in flexural systems\, Q. J. Mech. Ap pl. Math.\, hbz008\, https://eur02.safelinks.protection.outlook. com/?url=https%3A%2F%2Fdoi.org%2F10.1093%2Fqjmam%2 Fhbz008&\;data=02%7C01%7C%7Cca24c94f14fb47b2a98 908d6f19a9002%7Cd47b090e3f5a4ca084d09f89d269f175%7 C0%7C0%7C636962043472937444&\;sdata=hFcD7qiLBQw eKalUwfiI8DE4OoKVDBet7AwngVFgEf0%3D&\;reserved= 0. LOCATION:Seminar Room 1\, Newton Institute CONTACT:info@newton.ac.uk END:VEVENT END:VCALENDAR