TY - JOUR
T1 - Non-linear coupled transverse and axial vibration of a compliant structure, Part 1
T2 - formulation and free vibration
AU - Han, S. M.
AU - Benaroya, H.
N1 - Funding Information: This work is supported by the O$ce of Naval Research Grant No. N00014-97-1-0017. We would like to thank our program manager Dr Thomas Swean for his interest and "nancial support. The authors also are pleased to acknowledge the continued collaboration with our colleague, Professor Timothy Wei.
PY - 2000/11/9
Y1 - 2000/11/9
N2 - A compliant tower in the ocean environment is modelled as a beam undergoing coupled transverse and axial motion. The equations of motion are non-linear and coupled and are derived here. The beam is assumed to be supported by a linear-elastic torsional spring at one end and with a point mass at the other end. Such a model is representative of numerous applications. The equations of motion and boundary conditions are obtained using Hamilton's variational principle. It is assumed that strains are small but the rotation is moderate compared to the strain so that the equations of motion for the axial and transverse motion are non-linearly coupled. The free response in vacua and the free response in water are considered in particular. The fluid forces, the added mass and drag forces, are modelled using a semi-empirical Morison equation. The resulting non-linear coupled partial differential equations are solved numerically using the finite difference approach. In Part 2 of this work, various forced responses are studied.
AB - A compliant tower in the ocean environment is modelled as a beam undergoing coupled transverse and axial motion. The equations of motion are non-linear and coupled and are derived here. The beam is assumed to be supported by a linear-elastic torsional spring at one end and with a point mass at the other end. Such a model is representative of numerous applications. The equations of motion and boundary conditions are obtained using Hamilton's variational principle. It is assumed that strains are small but the rotation is moderate compared to the strain so that the equations of motion for the axial and transverse motion are non-linearly coupled. The free response in vacua and the free response in water are considered in particular. The fluid forces, the added mass and drag forces, are modelled using a semi-empirical Morison equation. The resulting non-linear coupled partial differential equations are solved numerically using the finite difference approach. In Part 2 of this work, various forced responses are studied.
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U2 - https://doi.org/10.1006/jsvi.2000.3147
DO - https://doi.org/10.1006/jsvi.2000.3147
M3 - Article
SN - 0022-460X
VL - 237
SP - 837
EP - 873
JO - Journal of Sound and Vibration
JF - Journal of Sound and Vibration
IS - 5
ER -