This study presents the application of vibration analysis in the determination of elastic constants (i.e. Young’s modulus in fiber direction, transverse Young’s modulus, and shear modulus) and modal damping ratios of a unidirectional composite beam. The frequency domain approach is used for the estimation of material constants, whereas modal damping ratios are predicted by the use of short-time Fourier transform (STFT). An analytical expression of the STFT for the free vibration response of a viscously damped system has been derived using the Hanning window. Analysis of a simulated vibration for a three-degree-of-freedom system has revealed that the STFT is capable of predicting the modal damping ratios accurately even when they are considerably large. For the experimental assessment of modal damping values of a composite beam, longitudinal, flexural, and torsional vibration responses are analyzed by both the STFT and well-known Q-factor approximation, and the obtained results show very good agreement.
The general three-dimensional linearized dynamic equations of a compliant riser, idealized as a rotationally nonuniform rod, around a nonlinear static configuration in the presence of general current and monochromatic wave excitation are formulated. Nonlinear forces such as quadratic drag are harmonically linearized by minimizing the mean square error between the linear approximation and the nonlinear force. The theory is implemented in a computer program which allows analysis of a variety of compliant riser configurations. Numerical examples for catenary risers are included. Comparisons of our theoretical predictions with experimental results obtained from a 1.5-m catenary compliant riser model excited monochromatically at the top parallel to a constant current are also presented to evaluate our ability to predict the response of compliant riser systems.
The objective of this paper is first to formulate the three-dimensional dynamic equations of a compliant riser, idealized as a rotationally nonuniform rod, around a nonlinear static configuration with linearized restoring force and inertial components in the presence of general current and monochromatic wave excitation. Next, to harmonically linearize nonlinear forces such as quadratic drag for the general three-dimensional problem by minimizing the mean square error between the linear approximation and the nonlinear force. Finally, to present an efficient numerical solution method appropriate for nonlinear boundary-value problems with sharp boundary layers such as the problem at hand. Numerical examples and comparisons with time-domain solutions for a catenary riser with a three-dimensional configuration and a steep-wave riser are included. Comparisons of our theoretical predictions with experimental results obtained from a small-scale riser model are also summarized to evaluate our theoretical ability to predict the response of compliant riser systems.
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