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A set of micro electro mechanical system (MEMS) ac-celerometer [17] is used to obtain the natural frequency and damp-ing during the free vibration testing. The tests were carried out inthe following procedures.(1) Before the cyclic loading is applied, a small amplitude freevibration test is performed, and the response signal is recordedin the time domain by accelerometers to obtain the initial naturalfrequency of the system.(2) The model turbine is then subjected to cyclic loading for achosen time of interval (typically 5000 cycles) with a certain level of frequency and amplitude. The dynamic property is then evalu-ated at the end of the chosen number of cycles through another freevibration test. This operation is repeated until sufficient number ofcycles was reached and a trend is established.(3) Another set of test under different cyclic loading is con-ducted by adjusting m1 and m2 in the gear system and the outputvoltage.Four groups of tests are performed on the 1:100 scaled windturbine model, aiming to study the long-term dynamic behaviorof monopile supported model in sand. The investigation focuseson the influence from the amplitude of cyclic loads. Bhattacharyaet al. [14] showed that the ratio of forcing frequency to natural fre-quency (ff/fn) is close to 1 in field, so the dynamic effects from theexciting loads is also considered by setting ff/fn as 1.302. It is sub-jected up to 196,515 cycles, and the innovative cyclic loading de-vice is used to apply one directional single frequency cyclic loadson themodel turbine, butwith different forcing amplitudes, corre-sponding to different non-dimensional P/GD2and M/GD3, whereP is lateral load in the foundation, M is the mudline bending mo-ment, G is the shear modulus of the soil, and D is the pile diame-ter. Lombardi et al. [1] showed that P/GD2and M/GD3representsthe shear strain in the soil around the pile. Throughout the tests,m1 = m2 is maintained, detailed information about all of the testsis given in Table 3.Test results and interpretation Figure 6(a) shows a typicaltime domain acceleration signal recorded by the accelerometerduring the free vibration test. Assessment of the model turbine’snatural frequency is performed in the frequency domain using theWelch method [19], and the result is given in Fig. 6(b). The firsttwo peaks in Fig. 6(b) correspond to the first two orders of naturalfrequency of the model structure.Changes of the 1st natural frequency (fn/fn-initial) of the systemwith respect to the number of cycles (N) in tests MST-1 to MST-4 are shown in Fig. 7(a).
It can be clearly seen that, in test MST-1, the structure’s natural frequency is almost around its initialvalue throughout the test; while in tests MST-2 to MST-4, theoverall trend of the change in natural frequency follows a similarnonlinear relationship, first increasing with a reduced rate, and L.-Q. Yu et al. / Theoretical and Appliethen stabilizing and later decreasing. The maximum increment ofthe system’s 1st natural frequency is around 4%–10% compared toits initial value. It can also be noted from Fig. 7(a), the amplitudeof the natural frequency’s increment increases with the increaseof the amplitude of cyclic load. High values of soil strain level(i.e., P/GD2) will lead to high increment of natural frequency.Taking into account the medium dense state sand used in thetest, with the decrease of soil void ratio under cyclic loading, thesand will get densified, and will lead to an increase in the foun-dation stiffness, which ultimately contribute to the increase ofstructure’s natural frequency. While the decrease of the system’snatural frequency during the late period could be attributed to thesand particles’ migration and loss mechanism, further details onthis aspect can be found in Ref. [13]. It is interesting to note that theresults from the resonant column test given in Fig. 7(b) [18] couldbe used to explain themodel test results. It can be clearly seen fromFig. 7(b), when the soil strain level is low (i.e., γc = 1.6 × 10−4),change of its shear modulus with respect to the number of cyclesis negligible. In contrast, when the soil strain reaches a high level(i.e., γc = 6 × 10−4), the soil’s shear modulus grows with the in-crease of cycles. This phenomenon matches well with the modeltest results as observed in Fig. 7(a): high values of soil strain level(i.e., P/GD2) will lead to high increment of natural frequency.Conclusions In this paper, a simple, economic, and innovativedevice has been adopted to apply cyclic loads. The natural fre-quency of the model turbine supported on pile in sand, is foundto increase with the load cycles, after reaching a certain number ofcycles, it tends to stabilize and then decreasewithmore load cycles.Higher level of the amplitude of cyclic loading will lead to higheramplitude of natural frequency’s increment. Increase of the modelstructure’s natural frequency is attributed to the densification ofthe surrounding soil under cyclic loading, while the soil particles’migration and lossmechanismwill lead to the decrease of the sys-tem’s natural frequency. Therefore, the natural frequency of OWTis recommended to put close to the upper limit of 1P band for thestrain stiffen sand field.Acknowledgment This work was supported by the NationalNatural Science Foundation of China (51109184, 51209183 and51325901).