DYNAMIC CHARACTERISTICS OF LAG VIBRATION OF A WIND TURBINE BLADE

Lagwise dynamic characteristics of a wind turbine blade subjected to unsteady aero- dynamic loads are studied in this paper. The partial differential equations governing the coupled longitudinal-transverse vibration of the blade with large bending deflection are obtained by ap- plying Hamilton＇s principle. The modal problem of the coupled vibration is handled by using the method of numerical integration of Green＇s function. Influences of the rotating speed, the pitch angle, the setting angle, and the aerodynamic loads on natural frequencies are discussed. Results show that： （I） Lagwise natural frequencies ascend with the increase of rotating speed; effects of the rotating speed on low-frequencies are dramatic while these effects on high-frequencies become less. （2） Influences of the pitch angle on natural frequencies are little; in the range of the normal rotating speed, the first frequency ascends with the increase of the absolute value of the pitch angle, while it is contrary to the second and third frequencies. （3） Effects of the setting angle on natural frequencies depend on the rotating speed; influences are not significant at low speed, while they are dramatic on the first frequency at high speed. （4） Effects of the aerodynamic loads on natural frequencies are very little; frequencies derived from the model considering aerodynamic loads are smaller than those from the model neglecting aerodynamic loads; relative errors of the results corresponding to two models ascend with the increase of the absolute value of the setting angle.

Radiological Characteristics and Anatomical Risk Factors in the Evaluation of Hallux Valgus in Chinese Adults

Background：There are no unified theories as to the anatomical changes that occur with hallux valgus,we investigated the radiological characteristics and anatomical risk factors for hallux valgus deformity in Chinese adults.Methods：We reviewed 141 patients with hallux valgus （206 feet; 15 males,126 females; mean age,58.5 years）.These patients attended Peking University People＇s Hospital from April 2008 to March 2014.All feet had intact radiological data,obtained using the Centricity RIS/PACS system.We measured hallux valgus angle （HVA）,1-2 intermetatarsal angle （IMA）,proximal articular set angle （PASA）,distal articular set angle,hallux interphalangeal angle,metatarsocuneiform angle,size of the medial eminence of the distal first metatarsal,tibial sesamoid position,and joint congruity of the first metatarsophalangeal joint （MTPJ）.Results：We found positive correlations between the HVA and IMA （r =0.279,P 〈 0.01） and HVA and PASA （r =0.358,P 〈 0.01）,but not for IMA and PASA （P 〉 0.05）.Feet were divided into three groups based on HVA severity.IMA （P 〈 0.05） and PASA （P 〈 0.05） in the mild group were significantly lower than that in the moderate and severe groups,with no significant difference determined for IMA or PASA between the moderate and severe groups （P 〉 0.05）.Feet were then grouped based on the shape of the first metatarsal head.Using this grouping,HVA was significant higher in the rounded shape （19.92°） than in a flat shape （17.66°）.The size of the medial eminence of the distal first metatarsal was positively correlated with HVA （r =0.185,P 〈 0.01）.The medial eminence in the moderate and severe groups was significantly larger than that in the mild group; moderate and severe groups were not significantly different.Conclusions：PASA enlargement is an adaptive change during early hallux valgus formation,and decompensation leads to subdislocation in the first MTPJ.A rounded first metatarsal head would thus predispose a foot to hallux valgus.Furthermore,bone proliferation at the medial eminence may also lead to early hallux valgus development.