Dynamic Analysis of Tapered Thin-Walled Beams Using Spectral Finite Element Method

Tapered thin-walled structures have been widely used in wind turbine and rotor blade. In this paper, a spectral finite element model is developed to investigate tapered thin-walled beam structures, in which torsion related warping effect is included. First, a set of fully coupled governing equations are derived using Hamilton’s principle to account for axial, bending, and torsion motion. Then, the differential transform method (DTM) is applied to obtain the semianalytical solutions in order to formulate the spectral finite element. Finally, numerical simulations are conducted for tapered thin-walled wind turbine rotor blades and validated by the ANSYS. Modal frequency results agree well with the ANSYS predictions, in which approximate 30,000 shell elements were used. In the SFEM, one single spectral finite element is needed to perform such calculations because the interpolation functions are deduced from the exact semianalytical solutions. Coupled axial-bending-torsion mode shapes are obtained as well. In summary, the proposed spectral finite element model is able to accurately and efficiently to perform the modal analysis for tapered thin-walled rotor blades. These modal frequency and mode shape results are important to carry out design and performance evaluation of the tapered thin-walled structures

Dynamic Analysis of a 5-DOF Flexure-Based Nanopositioning Stage

A multibody dynamic model is developed for dynamic analysis of a 5-DOF flexure-based nanopositioning stage in the projection optical system of the semiconductor lithography in this paper. The 5-DOF stage is considered as an assembly of rigid bodies interconnected by elastic flexure hinges. Considering the length effects of flexure hinges, multibody dynamic equations are established according to spatial motions of rigid bodies by using Lagrangian method. The shear effects and the torsional compliances of the commonly used circular flexure hinges are considered to enhance the modeling accuracy. The accuracies of various out-of-plane compliance formulas are also discussed. To verify the developed dynamic model, the finite element analyses (FEA) by using ANSYS and modal hammer experimental tests of the primary flexure-based composition structures and the integral 5-DOF stage are performed. The analytical modal frequencies are well in agreement with FEA and experimental test. The results are significant to analyze and optimize the 5-DOF flexure-based nanopositioning stage

Lamb Wave Directional Sensing with Piezoelectric Fiber Rosette in Structure Health Monitoring

Directional piezoelectric sensors can detect the Lamb wave propagation direction to locate damage in structural health monitoring (SHM). The directivity of the round piezoelectric fiber is exploited with a 0°/45°/90° rosette configuration to acquire flexural Lamb wave signals. The directional response of the piezoelectric fiber under narrowband tone-burst excitation is theoretically deduced. Experimental tests are conducted to demonstrate the directivity and the frequency response property of the piezoelectric fiber under different excitation central frequencies in comparison with the MFC, rectangular piezoelectric sheet, and circular piezoelectric disc. Continuous wavelet transform (CWT) is applied to extract the maximum response amplitude information of the acquired Lamb wave signal at a central frequency. Experimental test results indicate that the piezoelectric fiber is capable to be used as a Lamb wave directional sensor than other piezoelectric sensors. A numerical estimation method for the Lamb wave propagation direction is proposed by defining an error function between the theoretical and experimental normalized response amplitude. The proposed method is generally applicable for different rosette configurations. Experimental results validate the accuracy of the proposed estimation method. The research results are significant to design or select the piezoelectric sensor to measure Lamb wave signals