A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are ...A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are made to Akgun's method to allow treatment of eigensensitivity with repeated roots for general nondefective systems, and Bernard and Bronowicki's modal expansion approach is expanded to a family of modal methods.展开更多
The effect of tire repeated root modal（RRM）on tire modeling with an experimental modal is studied.Firstly,a radial tire with radial and tangential RRMs is tested and analyzed.By multi-point exciting of the radial ti...The effect of tire repeated root modal（RRM）on tire modeling with an experimental modal is studied.Firstly,a radial tire with radial and tangential RRMs is tested and analyzed.By multi-point exciting of the radial tire,a multiple reference frequency domain method based on a least squares（LMS PolyMAX）algorithm is used to identify modal parameters.Then,modal stability diagram（MSD）,modal indication function（MIF）and modal assurance criteria（Auto-MAC）matrix are utilized to induce multiple inputs multiple outputs（MIMO）frequency response function（FRF）matrixes.The tests reveal that notable repeated roots exist in both radial and tangential response modes.Their modal frequencies and damping factors are approximately the same,the amplitudes of modal vectors are in the same order of magnitude,and the mode shapes are orthogonal.Based on the works mentioned,the method of trigonometric series modal shapes fitting is adopted,the effects of RRM model on tire modeling with a vertical experimental modal are discussed.The final results show that the effects of considering the RRM shapes are equivalent to the tire mode shapes depended on rotating the tire’s different exciting points during tire modeling,and since considering the RRM,the tire mode shapes can be unified and fixed during tire modeling.展开更多
Most parallel manipulators have multiple solutions to the direct kinematic problem.The ability to perform assembly changing motions has received the attention of a few researchers.Cusp points play an important role in...Most parallel manipulators have multiple solutions to the direct kinematic problem.The ability to perform assembly changing motions has received the attention of a few researchers.Cusp points play an important role in the kinematic behavior.This study investigates the cusp points and assembly changing motions in a two degrees of freedom planar parallel manipulator.The direct kinematic problem of the manipulator yields a quartic polynomial equation.Each root in the equation determines the assembly configuration,and four solutions are obtained for a given set of actuated joint coordinates.By regarding the discriminant of the repeated roots of the quartic equation as an implicit function of two actuated joint coordinates,the direct kinematic singularity loci in the joint space are determined by the implicit function.Cusp points are then obtained by the intersection of a quadratic curve and a cubic curve.Two assembly changing motions by encircling different cusp points are highlighted,for each pair of solutions with the same sign of the determinants of the direct Jacobian matrices.展开更多
基金The project supported by the National Natural Science Foundation of China
文摘A family of modal methods for computing eigenvector derivatives with repeated roots are directly derived from the constraint generalized inverse technique which is originally formulated by Wang and Hu. Extensions are made to Akgun's method to allow treatment of eigensensitivity with repeated roots for general nondefective systems, and Bernard and Bronowicki's modal expansion approach is expanded to a family of modal methods.
文摘The effect of tire repeated root modal（RRM）on tire modeling with an experimental modal is studied.Firstly,a radial tire with radial and tangential RRMs is tested and analyzed.By multi-point exciting of the radial tire,a multiple reference frequency domain method based on a least squares（LMS PolyMAX）algorithm is used to identify modal parameters.Then,modal stability diagram（MSD）,modal indication function（MIF）and modal assurance criteria（Auto-MAC）matrix are utilized to induce multiple inputs multiple outputs（MIMO）frequency response function（FRF）matrixes.The tests reveal that notable repeated roots exist in both radial and tangential response modes.Their modal frequencies and damping factors are approximately the same,the amplitudes of modal vectors are in the same order of magnitude,and the mode shapes are orthogonal.Based on the works mentioned,the method of trigonometric series modal shapes fitting is adopted,the effects of RRM model on tire modeling with a vertical experimental modal are discussed.The final results show that the effects of considering the RRM shapes are equivalent to the tire mode shapes depended on rotating the tire’s different exciting points during tire modeling,and since considering the RRM,the tire mode shapes can be unified and fixed during tire modeling.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.U1813221 and 52075015).
文摘Most parallel manipulators have multiple solutions to the direct kinematic problem.The ability to perform assembly changing motions has received the attention of a few researchers.Cusp points play an important role in the kinematic behavior.This study investigates the cusp points and assembly changing motions in a two degrees of freedom planar parallel manipulator.The direct kinematic problem of the manipulator yields a quartic polynomial equation.Each root in the equation determines the assembly configuration,and four solutions are obtained for a given set of actuated joint coordinates.By regarding the discriminant of the repeated roots of the quartic equation as an implicit function of two actuated joint coordinates,the direct kinematic singularity loci in the joint space are determined by the implicit function.Cusp points are then obtained by the intersection of a quadratic curve and a cubic curve.Two assembly changing motions by encircling different cusp points are highlighted,for each pair of solutions with the same sign of the determinants of the direct Jacobian matrices.
