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In terms of the first- and second-order sensitivities of the complex mode for a symmetric damped linear discrete dynamic system with respect to design parameters, the algebraic method, direct method, full-mode method and truncated modal method corresponding to full-mode method are proposed. These four algorithms insist on using the expression forms in N-dimensional vector space, which provide the convenience in engineering application. In the numerical examples, the correctness and validity of all the proposed algorithms are demonstrated for the single-frequency, closed-frequency and multiple-frequency systems. The algebraic method, direct method and full-mode method are accurate algorithms. No statement is made that one method is absolutely superior to the other, but this paper provides the chance to compare their efficiency and accuracies of all the three accurate algorithms. Truncated modal method proposed here is an approximate algorithm. The truncation criterion is simple and efficient, which is a more competitive alternative to the full-mode method, and it is shown that the truncated modal method has high precision and good convergence speed for sensitivity analysis by numerical examples. [ABSTRACT FROM AUTHOR]

The present paper addresses the dynamical motion of two degrees-of-freedom (DOF) auto-parametric system consisting of a connected rolling cylinder with a damped spring. This motion has been considered under the action of an excitation force. Lagrange's equations from second kind are utilized to obtain the governing system of motion. The uniform approximate solutions of this system are acquired up to higher order of approximation using the technique of multiple scales in view of the abolition of emerging secular terms. All resonance cases are characterized, and the primary and internal resonances are examined simultaneously to set up the corresponding modulation equations and the solvability conditions. The time histories of the amplitudes, modified phases, and the obtained solutions are graphed to illustrate the system's motion at any given time. The nonlinear stability approach of Routh–Hurwitz is used to examine the stability of the system, and the different zones of stability and instability are drawn and discussed. The characteristics of the nonlinear amplitude for the modulation equations are investigated and described, as well as their stabilities. The gained results can be considered novel and original, where the methodology was applied to a specific dynamical system. [ABSTRACT FROM AUTHOR]

Yaw damper, widely employed in high-speed railway vehicles, has played an important role in improving the hunting stability. This paper mainly makes a comprehensive analysis on the effect of yaw damper with its series stiffness value on the stability and bifurcation type of the railway bogie. With the prerequisite of the linear critical speed calculated by mathematical method, Center Manifold Theorem is adopted to reduce the dimension of the model to a planar dynamical system. And the symbolic expression associated with yaw damper and its series stiffness to determine bifurcation type at the critical speed is obtained by the method of Normal Form. As a result, the influence of the variation tendency of the yaw damper and series stiffness on the bifurcation type of the bogie is given qualitatively in contrast to different couples. Finally, numerical analysis of corresponding bifurcation diagrams is given to verify the accuracy of the conclusion. [ABSTRACT FROM AUTHOR]