... Computational dynamics Continuation Methods Bio-mechanical systems Biological systems The continuum mechanics-based elastic rod models [ 1 , 2 ] have evolved as viable tools to efficiently simulate the bending and twisting deformations of a variety of slender structures. Slender structures occur...

.... 30 07 2017 30 10 2017 Analytical solution systems Continuation Methods Nonlinear dynamical systems Nonlinear oscillations Nonlinear phenomena Stability Stochastic systems Symbolic solution systems Vibration Writing Eq. (4) in state space form (5) { d...

... in different speed range. Jumping phenomenon is also observed for a high value of bearing parameter with unbalance. The dynamic stability of journal bearing system is analyzed with the variation of parameters ω ¯ , Γ and a ¯ . Equations (7) – (10) are solved by the continuation method using...

..., especially if some displacements are prescribed. Once a static solution has been found, the linearized equations of motion about this solution can be obtained in terms of a set of minimal coordinates, that is, in the degrees-of-freedom (DOFs). In addition, a continuation method is described for tracing...

... 2017 11 07 2017 Continuation Methods Fractional calculus In modeling of the anomalous transport phenomenon and in the complex phenomenon, fractional differential equation has very significant role. Fractional Riesz diffusion equation plays an important role in dynamical systems...

... received September 7, 2017; published online October 9, 2017. Assoc. Editor: Hiroshi Yabuno. 22 09 2016 07 09 2017 Algorithms Continuation Methods Fractional calculus Numerical Integration methods In the past few decades, fractional calculus has been used in several areas...

... domain via the harmonic balance method (HBM), and then, the equations of motion are solved by an arc-length continuation method. After comparisons with published data on beams with rectangular cross section and on carbon nanotubes (CNTs), the study focuses on the nonlinear modes of vibration of CNTs...

... Continuation Method-Application To Rotor Systems ,” ASME J. Vib. Acoust. , 119 ( 1 ), pp. 9 – 20 . 10.1115/1.2889694 [12] Sundararajan , P. , and Noah , S. T. , 1998 , “ An Algorithm for Response and Stability of Large Order Non-Linear Systems—Application to Rotor Systems ,” J. Sound Vib...

... Continuation Methods Design optimization Vehicular dynamics Design sensitivity Nonlinear systems Historically, the problem of obtaining the most fuel-efficient driving profile has been formulated as an optimal control problem. Most of the works in this field solved the problem numerically using...

... Continuation Methods Fractional calculus Integration methods Generally speaking, there are at least two reduction methods for ODEs, namely, center manifold reduction [ 1 , 2 ] and Lyapunov–Schmidt reduction [ 3 – 8 ]. By using these two reduction methods, the complex ODEs can be reduced...