... 2017 25 02 2018 Bifurcations Design optimization Nonlinear phenomena Perturbation Reduced-order models Dynamical analysis Dynamical method Asymptotic models Concurrent advances in precision manufacturing, material science, and computational design methods have produced...

... manuscript received April 9, 2018; published online May 17, 2018. Assoc. Editor: Firdaus Udwadia. 27 11 2017 09 04 2018 Control Nonlinear dynamical systems Perturbation Robotics Stability of nonlinear systems Mechanism systems Asymptotic models An industrial robot...

... Analytical solution systems Nonlinear dynamical systems Nonlinear oscillations Perturbation Symbolic solution systems Vibration Asymptotic models The linear normal mode is an established concept in the structural dynamics theory, which has been widely used in various industrial applications...

... bifurcation is observed corresponding to excitation forcing of γ  = 0.2 at different β 0 , the possibility of quasiperiodic and chaotic responses can also be probed at higher excitation forcing. Nonlinear oscillations Perturbation Vibration Asymptotic models Shape memory alloy (SMA) has...

... Analytical solution systems Computational mechanics Dynamics of MEMS Nano systems dynamics Nonlinear dynamical systems Nonlinear oscillations Nonlinear phenomena Perturbation Symbolic solution systems Vibration Dynamics of NEMS Dynamics of MEMS Asymptotic models Owing...

... for the equilibrium point is obtained, and averaging procedure is used to arrive at approximate analytical expressions of the periodic amplitude of oscillations around this fixed-point. For stick–slip oscillations, analytical expressions for amplitude are arrived at by using perturbation analysis for the finite time...

... + ε ( 2 D 0 D 1 ) + ε 2 ( 2 D 0 D 2 + D 1 2 ) + .. The MMS is a well-known singular perturbation method which examines the behavior of a nonlinear system of equations at various time scales to obtain insight into the behavior of a nonlinear...

... to investigate the response to a cognitive perturbation while walking simulating a realistic everyday situation, potentially resulting in falling. We found the IR to be sensitive to the pathology and, potentially, to risk of falling. In general, questions form the basis of everyday conversations. Caregivers...

..., such as the well-known perturbation technique applied in weakly nonlinear problems, because it is independent of any small physical or artificial parameters at all; thus, it can handle more nonlinear problems, including strongly nonlinear ones. Two typical cases are investigated by FPM in detail and the comparison...