Statistical properties of a modified standard map in quantum and classical regimes

Nonlinear Dynamics - We present a model—a modified standard map. This model has interesting properties that allow quantum–classical correspondences to be studied. For some range of...     

Self-/mutual-symmetric rhythms and their coexistence in a delayed half-center oscillator of the CPG neural system

Nonlinear Dynamics - Most animals are capable of efficient locomotion owing to a special neural network—the central pattern generator (CPG) located in the central nervous system. The...     

Parrondo’s paradox from classical to quantum: A review

Nonlinear Dynamics - Two losing games can be combined in a certain manner to give a winning outcome—this is known as Parrondo’s paradox. Parrondo’s paradox has found its...     

Stability analysis of whirl flutter in rotor-nacelle systems with freeplay nonlinearity

Nonlinear Dynamics - Tiltrotor aircraft are growing in prevalence due to the usefulness of their unique flight envelope. However, aeroelastic stability—particularly whirl flutter...     

Dynamics of coupled nonlinear oscillators: The formation of long-lived vibrational states in the case of molecular systems

Nonlinear vibrations in a closed system of coupled nonlinear oscillators are studied using acetylene type molecules as an example. A criterion for the stable existence of long-lived vibrational states—local modes—in one of the oscillators is obtained. It is shown that the disappearance of a local mode, as well as its appearance, proceeds abruptly, and the mechanism of stabilization of these excitations is due to the presence or absence of internal resonances of an oscillatory system such as any polyatomic molecule. Energy values needed to excite vibrations in which local modes can appear are determined. It is shown that calculation results agree with experimental data.     

Mathematical modelling of nonlinear dynamics generated from modular interconnections in cellular SOS response system

Nonlinear Dynamics - Nonlinear dynamics in synthetic biology systems, generated as a consequence of interconnections between biological modules, poses challenges to the objective of engineering...     

Nonlinear vibration isolation via a compliant mechanism and wire ropes

Nonlinear Dynamics - Nonlinear vibration isolation systems with both stiffness and damping nonlinearities are promising for a broad-band and high-efficient isolation performance. In this research,...     

Nonlinear vibration absorption of laminated composite beams in complex environment

Nonlinear Dynamics - Nonlinear vibration absorption of a laminated composite beam is investigated with the account of complex environment (moisture and temperature). A passive efficient nonlinear...     

Nonlinear free vibration of a beam on Winkler foundation with consideration of soil mass motion of finite depth

Nonlinear Dynamics - Nonlinear free vibration characteristics of a beam on elastic foundation are investigated. Considering the effect of soil–structure interaction on the nonlinear dynamic...     

Comment on “Study of mixed-mode oscillations in a nonlinear cardiovascular system” [Nonlinear Dyn,doi: 10.1007/s11071-020-05612-8]

Nonlinear Dynamics - This note comments on the questionable approach and claims made in “Study of mixed-mode oscillations in a nonlinear cardiovascular system” [Nonlinear Dyn, doi:...     

Investigation of quasi-periodic response of a buckled beam under harmonic base excitation with an “unexplained” sideband structure

Nonlinear Dynamics - The aim of this paper is to investigate quasi-periodic response of a fixed–fixed buckled beam experimentally studied in detail by Kreider and Nayfeh (Nonlinear Dyn...     

Dynamic effect of constant inertial acceleration on vibration isolation system with high-order stiffness and Bouc–Wen hysteresis

Nonlinear Dynamics - Nonlinear vibration isolation provides with an effective way for vibration reduction with broad band and high efficiency. This investigation focuses on the dynamic effects of a...     

Dynamic analysis of 1-dof and 2-dof nonlinear energy sink with geometrically nonlinear damping and combined stiffness

Nonlinear Dynamics - Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study...     

The missing mem-inerter and extended mem-dashpot found

Nonlinear Dynamics - This work explores complex dynamics of a new mass excited impact oscillator reported in Wiercigroch et al. (Nonlinear Dyn 99:323–339, 2020) both experimentally and...     

High-order study of the canard explosion in an aircraft ground dynamics model

Nonlinear Dynamics - A planar system has been proposed in the paper Rankin et al. (Nonlinear Dyn 66:681–688, 2011) to understand the canard explosion detected in a 6D aircraft ground dynamics...     

On the inelastic behavior of solids — Part 1: Twinning

Recently, Wineman and Rajagopal [1990] “On a Constitutive Theory for Materials Undergoing Microstructural Changes,” Arch. Mech., 42, 53 and Rajagopal and Wineman [1992] “A Constitutive Equation for Nonlinear Solids which Undergo Deformation Induced Microstructural Changes,” Int. J. Plasticity, 8, 385, developed a theory that was particularly well suited to describing the inelastic behavior of polymeric materials. Here, we draw upon their ideas and generalize them to include a much larger class of materials. The versatility and efficacy of the theory are illustrated by studying the problem of twinning within the context of the theory. We find that the predictions of the theory are remarkably close — both qualitatively and quantitatively — with the experimental results of Madhava et al. [1972] “Discontinuous Twinning during Essentially Elastic Compression of Steel at 4.2K,” Phil. Mag., 25(2), 519 and Madhava and Armstrong [1974] “A Constitutive Relation for Deformation Twinning at High Strain Rates,” in Rohde, R.W., Butcher, B.M., Holland, J.R., and Karnes, C.H., eds., Metallurgical Effects at High Strain Rates. Plenum, New York, 1974.     

Bifurcations in basic models of delayed force control

Nonlinear Dynamics - Basic single-degree-of-freedom mechanical models of force control are presented to achieve desired contact forces between actuators and objects. Nonlinear governing equations...     

High-efficiency nonlinear dynamic analysis for joint interfaces with Newton–Raphson iteration process

Nonlinear Dynamics - Nonlinear dynamic analysis of the assembled structures involves the complex nonlinearity of the joint interfaces. By combining the multi-harmonic balance method with the...     

Nonlinear dynamics in mechanics and engineering: 40 years of developments and Ali H. Nayfeh’s legacy

Nonlinear Dynamics - Nonlinear dynamics of engineering systems has reached the stage of full maturity in which it makes sense to critically revisit its past and present in order to establish an...     

An analytical approximated solution and numerical simulations of a non-ideal system with saturation phenomenon

Nonlinear Dynamics - Nowadays, researches about non-ideal problems have been increased considerably in technical-scientific community. Nonlinear problems have been widely studied due to their...