Nonlinear Dynamics

http://link.springer.com/journal/11071

List of Papers (Total 159)

Application of the finite segment method to stabilisation of the force in a riser connection with a wellhead

This paper presents a spatial model of riser dynamics formulated using the segment method and its applications. The model has been validated by comparison of the authors’ own results with those obtained from experimental measurements and Abaqus on the basis of forced vibration with large amplitude for the riser submerged in water. The influence of the sea environment is...

Dynamic stability of a nonlinear multiple-nanobeam system

We use the incremental harmonic balance (IHB) method to analyse the dynamic stability problem of a nonlinear multiple-nanobeam system (MNBS) within the framework of Eringen’s nonlocal elasticity theory. The nonlinear dynamic system under consideration includes MNBS embedded in a viscoelastic medium as clamped chain system, where every nanobeam in the system is subjected to time...

How to find simple nonlocal stability and resilience measures

Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena cannot be traced by the widespread local...

Research of giant magnetostrictive actuator’s nonlinear dynamic behaviours

The multi-coupled nonlinear factors existing in the giant magnetostrictive actuator (GMA) have a serious impact on its output characteristics. If the structural parameters are not properly designed, it is easy to fall into the nonlinear instability, which has seriously hindered its application in many important fields. The electric–magnetic-machine coupled dynamic mathematical...

On the mathematical models of the Timoshenko-type multi-layer flexible orthotropic shells

Mathematical models of multi-layer orthotropic shells were reconsidered based on the Timoshenko hypothesis. A new mathematical model with \(\varepsilon \)-regularisation was proposed, and the theorem regarding the existence of a generalised solution to the model was formulated and proved. The algorithms of numerical investigation of models studied with the aid of the variational...

Nonlinear dynamics and triboelectric energy harvesting from a three-degree-of-freedom vibro-impact oscillator

A triboelectric energy harvester based on a three-degree-of-freedom vibro-impact oscillator is presented. Both the dynamic model of the oscillator and the theoretical model of the oscillator-based triboelectric energy harvester are established. The dynamic response and its effect on the electrical output are considered for various mass ratios and mass spacings. The study leads to...

On the dynamics of a nonlinear energy harvester with multiple resonant zones

The dynamics of a nonlinear vibration energy harvester for rotating systems is investigated analytically through harmonic balance, as well as by numerical analysis. The electromagnetic harvester is attached to a spinning shaft at constant speed. Magnetic levitation is used as the system nonlinear restoring force for broadening the resonant range of the oscillator. The system is...

Spatial evolution of Hindmarsh–Rose neural network with time delays

Spatial relations between neurons in the network with time delays play a crucial role in determining dynamics of the system. During the development of the nervous system, different types of neurons group together to enable specific functions of the network. Right spatial distances, thus right time delays between cells are crucial for an appropriate functioning of the system. To...

The essence of neuronal activity from the consistency of two different neuron models

Based on the H–H equation, this study has proposed the calculation and analysis of energy expenditure for a single neuron which is activated at sup-threshold and subthreshold, as well as the criterion of the energy expenditure of neurons activated sup-threshold and subthreshold, which was the maximum power of a sodium ion pump. Results of the study showed that not only the...

Pruning of recurrent neural models: an optimal brain damage approach

This paper considers the problem of pruning recurrent neural models of perceptron type with one hidden layer which may be used for modelling of dynamic system. In order to reduce the number of model parameters (i.e. the number of weights), the Optimal Brain Damage (OBD) pruning algorithm is adopted for the recurrent neural models. Efficiency of the OBD algorithm is demonstrated...

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a hidden attractor in the case of multistability as well as a classical self-excited attractor. The hidden attractor in this system can be localized by analytical/numerical methods based on the continuation and perpetual points...

Chaotic vibrations of flexible shallow axially symmetric shells

In this work, chaotic dynamics of flexible spherical axially symmetric shallow shells subjected to sinusoidal transverse load is studied with emphasis put on the vibration modes. Chaos reliability is verified and validated by solving the implemented mathematical model by partial nonlinear equations governing the dynamics of flexible spherical shells and by estimating the signs of...

Correction to: Adaptive RBFNN finite-time control of normal forms for underactuated mechanical systems

The list of authors in the original publication was incomplete. The complete list of authors is shown here, including the third author, Faiçal Mnif.

Effect of pressure on nonlinear dynamics and instability of electrically actuated circular micro-plates

Characterization of nonlinear behavior of micro-mechanical components in MEMS applications plays an important role in their design process. In this paper, nonlinear dynamics, stability and pull-in mechanisms of an electrically actuated circular micro-plate subjected to a differential pressure are studied. For this purpose, a reduced-order model based on an energy approach is...

Contact interaction of two rectangular plates made from different materials with an account of physical nonlinearity

A mathematical model of a contact interaction between two plates made from materials with different elasticity modulus is derived taking into account physical and design nonlinearities. In order to study the stress–strain state of this complex mechanical structure, the method of variational iteration has been employed allowing for reduction of partial differential equations to...

Superposition solutions to the extended KdV equation for water surface waves

The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher-order effects. Although this equation has only one conservation law, exact periodic and solitonic solutions exist. Khare and Saxena (Phys Lett A 377:2761–2765, 2013; J Math Phys 55:032701, 2014; J Math Phys 56:032104, 2015...

Nonlinear dynamics of a spinning shaft with non-constant rotating speed

Research on spinning shafts is mostly restricted to cases of constant rotating speed without examining the dynamics during their spin-up or spin-down operation. In this article, initially the equations of motion for a spinning shaft with non-constant speed are derived, then the system is discretised, and finally a nonlinear dynamic analysis is performed using multiple scales...

Asymptotical stability of the motion of mechanical systems with partial energy dissipation

We consider a linear mechanical system under the action of potential, gyroscopic and dissipative (partial) forces. The classical Kelvin–Chetaev theorems are not applicable here, and another approach, which is based on Barbashin–Krasovskii theorem, is suggested. This approach is based on decomposition of the whole system and is convenient for systems of high dimension or with...

Numerical and experimental studies of stick–slip oscillations in drill-strings

The cyclic nature of the stick–slip phenomenon may cause catastrophic failures in drill-strings or at the very least could lead to the wear of expensive equipment. Therefore, it is important to study the drilling parameters which can lead to stick–slip, in order to develop appropriate control methods for suppression. This paper studies the stick–slip oscillations encountered in...

Experimental investigation of perpetual points in mechanical systems

In dissipative dynamical systems, equilibrium (stationary) points have a dominant organizing effect on transient motion in phase space, especially in nonlinear systems. These time-independent solutions are readily defined in the context of ordinary differential equations, that is, they occur when all the time derivatives are simultaneously zero. However, there has been some...

Correction to: Stabilization of a class of fractional-order chaotic systems using a non-smooth control methodology

This note provides a corrigendum to the paper “Stabilization of a class of fractional-order chaotic systems using a non-smooth control methodology” [Nonlinear Dynamics, 89 (2017) 1357–1370]. It is pointed out that we have relied on a wrong formula in [2] to compute the upper bounds of the finite settling times of the proposed control methods in [1]. Fortunately, the minor errors...