Nonlinear Elastic Systems Research Articles

Dynamics of a one-dimensional nonlinear poroelastic system weakly damped

In this paper, we study the long-time behavior of a nonlinear porous elasticity system. The system is subject to a viscoporous damping and a nonlinear source term which is locally Lipschitz and depends only on the volume fraction. The dynamical system associated with the solutions of the model is gradient, and under the hypothesis of equal speeds of propagation for the waves, we prove that it is also quasi-stable, which allows us to show the existence of a global attractor for the system, which is the main result of the paper.

On global attractors for a nonlinear porous elastic system with fractional damping and memory term

On global attractors for a nonlinear porous elastic system with fractional damping and memory term

Exponential stability for a nonlinear porous-elastic system with delay

In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to obtain the existence and uniqueness of a global solution, we will use the semigroup theory of linear operators and under a certain relation involving the coefficients of the system together with a Lyapunov functional, we will establish the exponential decay of the energy associated to the system.

Spectro-spatial analysis of elastic wave propagation in nonlinear elastic metamaterial systems with damping.

Different from the linear counterpart, elastic wave propagation in nonlinear elastic metamaterials with damping (EMD) systems has much more novel behaviors. It is little work that reveals the nonlinear wave propagation mechanism in the nonlinear EMD in the literature. In this paper, nonlinear EMD systems with different configurations for the nonlinear elements are constructed to study the nonlinear wave propagation characteristics based on the analytical formulation. Nonlinear wave propagation attenuation characteristics in nonlinear EMD systems are studied in the frequency-domain. Spectro-spatial characteristics of nonlinear traveling wave packet in space- and time-domain are also analyzed to reveal space frequency-domain characteristics. Influences of different configurations for the nonlinear elements on wave propagation in nonlinear EMD systems are discussed. Results shown that locations of band structures can be tuned by changing intensities of nonlinearities in the nonlinear EMD systems, which are not found in the linear system. Moreover, different configurations for the nonlinear elements can lead to localization feature emerged in a nonlinear EMD system, which indicates solitary waves causing from the interaction between dispersion and nonlinearity exist in the nonlinear systems. This interesting wave propagating properties can be used to design new devices for acoustic switches, energy harvesting, and broadband vibration control.

Advancing asymptotic approaches to studying the longitudinal and torsional oscillations of a moving beam

This paper analyzes the influence of kinetic and physical-mechanical parameters of systems on the characteristics of dynamic processes in moving one-dimensional nonlinear-elastic systems. Improved convenient calculation formulas have been derived that describe the laws of changing the amplitude-frequency characteristics of systems for both a non-resonant case and a resonant one. An important issue of studying the influence of the speed of movement of elements of mechanisms on the oscillations of one-dimensional nonlinear-elastic systems has not been considered in detail until now in the scientific literature. This issue relates to the vibrations of shafts in gears, pipe strings when drilling oil and gas wells, the oscillations of turbine blades and rotating turbine discs, the longitudinal vibrations of the beam as an element of structures. The main reason for this in the analytical study of dynamic processes were the shortcomings of the mathematical apparatus for solving the corresponding nonlinear differential equations that describe the laws of motion of those systems. It was found that in the case of longitudinal oscillations in the moving beam with an increase in the longitudinal speed of the medium to 10 m/s, the amplitude of the oscillation also increases by 13.5 %. However, when the longitudinal velocity of the beam is 5 m/s, the amplitude will increase by only 3 %. It is established that with the growth of the amplitude, the frequency of longitudinal oscillations decreases sharply, and if the system moves at a higher speed, for example, 20 m/s, it reduces the frequency of oscillation by about 13 %. The results reported here make it possible to assess the effect of kinetic and physical-mechanical parameters on the frequency and amplitude of oscillations. The research that involved the asymptotic method makes it possible to predict resonant phenomena and obtain engineering solutions to improve the efficiency of technological equipment.

On a pure traction problem for the nonlinear elasticity system in Sobolev spaces with variable exponents

"The paper deals with a nonlinear elasticity system with nonconstant coe cients. The existence and uniqueness of the solution of Neumann's problem is proved using Galerkin techniques and monotone operator theory, in Sobolev spaces with variable exponents."

T–S Fuzzy-Based Event-Triggering Attitude-Tracking Control for Elastic Spacecraft With Quantization

Based on the T–S fuzzy modeling method, this article aims to deal with the problem of event-triggered integral sliding-mode attitude-tracking control for a nonlinear elastic spacecraft system with the unknown actuator dead-zone and a redundant reaction wheel over digital communication channels. Considering the effect of external disturbance and the restrictions imposed by wireless network transmission, a classical dynamic logarithmic sensor-to-controller quantizer and an event-triggered mechanism are introduced to perform the analysis and design work. The T–S fuzzy model is introduced to describe the nonlinear attitude dynamic property of the flexible spacecraft, and an integral sliding surface is employed in this article. The robustness of the closed-loop attitude-tracking control system and the finite-time reachability of the sliding-surface domain are guaranteed by the presented quantized event-triggering adaptive sliding-mode control law. Simulation results are provided to verify the feasibility of the proposed attitude-tracking control strategy.

Study of a mixed problem for a nonlinear elasticity system by topological degree

"In this paper, we consider a mixed problem for a nonlinear elasticity system with laws of general behavior. The coefficients of elasticity depends on x meanwhile the density of the volumetric forces depends on the displacement. The main aim of this paper is to apply the Schauder's fixed point theorem and the techniques of topological degree to prove a theorem of the existence and the uniqueness of the solution of the corresponding variational problem."

Optimizing elastic potential energy via geometric nonlinear stiffness

In this paper, it is shown how a nonlinear elastic mechanical system can be exploited to increase the elastic potential energy compared to its linear counterpart. A strategy for optimizing the system parameters is proposed, and performance is compared considering equal maximum displacement and maximum force. A theoretical insight is presented, and some asymptotic trends for optimum parameters selection are derived in closed-form and highlighted to help the design. A specific nonlinear mechanical system is considered, but the overall approach can be generalized. The actual system consists of a set of linear springs arranged to achieve geometric nonlinearity, and its configuration is selected based on a practical realization. A prototype device is finally assembled and tested to show evidence of the theoretical discussion.

Structural Mechanics of Negative Stiffness Honeycomb Metamaterials

AbstractThe development of multi-stable structural forms has attracted considerable attention in the design of architected multi-materials, metamaterials, and morphing structures, as a result of some unusual properties such as negative stiffness and, possibly, negative Poisson's ratio. Multi-stability is achieved through a morphological change of shape upon loading, and in doing so multi-stable structures undergo transitions from one equilibrium state to another. This paper investigates the structural performance of the negative stiffness honeycomb (NSH) metamaterials made of double curved beams which are emerging in various applications such as sensors, actuators, and lightweight impact protective structures with structural tunability and recoverability. An analytical treatment is pursued using the Euler–Lagrange theorem and the stability of the honeycomb has been studied. Based on a static analysis of the nonlinear elastic system, the developed tangent stiffness matrix and ensuing deformation curve were assessed through multiple phases of deformation. The closed-form solution was in good agreement with the numerical finite element (FE) model at different bistability ratios. It was shown that the bistability ratio had a pronounced effect on the overall response of the honeycomb and the desired negativity in the stiffness matrix could be achieved with high bistability ratios.

Vibration analysis of nonlinear and linear elastic systems

Objective. In this study, the task is to establish the theoretical prerequisites for the operability of a regressive-progressive elastic mechanism by comparing the amplitude-frequency characteristics and phase trajectories with a linear elastic system of comparable stiffness in a static equilibrium position.Methods. The article presents a comparative dynamic analysis of vibrations of elastic systems with linear rigidity and regressive-progressive characteristics obtained as a result of the use of elastic elements in the form of high flexibility rods with longitudinal eccentric compression. Such elastic elements in various design variants have been tested and patented as damping elements for use in the construction of vibration dampers for construction structures and vehicle suspensions, and have experimentally shown their effectiveness in damping vibrations.Results. The regressiveprogressive elastic characteristic obtained by the elliptic parameters method and using the ANSIS calculation complex is used in the dynamics equations in an approximated form, which expands the capabilities of the method. It is shown that increasing the energy intensity of a curvilinear system reduces the vibration amplitude.Conclusion. The regressive-progressive change of the stiffness of curvilinear elastic systems can be achieved using an elastic element with eccentric longitudinal compression; the regression plot of elastic properties is achieved due to eccentric compression; the progressive plot – through the use of a guide or other design solutions. The implementation of this characteristic allows using such elastic mechanisms in systems where the accumulation of potential energy occurs with a smaller compression stroke for the same perturbation than for linear systems.

Global and exponential attractors for a nonlinear porous elastic system with delay term

<p style='text-indent:20px;'>This paper is concerned with the study on the existence of attractors for a nonlinear porous elastic system subjected to a delay-type damping in the volume fraction equation. The study will be performed, from the point of view of quasi-stability for infinite dimensional dynamical systems and from then on we will have the result of the existence of global and exponential attractors.

Stochastic analysis of strongly non-linear elastic impact system with Coulomb friction excited by white noise

The stochastic response of frictionally damped strongly non-linear elastic impact oscillator subjected to white noise excitation and its stochastic bifurcation are considered. By the stochastic averaging method based on generalized harmonic function, one can obtain the stationary probability density function of this system. The effects of system parameters on the responses are investigated and the analytical results were verified by comparing with numerical results from Monte Carlo simulations. Stochastic bifurcations are discussed through a qualitative change of the stationary probability distribution, which indicates that the coefficient of friction, damping constant of the elastic impact force respectively, can be treated as bifurcation parameters.

Internal resonance and stress distribution of pipes conveying fluid in supercritical regime

Internal resonance and stress distribution of pipes conveying fluid at the supercritical flow around curves have been firstly investigated, with the goal of improving the mechanical fatigue properties of such pipes. Axial pre-pressure as a way of regulating the onset and growth of 1:3 internal resonance has been examined. Based on the direct multi-scale method and the Galerkin method, an approach has been proposed to analyze the nonlinear gyroscopic elastic system with time-dependent nonlinear perturbations. The tensile, bending, and resultant vibratory stress distributions of the pipe system have been determined in the presence of 1:3 internal resonance. Internal resonance degrading fatigue properties of the pipes has been highlighted. The numerical simulations support the analytical results. Then the analytical frequency responses are employed to identify factors that govern the internal resonance and stress distribution and to offer explanations as to why improving fatigue life is accompanied by suppression in the internal resonance. The boundary for incurring internal resonance suggests that appropriate axial pre-pressure should be modified in the presence of 1:3 internal resonance at different fluid velocities.

Reliability of elastic impact system with Coulomb friction excited by Gaussian white noise

Abstract The reliability of nonlinear Elastic impact oscillator with Coulomb friction subjected to Gaussian white noise excitation is investigated. Firstly, the stochastic averaging method for the nonlinear Elastic impact system with Coulomb friction is proposed and the averaged Ito equation for the system energy is obtained. Secondly, the Backward Kolmogorov(BK) equation and Generalized Pontryagin(GP) equation are established to achieve the conditional reliability function and the mean first-passage time of the Elastic impact system. Finally, two examples are worked out in detail to illustrate the feasibility of the proposed procedures. The accuracy and efficiency of the proposed procedures are validated by Monte Carlo simulations. We can conclude that the increase of the Coulomb friction, noise intensity and damping constants of the elastic impact force can improve the reliability of the Elastic impact system.

Exponentially Complex "Classically Entangled" States in Arrays of One-Dimensional Nonlinear Elastic Waveguides.

We demonstrate theoretically, using multiple-time-scale perturbation theory, the existence of nonseparable superpositions of elastic waves in an externally driven elastic system composed of three one-dimensional elastic wave guides coupled via nonlinear forces. The nonseparable states span a Hilbert space with exponential complexity. The amplitudes appearing in the nonseparable superposition of elastic states are complex quantities dependent on the frequency of the external driver. By tuning these complex amplitudes, we can navigate the state’s Hilbert space. This nonlinear elastic system is analogous to a two-partite two-level quantum system.

A K-shaped spring configuration to boost elastic potential energy

In this paper, a nonlinear elastic system is presented to increase the elastic potential energy for storage and release. The system consists of four linear mechanical springs arranged in a K-shaped configuration to achieve a specific form of nonlinearity. The arrangement is inspired by the interaction among the filaments of protein in the sarcomere, which is the fundamental unit of the skeletal muscles. Similarly to the sarcomere, where synergy is exploited from active and passive components, a bi-stable system is coupled to a hardening one, and an insight is provided for design and optimization. The theoretical formulation is validated through numerical simulations and experimental results. The insight provided could be exploited in the conception of advanced bio-inspired structures, materials and actuators to effectively store and release energy.

Comparison of anterior capsulotomy techniques: continuous curvilinear capsulorhexis, femtosecond laser-assisted capsulotomy and selective laser capsulotomy

PurposeTo compare the anterior capsulotomy edge tear strength created by manual continuous curvilinear capsulorhexis (CCC), femtosecond laser-assisted capsulotomy (FLACS), and selective laser capsulotomy (SLC).SettingSingapore National Eye Centre, Singapore and Excel-Lens,...

DUCTILITY OF REINFORCED CONCRETE SUB FRAME FOR INDUSTRIALIZED BUILDING SYSTEM

An accurate determination of industrialized building system (IBS) frames ductility under alternating lateral loads is the key issue of this study. The performance features of IBS H frame assembly subjected to cyclic lateral pushover test with six attached IBS components are reported. A test scheme of nonlinear elastic sub-frame system is proposed to build an IBS structural building system. This system complies with the requirements of strength and ductility governed by European Codes 2 and 8. The three models are a conventional reinforced concrete H frame system CRCH (Model 1), IBS with steel conventional links as reinforcements IBSHN (Model 2), and special spiral links concrete IBSHS (Model 3). Each model is scaled to 1:5. All models are laboratory examined under cyclic lateral pushover test to failure, where the IBS connections are considered as hybrid partial rigid linking beams to columns. The beam ends are connected to column boxes via a U shaped steel plate. The experimental results of the IBS specimens are compared with the conventional reinforced concrete connection of similar shapes and size in the form of H sub-frame mechanism tested under the same condition. The models are subjected to cyclic lateral load controlled applied at the beam-column connection. The performance evaluation of IBS connections is made via load displacement hysteresis, ultimate and collapse parameter, ductility index, and surface cracks appearances. The conventional concrete specimen is obviously found to display better strength compared to IBS. Conversely, the ductility of IBS H frame specimen with spiral shear links and conventional closed loop links exhibits superior features compared to the conventional concrete specimen which is beneficial to earthquake engineering. It is demonstrated that the performance of the precast concrete structure is highly dependent on the ductile capacity of connectors to each of the IBS component. This is significant especially at the joints such as the beam-to-column connections. Our systematic methods on ductility characterizations of reinforced concrete beams may contribute toward the development of IBS in resisting earthquakes.

Evidence for hidden order in a nonlinear model elastic system

Hidden order may arise in strongly correlated systems even if there is an apparent lack of long-range order as measured by local order parameters. This phenomenon has been essentially associated with topological order in quantum systems. Here, we demonstrate the emergence of hidden order in a 1D non-linear classical mechanical system that supports rotational degrees of freedom. The potential energy of the model system creates a bistable system for which hidden order emerges with the introduction of a biquadratic term. To our surprise, we discover that varying the strength of the biquadratic term leads to four distinct phases quantified by the behaviors of the Néel and string order parameters. Three of these phases are locally disordered. Hidden order is identified by a string order parameter that shows correlations with significantly longer range than the Néel order parameter. The hidden order correlation length diverges as the kinetic energy of the system is lowered with a critical exponent ~0.5. The observation of hidden order in a mechanical system reveals that instability and non-linearity may play critical roles in the generation of nonlocal long-range correlations in apparently locally disordered systems.