Jerzy Warminski

A review on the mechanical behaviour of curvilinear fibre composite laminated panels

A review on works that investigate the mechanical behaviour of variable stiffness composite laminated panels is carried out in this paper. The review mostly focuses on buckling, failure and vibrations in laminates reinforced by curvilinear fibres, although other issues related to variable stiffness laminates are also addressed. The peculiarities in the formulation of curvilinear fibre reinforced plates are briefly described. As an illustration, the natural frequencies of vibration of variable stiffness composite laminated plates with curvilinear fibres are computed by an h-version type finite element code and are compared with the ones calculated using another model, based on a Third-order Shear Deformation Theory. Areas of research to explore on variable stiffness composite laminates are suggested.

Autoparametric vibrations of a nonlinear system with pendulum

Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations. It has been found that the motion of the oscillator, forced by an external harmonic force, has been dynamically eliminated by the pendulum oscillations. Influence of a nonlinear spring on the vibration absorption near the main parametric resonance region has been carried out analytically, whereas the transition from regular to chaotic vibrations has been presented by using numerical methods. A transmission force on the foundation for regular and chaotic vibrations is presented as well.

Bending–twisting vibrations of a rotating hub–thin-walled composite beam system

The dynamics of a system consisting of a rotating rigid hub and a flexible composite thin-walled beam is discussed. The nonclassical effects like material anisotropy, rotary inertia and transverse shear are considered in the mathematical model of the structure. Moreover, the hub mass moment of inertia is taken into account. The differential equations of motion featuring beam bending–twist elastic coupling are derived using the Hamilton principle, and the Galerkin method is applied in order to reduce the partial differential governing equations to the ordinary differential equations. Parametric studies are conducted to evaluate beam stiffness coefficients depending on the fiber lamination angle. Next, numerical results are obtained to investigate the impact of hub to beam relative inertia on the natural frequencies of the structure. Cases of forced vibrations of the system are examined where the driving torque is considered as the sum of a constant (mean value) and a periodic component. Simulations show the importance of the hub inertia on the complete system dynamics. A shift of the resonance zones and a vibration absorption are observed.

Dynamics of an Autoparametric Pendulum-Like System with a Nonlinear Semiactive Suspension

This paper presents vibration analysis of an autoparametric pendulum-like mechanism subjected to harmonic excitation. To improve dynamics and control motions, a new suspension composed of a semiactive magnetorheological damper and a nonlinear spring is applied. The influence of essential parameters such as the nonlinear damping or stiffness on vibration, near the main parametric resonance region, are carried out numerically and next verified experimentally in a special experimental rig. Results show that the magnetorheological damper, together with the nonlinear spring can be efficiently used to change the dynamic behaviour of the system. Furthermore, the nonlinear elements applied in the suspension of the autoparametric system allow to reduce the unstable areas and chaotic or rotating motion of the pendulum.

Synchronisation and Chaos in a Parametrically and Self-Excited System with Two Degrees of Freedom

Vibration analysis of a non-linear parametrically andself-excited system of two degrees of freedom was carried out. The modelcontains two van der Pol oscillators coupled by a linear spring with a aperiodically changing stiffness of the Mathieu type. By means of amultiple-scales method, the existence and stability of periodicsolutions close to the main parametric resonances have beeninvestigated. Bifurcations of the system and regions of chaoticsolutions have been found. The possibility of the appearance ofhyperchaos has also been discussed and an example of such solution hasbeen shown.

Modeling of high-speed milling process with frictional effect

This article deals with the problem of chatter vibrations in high-speed milling process taking into account both regeneration and frictional chatter. In this aim, a nonlinear model of high-speed down milling is developed. The proposed model includes friction force produced between an edge of a tool and a workpiece, modeled by nonlinear and nonsmooth function and also the time delay effect, which is responsible for a vibration regeneration. The influence of friction on the process stability is compared with results obtained in a classical way using a commercial software. Finally, numerical tests are compared with the stability lobe diagrams obtained experimentally during real machining of nickel superalloys.

Chatter control in the milling process of composite materials

In this paper, a model of the milling process of fibre reinforced composite material is shown. This classical one degree of freedom model of the milling process is adjusted for composite materials by variable specific cutting forces, which describe the fibre resistance. The stability lobe diagrams are determined numerically. Additionally, to eliminate the chatter vibration, small relative oscillations between the workpiece and the tool are introduced. Basing on numerical simulations the range of amplitude and the frequency of excitation is found for chatter reduction.

Active Vibration Control of a Nonlinear Beam with Self- and External Excitations

An application of the nonlinear saturation control (NSC) algorithm for a self-excited strongly nonlinear beam structure driven by an external force is presented in the paper. The mathematical model accounts for an Euler-Bernoulli beam with non- linear curvature, reduced to first mode oscillations. It is assumed that the beam vibrates in the presence of a harmonic excitation close to the first natural frequency of the beam, and additionally the beam is self-excited by fluid flow, which is modelled by a nonlinear Rayleigh term for self-excitation. The self- and externally excited vibrations have been reduced by the application of an active, saturation-based controller. The approximate analytical solutions for a full structure have been found by the multiple time scales method, up to the first-order approximation. The analytical solutions have been compared with numerical results obtained from direct integration of the ordinary differential equations of motion. Finally, the influence of a negative damping term and the controllers parameters for effective vibrations suppression are presented.

Autoparametric Vibrations of a Nonlinear System with a Pendulum and Magnetorheological Damping

The chapter deals with autoparametric vibrations of a system composed of a nonlinear oscillator with an attached pendulum. Dynamics of the mechanical structure is studied analytically around the principal parametric resonance region, numerically and experimentally for a wide range of parameters. The influence of damping, nonlinear stiffness (hard and soft), amplitude and frequency of excitation on the system’s behaviour is analysed in details. The obtained results show that the pendulum can be applied as a dynamical absorber. However, for selected parameters, near the main parametric resonance, instability, which transits the pendulum to chaotic oscillations or to a full rotation, occurs. Therefore, the application of a magnetorheological (MR) damper and a nonlinear spring is proposed to improve the dynamics and to control the response online. Periodic vibrations, chaotic motions or a full rotation of the pendulum obtained numerically are confirmed by the experiment. The chaotic nature of motion is determined from real signals by the attractor reconstruction and the recurrence plot calculation. The results show that the semi-active suspension may reduce dangerous motion and it also allows to maintain the pendulum at a given attractor or to jump to another one.

Nonlinear Vibrations of a Beam With a Tip Mass Attached to a Rotating Hub

A model of a light beam mounted to a rigid hub and forced by an external torque has been analysed in the paper. An additional loading caused by a small mass attached to the end of the beam and the influence of mass moment of inertia of the hub have been also taken into account. The motion of a flexible light beam is a composition of slewing motion and undesired vibrations, which can be crucial if the stiffness of the structure is not high, comparing to the external dynamical load. The nonlinear model of the beam proposed in [2], [3] have been applied to explain behaviour of the system. That model has taken into account bending, tension and a non-linear curvature, which differs the system from the classical approach [4] or the approach presented in [5] for large displacement of a beam model. The influence of the mass moment of inertia of the hub and the tip-mass is investigated in the paper. Differential equation of motion and dynamical boundary conditions are derived by applying the Hamilton’s principle whilst the reduced model have been obtained by virtue of the Galerkin’s procedure.Copyright