Proceedings of the Institution of Mechanical Engineers,Part C: Journal of Mechanical Engineering Science

Nonlinear dynamic interactions in harbour quayside cranes due to a two-to-one internal resonance between the lowest bending mode of the deformable boom and the in-plane pendular mode of the container are investigated. To this end, a three-dimensional model of container cranes accounting for the elastic interaction between the crane boom and the container dynamics is proposed. The container is modelled as a three-dimensional rigid body elastically suspended through hoisting cables from the trolley moving along the crane boom modelled as an Euler-Bernoulli beam. The reduced governing equations of motion are obtained through the Euler-Lagrange equations employing the boom kinetic and stored energies, derived via a Galerkin discretisation based on the mode shapes of the two-span crane boom used as trial functions, and the kinetic and stored energies of the rigid body container and the elastic hoisting cables. First, conditions for the onset of internal resonances between the boom and the container are found. A higher order perturbation treatment of the Taylor expanded equations of motion in the neighbourhood of a two-to-one internal resonance between the lowest boom bending mode and the lowest pendular mode of the container is carried out. Continuation of the fixed points of the modulation equations together with stability analysis yields a rich bifurcation behaviour, which features Hopf bifurcations. It is shown that consideration of higher order terms (cubic nonlinearities) beyond the quadratic geometric and inertia nonlinearities breaks the symmetry of the bifurcation equations, shifts the bifurcation points and the stability ranges, and leads to bifurcations not predicted by the low order analysis.

The paper considers dynamic response of primary linear oscillator with nonlinear energy sink (NES) that comprises purely cubic oscillator with internal rotator. It is demonstrated that this NES exhibits enhanced mitigation capabilities and, in particular, remains efficient for much broader range of initial energies as compared to regular cubic NES with the same mass. This enhanced performance is related to very special response regime revealed in “detached” cubic-rotatory NES and referred to as “amplitude locking”. In this regime, the amplitude of the oscillator remains independent on frequency of the system for very broad frequency range. This phenomenon is explored analytically and numerically, and possible applications are discussed.

The vibrations of beams with a breathing crack are investigated taking into account geometrical non-linear effects. The crack is modeled via a function that reduces the stiffness, as proposed by Christides and Barr (One-dimensional theory of cracked Bernoulli–Euler beams. Int J Mech Sci 1984). The bilinear behavior due to the crack closing and opening is considered. The equations of motion are obtained via a p-version finite element method, with shape functions recently proposed, which are adequate for problems with abrupt localised variations. To analyse the dynamics of cracked beams, the equations of motion are solved in the time domain, via Newmark's method, and the ensuing displacements, velocities and accelerations are examined. For that purpose, time histories, projections of trajectories on phase planes, and Fourier spectra are obtained. It is verified that the breathing crack introduce asymmetries in the response, and that velocities and accelerations can be more affected than displacements by the breathing crack.

The assumed-modes method is applied to obtain the dynamical model of the ring-stiffened conical shells in a supersonic gas stream. The pressure acting on the shell is described by the piston theory. The displacements of the rings are functions of the shell displacements. The kinetic and the potential energies of the structure are obtained as the functions of the shell displacements. It is suggested the approach to calculate the shell spatial mode, when the shell dynamic stability is lost. The free vibrations of the structures with different numbers of the rings are analyzed. The loss of the structure dynamic stability is investigated.

The compliant tilting pad air bearing concept, a tilting pad bearing with the pivot of the pads placed on radial springs, is a promising aerodynamic bearing solution. Nevertheless, its non-linear dynamics make a time domain dynamic simulation model an essential tool for the design of rotor systems with these bearings. Development of these dynamic simulation models is the subject of this paper that provides a detailed description of an extendible model of the compliant tilting pad air bearing concept suitable for non-linear time domain analysis. 2D and 3D time domain simulations implementing the model are discussed in detail and some of their capabilities to model the non-linear behaviour of the bearing concept are demonstrated with examples.

In this work, the large amplitude vibration of a heated Timoshenko composite beam having delamination is studied. The model of delamination considers the contact interaction between sublaminates including normal forces, shear forces, and additional damping due to the interaction of sublaminates. This work is an extension of the previous analysis based on a model of the dynamic behavior of a beam with delamination considering additionally the nonlinearities due to large displacements and temperature changes. Numerical calculations are performed in order to estimate the influence of the delamination, the geometrically nonlinear terms, and elevated temperature on the response of the beam.

In the recent years, functionally gradient materials (FGMs) have gained considerable attention with possible applications in several engineering fields, especially in a high-temperature or hazardous environment. In this work, the nonlinear vibrations of a simply supported fluid-filled functionally graded cylindrical shell subjected to a lateral time-dependent load and axial static preload are analyzed. To model the shell, the Donnell nonlinear shell theory is used. The fluid is assumed to be incompressible, nonviscous, and irrotational. A new function to describe the variation in the volume fraction of the constituent material through the shell thickness is proposed, extending the concept of sandwich structures to a functionally graded material. Material properties are graded along the shell thickness according to the proposed volume fraction power law distribution. A consistent reduced order model derived from a perturbation technique is used to describe the displacements of the shell and, the Galerkin method is applied to derive a set of coupled nonlinear ordinary differential equations of motion. Results show the influence of the variation of the two constituent materials along the shell thickness, internal fluid, static preload, and shell geometry on the natural frequencies, nonlinear frequency–amplitude relation, resonance curves, and bifurcation scenario of the FG cylindrical shell.

The nonlinear dynamics of a shape memory oscillator (SMO) subjected to an ideal or nonideal excitation is studied. The restoring force of the oscillator is provided by a shape memory device (SMD), described by a thermomechanical model capable of reproducing the hysteretic behavior via the evolution of a suitable internal variable. Due to nonlinearities in the model, the SMO can exhibit periodic or non-periodic behaviors. The effects of the external sources on the response of SMO are studied through the scalogram analysis of continuous wavelet transform by using a new measure, called the Scale index (Benitez R, Bolos VJ and Ramirez ME. A wavelet-based tool for studying non-periodicity. Comput Math Appl 2010; 60: 634–641). Numerical results show that the Scale index can successfully detect the behavior of the system when the signal is periodic or nonperiodic, and distinguish between them in a way consistent with the indications provided by the alternative 0-1 test.

Regenerative chatter is a well-known form of self-excited vibration that limits the productivity of machining operations, in particular for milling. Variable helix tools have been previously proposed as a means of avoiding regenerative chatter, and although recent work has analysed the stability of such tools there has not always been a strong agreement with experimentally observed behaviour. Furthermore, the analysis of variable helix tool stability can be tedious and numerically slow, compared to standard tools. Consequently it has been difficult to gain insight into the potential advantages of variable helix tools. The present work attempts to address these issues, by first developing an efficient approach to variable helix tool stability based upon the Laplace transform. Then, this new analysis method is used to demonstrate the importance of multi-frequency effects and nonlinear cutting stiffness. The work suggests that whilst variable-helix tools can have more operating regions that are stable, un-modelled behaviour (such as nonlinearity and multi-frequency effects) can have a critical influence on the accuracy of model predictions.