Avoiding/inducing dynamic buckling in a thermomechanically coupled plate: a local and global analysis of slow/fast response.

The nonlinear response of a reduced model of an orthotropic single-layered plate with thermomechanical coupling is investigated in the presence of thermal excitations, in addition to mechanical ones. Different issues are addressed via accurate and extended local and global analyses. (i) Assessing the possible occurrence, disappearance or modification of mechanical buckling as a result of thermal aspects; (ii) exploiting global dynamics to unveil the effects of coupling; (iii) highlighting the crucial role played by the slow thermal transient evolution in modifying the fast steady mechanical response; (iv) framing the influence of coupling and underlining the need to use a thermomechanical model to grasp the actual plate dynamics; and (v) getting hints of technical interest as to the outcome robustness with respect to variations in the external/internal thermal parameters.

Axial-transversal coupling in the free nonlinear vibrations of Timoshenko beams with arbitrary slenderness and axial boundary conditions.

The nonlinear free oscillations of a straight planar Timoshenko beam are investigated analytically by means of the asymptotic development method. Attention is focused for the first time, to the best of our knowledge, on the nonlinear coupling between the axial and the transversal oscillations of the beam, which are decoupled in the linear regime. The existence of coupled and uncoupled motion is discussed.

The dynamical integrity concept for interpreting/ predicting experimental behaviour: from macro- to nano-mechanics.

The dynamical integrity, a new concept proposed by J.M.T.

Controlling practical stability and safety of mechanical systems by exploiting chaos properties.

In this paper, a method for controlling the global nonlinear dynamics of mechanical systems is applied to two models: the model of Augusti and an inverted guyed pendulum. These simplified models represent a large class of structures liable to buckling exhibiting interacting buckling phenomena. These structures may fail at load levels well below the theoretical buckling load due to complex nonlinear phenomena that decrease the safety and the dynamic integrity of the structure; this often occur as a consequence of imperfections and of the erosion of the basins of attraction of the safe pre-buckling solutions.

Introduction to the focus issue: fifty years of chaos: applied and theoretical.

The discovery of deterministic chaos in the late nineteenth century, its subsequent study, and the development of mathematical and computational methods for its analysis have substantially influenced the sciences. Chaos is, however, only one phenomenon in the larger area of dynamical systems theory. This Focus Issue collects 13 papers, from authors and research groups representing the mathematical, physical, and biological sciences, that were presented at a symposium held at Kyoto University from November 28 to December 2, 2011.

Optimal control and anti-control of the nonlinear dynamics of a rigid block.

This paper deals with control and anti-control of overturning of a rigid block subjected to a generic periodic excitation. Attention is focused on two relevant thresholds, corresponding to heteroclinic bifurcation and immediate overturning, and representing lower and upper bounds of the region where toppling can occur. The two opposite problems of increasing (control) or decreasing (anti-control) of these two curves by properly modifying the shape of the excitation are investigated in depth and the optimal excitations permitting their maximum variations are determined.