Extremely Large Oscillations of Cantilevers Subject to Motion Constraints

The nonlinear extremely large-amplitude oscillation of a cantilever subject to motion constraints is examined for the first time. In order to be able to model the large-amplitude oscillations accurately, the equation governing the cantilever centerline rotation is derived. This allows for analyzing motions of very large amplitude even when tip angle is larger than π/2. The Euler–Bernoulli beam theory is employed along with the centerline inextensibility assumption, which results in nonlinear inertial terms in the equation of motion. The motion constraint is modeled as a spring with a large stiffness coefficient. The presence of a gap between the motion constraint and the cantilever causes major difficulties in modeling and numerical simulations, and results in a nonsmooth resonance response. The final form of the equation of motion is discretized via the Galerkin technique, while keeping the trigonometric functions intact to ensure accurate results even at large-amplitude oscillations. Numerical simulations are conducted via a continuation technique, examining the effect of various system parameters. It is shown that the presence of the motion constraints widens the resonance frequency band effectively which is particularly important for energy harvesting applications.

Improved Boosting Model for Unsteady Nonlinear Aerodynamics based on Computational Intelligence

The large-amplitude-oscillation experiment was carried out with two levels of freedom to provide data. Based on the wind tunnel data, polynomial regression, least-square support vector machines and radial basis function neural networks are studied and compared in this paper. An improved model was also developed in this work for unsteady nonlinear aerodynamics on the basis of standard boosting approach. The results on the wind tunnel data show that the predictions of the method are almost consistent with the actual data, thus demonstrating that these methods can model highly nonlinear aerodynamics. The results also indicate that improved boosting model has better accuracy than the other methods.

Rheological Behavior of Polystyrene-Based Nanocomposite Suspensions under LAOS

Polymer nanocomposites based on polyhedral oligomeric silsesquioxanes (POSS) and their solutions and suspensions are promising systems for fundamental research which could potentially utilize self-assembly approach in designing new nanocomposite materials. Numerous applications could benefit from understanding of these systems, for instance polymer solution based paints and varnishes. This work is an initial stage of a study which aim is to link macroscale thermomechanical properties with nanoscale structures found in polymer nanocomposites. To do so, a suitable experimental protocol for preparing differently organized NPs in polymer matrix has to be find first in which both kinetic and thermodynamical parameters should be taken into account, i.e. solution casting has being investigated. The results presented here found differences between nanoparticle induced changes on rheological behavior of polystyrene solution under large amplitude oscillation shear (LAOS). High-affinity OP-POSS NPs seem to interact with PS at low loadings and form stiffened aggregates, whereas low-affinity OM-POSS NPs remained rather uninvolved. Effect of hydrodynamic forces independent of the NPs chemical nature was also observed.

Normal form method for large/small amplitude instability criterion with application to wheelset lateral stability

Subcritical and supercritical bifurcations are two typical behaviors that exist in high speed railway vehicles. In the presence of instability, the former and the latter behaviors may lead to large amplitude oscillation and small amplitude swaying, respectively. The normal form (NF) method of Hopf bifurcation provides a way to study the supercritical and subcritical bifurcation. The wheelset is a key component in the vehicle system and it plays an important role in vehicle lateral stability. To study the lateral stability problems, three wheelset models are considered, which involve the NF theory. This method is an algebraic approach as opposed to the integration approach. Like the sign of Re (λ) that determines the stability of linear system, the sign of Re c1(0) determines the two bifurcation modes, meaning that Re c1(0) > 0 for supercritical bifurcation and Re c1(0) < 0 for subcritical bifurcation. Furthermore, if the ordinary differential equation (ODE) is local linear near the equilibrium position, it leads to the condition of Re c1(0) = 0, resulting in the jumping phenomenon. Besides, the expression of the 1/2-order approximation of limit cycle can be further obtained.