A geometrically nonlinear shear deformable beam model for piezoelectric energy harvesters

An electromechanical model for beam-like piezoelectric energy harvesters based on Reissner’s beam theory is developed in this paper. The proposed model captures first-order shear deformation and large displacement/rotation, which distinguishes this model from other models reported in the literature. All governing equations are presented in detail, making the associated framework extensible to investigate various piezoelectric energy harvesters. The weak formulation is then derived to obtain the approximate solution to the governing equations by the finite element method. This solution scheme is completely coupled, and thus allows for two-way interaction between mechanical and electrical fields. To validate this model, extensive numerical examples are implemented in the linear and nonlinear regime. In the linear limit, this model produces results in excellent agreement with reference data. In the nonlinear regime, the large amplitude response of the piezoelectric beam induced by strong base excitation or fluid flow is considered, and the comparison of results with literature data is encouraging. The ability of this nonlinear model to predict limit cycle oscillations in axial flow is demonstrated.

Nonlinear time series analysis of palaeoclimate proxy records

Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability.In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These includeapproaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling.Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5~million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series.We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate.Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone.