Toward Wideband Piezoelectric Harvesters Through Self-Powered Transitions to High-Energy Response

Convergence to low-energy responses arising from coexistence of multiple stable nodes is the main drawback of a nonlinear energy harvester preventing it from efficient wideband operation. A switching circuit with a boost-like topology has been proposed in this paper to overcome this substantial challenge. The circuit uses the energy harvested by the device to trigger it to jump from the low- to high-energy response. The performance of the proposed harvesting system when subjected to single harmonic excitations covering a wide range of frequencies is verified through both analytical and numerical investigations. Results indicate that by proper selection of timing parameters of the circuit including ON-time period of the switches together with the phase differences between the switching signals and the mechanical excitation, the applied electrical perturbation will be able to trigger the nonlinear resonating beam to jump from a low-energy response to the basin of attraction of the high-energy one within the whole frequency band in which a multivalued solution exists. Also, a probabilistic study is performed on a system with random phases of switching signals which shows that a successful switching from low- to high-energy response is achievable with a probability more than 80% by just controlling the ON-time period of the switch within the proper ranges with respect to the excitation frequency.

Stochastic inclusions and set-valued stochastic equations driven by a two-parameter Wiener process

In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations driven by a two-parameter Wiener process. We establish new connections between their solutions. We prove that attainable sets of solutions to such inclusions are subsets of values of multivalued solutions of associated set-valued stochastic equations. Next we show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. Additionally we establish other properties of such solutions. The results obtained in the paper extends results dealing with this topic known both in deterministic and stochastic cases.

Determining the Number of Inverse Kinematic Solutions of a Constrained Parallel Mechanism Using a Homotopy Algorithm

This paper numerically determines the number of real-valued inverse kinematic solutions to a constrained parallel mechanism composed of three triangular platforms. The base and middle platforms are connected by three fixed-length legs, while the middle and distal platforms are connected by three variable length legs that extend out of the fixed-length legs in a collinear fashion. All legs are connected to the platforms via spherical joints at the corners. This mechanism is intended to replicate the motion of a human shoulder girdle. The constrained parallel mechanism has a multivalued solution to the inverse kinematics problem. A homotopy method was used to numerically compute the inverse kinematic solutions for over 100 cases. Each case was filtered for the number of real-valued solutions. The maximum number of real solutions was found to be 8, but in some cases there were fewer solutions.

THE VLASOV–POISSON EQUATIONS AS THE SEMICLASSICAL LIMIT OF THE SCHRÖDINGER–POISSON EQUATIONS: A NUMERICAL STUDY

In this paper, we numerically study the semiclassical limit of the Schrödinger–Poisson equations as a selection principle for the weak solution of the Vlasov–Poisson in one space dimension. Our numerical results show that this limit gives the weak solution that agrees with the zero diffusion limit of the Fokker–Planck equation. We also numerically justify the multivalued solution given by a moment system of the Vlasov–Poisson equations as the semiclassical limit of the Schrödinger–Poisson equations.