In this paper, we present the benefits of bond-graph analysis for mechanical-electrical systems, which are energy-harvesters based on structural vibrations and electric loads. The bond-graph is an energy-based approach to describing physical-dynamic systems. It shows power flow graphically, which helps us understand the behavior of complicated systems in simple terms. Energy-harvesting involves conversion of power in mechanical form to the electrical one and the bond-graph is a good tool to analyze this flow. The bond-graph method can be used to calculate the dynamics of the combining mechanical and electrical systems simultaneously. The biggest advantage of the bond-graph technique is that it can be used with the systems that are subject to component alternations, such as inserting, removing and swapping. The bond-graph method involves solving simultaneous algebraic equations, instead of differential equations. On the other hand, in common simulation methods, such as solving differential equations, it is difficult to change the number of components because the differential equations will have to be reconstructed. Because the bond-graph has not been used for harvesting analysis, bond-graph models for harvesting need to be created in advance of numerical analysis. In this paper, we first proposed a piezoelectric model that matches the bond-graph method. We also propose a diode-bridge model and a harvesting controller model that are suitable for bond-graph analysis. We then analyze a self-powered energy harvester that has multi-bifurcated and looped flow in the mechanical-electrical coupled dynamics.

Photonic crystals are widely employed in industry fields due to their bandgap property, which can confine and propagate electromagnetic waves inside the structure as a photonic waveguide. As this property can be adopted to propagate distinct frequency waves by changing the photonic structure, photonic crystals are also applied in frequency demultiplexer design. The finite-difference time-domain (FDTD) method is commonly applied to simulate electromagnetic wave propagations in photonic crystals, helping determine the desired bandgaps for frequency demultiplexers. Meanwhile, the multivariate empirical mode decomposition (MEMD) nonlinearly decomposes multivariate signals in the instantaneous frequency domain. Therefore, MEMD can verify and visualize the designed frequency demultiplexer made of photonic crystals by considering simulation results as a multi-channel signal. This research aims to propose a method to design and evaluate frequency demultiplexers using FDTD and MEMD. In this paper, photonic crystal bandgaps are adopted to design a frequency demultiplexer to separate two different frequency electromagnetic waves. Then, MEMD is employed to the result of frequency demultiplexer propagation simulated by FDTD. Our results reveal that the frequency demultiplexer made of photonic crystals can be designed using the bandgap properties, and its simulation results by FDTD method can be verified and visualized in the instantaneous frequency domain using MEMD.

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