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In this paper, the Nonlinear Normal Modes (NNMs) analysis for the case of three-to-one (3:1) internal resonance of a slender simply supported beam in presence of compressive axial load resting on a nonlinear elastic foundation is studied. Using the EulerBernoulli beam model, the governing nonlinear PDE of the beam's transverse vibration and also its associated boundary conditions are extracted. These nonlinear motion equation and boundary condition relations are solved simultaneously using four different approximate-analytical solution techniques, namely the method of Multiple Time Scales, the method of Normal Forms, the method of Shaw and Pierre, and the method of King and Vakakis. The obtained results at this stage using four different methods which are all in time-space domain are compared and it is concluded that all the methods result in a similar answer for the amplitude part of the transverse vibration. At the next step, the nonlinear normal modes are

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With the revolution in power generation and the development of electrification, portable electronic gadgets have recently posed escalating needs for suitable energy storage applications. The lithium-ion battery (LIB) is an electrochemical energy storage device that can achieve high energy density while retaining high power density. Here, we build a high energy density LIB module with a ~12.10% increase in energy density over the previous cell. For environmental and safety reasons, several design elements such as electrode thickness, porosity, current density, and particle size were iterated to improve specific capacity and energy density without changing the ambient temperature increment. We have used a simple heat generation system; the temperature raised by ~18.96% from the room environment was close to 29.74 °C. The specific capacity was also improved by ~14.56% as compared to commercial LIB. Besides, we used the gassing and plating methods to reduce the integrated Li-ion loss for both the cathode and anode. All of the remarkable findings in this work will aid in the optimization and design of next-generation LIB cells.

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