Dynamic analysis of piezoelectric energy harvester under combination parametric and internal resonance: a theoretical and experimental study

In this work, theoretical and experimental analysis of a piezoelectric energy harvester with parametric base excitation is presented under combination parametric resonance condition. The harvester consists of a cantilever beam with a piezoelectric patch and an attached mass, which is positioned in such a way that the system exhibits 1:3 internal resonance. The generalized Galerkin’s method up to two modes is used to obtain the temporal form of the nonlinear electromechanical governing equation of motion. The method of multiple scales is used to reduce the equations of motion into a set of first-order differential equations. The fixed-point response and the stability of the system under combination parametric resonance are studied. The multi-branched non-trivial response exhibits bifurcations such as turning point and Hopf bifurcations. Experiments are performed under various resonance conditions. This study on the parametric excitation along with combination and internal resonances will help to harvest energy for a wider frequency range from ambient vibrations.

     

A combined experimental and computational studies of 3,3,6,6-Tetramethyl-9-(4-Methoxyphenyl)3,4,6,7,9,10 hexahydroacridine-1,8-dione

ABSTRACT

In this work, we have recorded the Fourier Transform Infrared (FTIR) and Ultra-Violet Visible (UV–Vis) spectra of 3,3,6,6-Tetramethyl-9-(4-Methoxyphenyl)3,4,6,7,9,10 hexahydroacridine-1,8-dione (C₂₄H₂₉NO₃) in the spectral range 4000–400?cm^?1 and 190–1400?nm, respectively. The thermo gravimetric (TG) analysis of the compound has been performed to check the thermal stability of the compound. The molecular geometry and complete vibrational spectra in the ground state are calculated by Hartree Fock (HF) and Density Functional Theory (DFT) using6-311G(d,p) basis set. The calculated vibrational harmonic frequencies are scaled using a proper scale factor, yielding a good agreement with the experimental data. Stability of the molecule arising from hyperconjugative interactions, charge delocalisation has been studied using natural bond orbital analysis (NBO). Mulliken charges, MEP mapping and temperature dependence on the thermodynamic properties in the optimised ground state have been calculated. UV–Visible spectrum of the molecule was calculated by using TD-DFT approach and the results were compared with the experimental one. We have calculated the several molecular parameters like ionisation potential, electron affinity, global hardness, electron chemical potential, electronegativity and global electrophilicity based on HOMO and LUMO energy values calculated at B3LYP/6-311G(d,p) level of theory. The calculated optimised structural parameters and vibrational wavenumbers are found to be in good agreement with the experimental results.     

Identifying the interacting positions of a protein using Boolean learning and support vector machines

It is known that in the three-dimensional structure of a protein, certain amino acids can interact with each other in order to provide structural integrity or aid in its catalytic function. If these positions are mutated the loss of this interaction usually leads to a non-functional protein. Directed evolution experiments, which probe the sequence space of a protein through mutations in search for an improved variant, frequently result in such inactive sequences. In this work, we address the use of machine learning algorithms, Boolean learning and support vector machines (SVMs), to find such pairs of amino acid positions. The recombination method of imparting mutations was simulated to create in silico sequences that were used as training data for the algorithms. The two algorithms were combined together to develop an approach that weighs the structural risk as well as the empirical risk to solve the problem. This strategy was adapted to a multi-round framework of experiments where the data generated in the present round is used to design experiments for the next round to improve the generated library, as well as the estimation of the interacting positions. It is observed that this strategy can greatly improve the number of functional variants that are generated as well as the average number of mutations that can be made in the library.     

Band head spin assignment of superdeformed bands in 86Zr

Two parameter expressions for rotational spectra viz. variable moment of inertia (VMI), ab formula and three parameter Harris ω² expansion are used to assign the band head spins (I₀) of four rotational superdeformed bands in ⁸⁶Zr. The least-squares fitting method is employed to obtain the band head spins of these four bands in the A~80 mass region. Model parameters are extracted by fitting of intraband γ-ray energies, so as to obtain a minimum root-mean-square (rms) deviation between the calculated and the observed transition energies. The calculated transition energies are found to depend sensitively on the assigned spins. Whenever an accurate band head spin is assigned, the calculated transition energies are in agreement with the experimental transition energies. The dynamic moment of inertia is also extracted and its variation with rotational frequency is investigated. Since a better agreement of band head spin with experimental results is found using the VMI model, it is a more powerful tool than the ab formula and Harris ω² expansion.     

Effect of silver nanoparticles on frequency and temperature-dependent electrical parameters of a discotic liquid crystalline material

The effect of silver nanoparticles (AgNPs) of diameters 6 and 100 nm on a discotic liquid crystalline material, namely 2,3,6,7,10,11-hexabutyloxytriphenylene (in short HAT4), has been observed in thermodynamic, electrical and optical texture studies. Silver nanoparticles (0.6 wt%) of diameter ~6 nm demonstrate a negligible (but ~100 nm shows appreciable) effect on the broad temperature range plastic columnar hexagonal (Col_hex) phase (~65.0°C) of pure HAT4. The dielectric studies have been carried out in the frequency range of 10 Hz–35 MHz under homeotropic anchoring conditions of the molecules. In the low frequency region of pure HAT4 and its AgNP composites, a relaxation mode has been observed. AgNPs of 6 nm elevate the value of dielectric permittivity of the plastic columnar hexagonal phase of pure HAT4. The dc conductivity of pure HAT4 and its AgNP composite (6 and 100 nm) material has been determined. The optical band gap for pure and AgNP composites of HAT4 has been determined by the ultraviolet-visible study. Due to insertion of AgNPs, the optical band gap of HAT4 has reduced.     

Electrical and electro-optical parameters of 4ʹ-octyl-4-cyanobiphenyl nematic liquid crystal dispersed with gold and silver nanoparticles

Thermodynamical, dielectric, optical and electro-optical characterisation of pure 8CB and its composites with gold and silver nanoparticles have been studied. Thermodynamical studies suggest a decrease in clearing temperature of the nanocomposite systems as compared to the pure system. Dielectric parameters of pure nematic liquid crystal and nanocomposites in the homeotropic and planar aligned samples have been measured in the frequency range of 1–35 MHz. Ionic conductivity increases significantly in nematic and smectic A_d (SmA_d) phases, whereas dielectric anisotropy is almost unchanged for both the nanocomposites. Threshold voltage for Freederick transition, switching voltage and splay elastic constant have decreased in the case of nanocomposite systems. Relaxation frequency and activation energy of an observed relaxation mode corresponding to molecular rotation about the short axis increase in the SmA_d phases of both the nanocomposites. The optical study suggests that due to dispersion of nanoparticles, the optical band gap has decreased.