Vibrational Basis Research Articles

Review of vibration‐based electromagnetic–piezoelectric hybrid energy harvesters

SummaryThese days the health monitoring of machines and structures is performed using wireless sensor nodes (WSNs). The disadvantage of short life span of batteries in WSN is overcome by using energy harvesting techniques and the required power is extracted from the environment for operating WSNs. The energy available in environment is in the form of thermal, solar, wind, vibration, RF and acoustic energy. The Piezoelectric (PE), electromagnetic (EM), electrostatic and triboelectric transduction may be utilized to harvest power from vibration energy available on structure which otherwise may be going waste. Moreover, for enhancing power generation hybrid vibration energy harvesters are developed by combining two of such transduction mechanisms. The piezoelectric and electromagnetic based hybrid harvesters are discussed in this work for vibration energy harvesting. The hybrid vibration energy harvesters are classified here as resonant, frequency tuned, nonlinear, non‐resonant, multi‐mode and frequency up conversion harvesters. The architecture, input excitation levels and performance of the reported hybrid harvesters is discussed and compared to know the advantage of harvester's configuration. Moreover, all the reported harvesters are compared on the basis of input vibration to which these harvesters are subjected, their resonant frequencies, size, output voltage, power levels and power density. Most of the developed hybrid energy harvesters are resonant harvesters. The multi‐mode hybrid energy harvesters are generating comparatively higher power levels of up to 250.25 mW and power density 2669.3 µW/cm3 in the reported literature. The overall voltage and power generation range of the hybrid harvesters is from 0.131 mV to 26 V and 0.637 µW to 250.25 mW. Moreover, the power density for the reported energy harvesters is in the range from 1.96 µW/cm3 to 2669 µW/cm3.

Simulation of the Conveying Speed on Vibration Conveyors Using 1D-Mechanical Modules in SimulationX

Vibration conveyors are technical systems which generate a stream of materials on basis of vibrations. The vibrations lead to continuous change between acceleration forces and friction. In the practical operation high conveying speeds shall be accomplished with a defined use of the driving force. In this article a simulation model in the software SimulationX is introduced which utilities basic mechanical correlations to calculate the conveying speed. With the help of the presented model influences of vibration movement curve on the conveying speed can be portrayed and analyzed.

Molecular second-quantized Hamiltonian: Electron correlation and non-adiabatic coupling treated on an equal footing.

We introduce a new theoretical and computational framework for treating molecular quantum mechanics without the Born-Oppenheimer approximation. The molecular wavefunction is represented in a tensor-product space of electronic and vibrational basis functions, with electronic basis chosen to reproduce the mean-field electronic structure at all geometries. We show how to transform the Hamiltonian to a fully second-quantized form with creation/annihilation operators for electronic and vibrational quantum particles, paving the way for polynomial-scaling approximations to the tensor-product space formalism. In addition, we make a proof-of-principle application of the new Ansatz to the vibronic spectrum of C2.

Crystal structure and spectroscopy studies of the thulium acid pyrophosphate HTmP2O7·3H2O

Crystals of HTmP2O7·3H2O were prepared via a soft chemistry route. Its crystal structure was solved from single-crystal diffraction data. The compound crystallises in the triclinic space group P-1, with the unit cell parameters: a = 6.3724(4) Å, b = 6.8224(3) Å, c = 9.7299(5) Å, α = 82.039(4) °, β = 79.758(5) °, γ = 88.200(4) ° and Z = 2. In its lamellar structure, edge-sharing polyhedra of eightfold coordinated Tm(III) form chains along [010]. These chains are joined in turn to each other using pyrophosphates O-P-O bridges. A network of OH…O hydrogen bonds reinforces the cohesion of the structure. The IR spectrum of HTmP2O7·3H2O is interpreted on the basis of characteristic vibrations of PO3 group, POP bridge, and in addition, H2O. The optical properties of HTmP2O7·3H2O were analysed with UV–Vis. The spectrum is characterized by bands corresponding to the transitions starting from the 3H6 ground state to the different higher levels 1G4, 3F2, 3F3, 3H5, and 3F4 of Tm3+ ion.

Compact Bases for Vibronic Coupling in Spectral Simulations: The Photoelectron Spectrum of Cyclopentoxide in the Full 39 Internal Modes.

We report an algorithm to automatically generate compact multimode vibrational bases for the Köppel-Domcke-Cederbaum (KDC) vibronic coupling wave function used in spectral simulations of moderate-sized molecules. As a full quantum method, the size of the vibronic expansion grows exponentially with respect to the number of vibrational modes, necessitating compact bases for moderate-sized systems. The problem of generating such a basis consists of two parts: one is the choice of vibrational normal modes, and the other is the number of phonons allowed in each mode. A previously developed final-state-biased technique addresses the former part, and this work focuses on the latter part: proposing an algorithm for generating an optimal phonon distribution. By virtue of this phonon distribution, compact and affordable bases can be automatically generated for systems with on the order of 15 atoms. Our algorithm is applied to determine the nonadiabatic photoelectron spectrum of cyclopentoxide in the full 39 internal modes.

OM, SEM-EDX, and micro-FTIR analysis of the Bronze Age pottery from the Băile Figa salt production site (Transylvania, Romania).

This article presents the results of analyses carried out on a lot of 11 fragments of Bronze Age ceramics discovered in the site from Băile Figa (Beclean town, Transylvania, Romania), where salt exploitation occurred. The samples were analyzed by means of optical microscopy, on the basis of which the morphology and distribution of the inclusions in the ceramic paste was established. Likewise, the samples were analyzed by scanning electron microscopy with energy-dispersive X-ray spectrometry, producing microphotographs for each sample, and on the basis of the X-ray spectra, the elemental composition in gravimetric percentages was established. Through the micro-Fourier-transform infrared spectroscopy analysis, on the basis of characteristic group vibrations, it was possible to ascertain the nature of the compounds from the ceramic samples. These analyses will contribute to the reconstruction of the prehistoric technologies for salt exploitation.

Dissociative Recombination of Cold HeH^{+} Ions.

The HeH^{+} cation is the simplest molecular prototype of the indirect dissociative recombination (DR) process that proceeds through electron capture into Rydberg states of the corresponding neutral molecule. This Letter develops the first application of our recently developed energy-dependent frame transformation theory to the indirect DR processes. The theoretical model is based on the multichannel quantum-defect theory with the vibrational basis states computed using exterior complex scaling of the nuclear Hamiltonian. The abinitio electronic R-matrix theory is adopted to compute quantum defects as functions of the collision energy and of the internuclear distance. The resulting DR rates are convolved over the beam energy distributions relevant to a recent experiment at the Cryogenic Storage Ring, giving good agreement between the experiment and the theory.

Using computed infrared intensities for the reduction of vibrational configuration interaction bases.

The Adaptive Vibrational Configuration Interaction (A-VCI) algorithm is an iterative process that computes the anharmonic spectrum of a molecule using nested bases to discretize the Hamiltonian operator. For large molecular systems, the size of the discretization space and the computation time quickly become prohibitive. It is therefore necessary to develop new methods to further limit the number of basis functions. Most of the time, the interpretation of an experimental infrared spectrum does not require the calculation of all eigenvalues but only those corresponding to vibrational states with significant intensity. In this paper, a technique that uses infrared intensities is introduced to select a subset of eigenvalues to be precisely calculated. Thus, we build smaller nested bases and reduce both the memory footprint and the computational time. We validate the advantages of this new approach on a well-studied 7-atom molecular system (C2H4O), and we apply it on a larger 10-atom molecule (C4H4N2).

A quantum-mechanical tier model for phonon-driven vibrational relaxation dynamics of adsorbates at surfaces.

We present a quantum-mechanical tier model for vibrational relaxation of low-lying excited states of an adsorbate vibrational mode (system), coupled to surface phonons (bath), at zero temperature. The tier model, widely used in studies of intramolecular vibrational energy redistribution in polyatomics, is adapted here to adsorbate-surface systems with the help of an embedded cluster approach, using orthogonal coordinates for the system and bath modes, and a phononic expansion of their interaction. The key idea of the model is to organize the system-bath zeroth-order vibrational space into a hierarchical structure of vibrational tiers and keep therein only vibrational states that are sequentially generated from the system-bath initial vibrational state. Each tier is generated from the previous one by means of a successor operator, derived from the system-bath interaction Hamiltonian. This sequential procedure leads to a drastic reduction of the dimension of the system-bath vibrational space. We notably show that for harmonic vibrational motion of the system and linear system-bath couplings in the system coordinate, the dimension of the tier-model vibrational basis scales as ∼Nl×υ. Here, N is the number of bath modes, l is the highest-order of the phononic expansion, and υ is the size of the system vibrational basis. This polynomial scaling is computationally far superior to the exponential scaling of the original zeroth-order vibrational basis, ∼MN, with M being the number of basis functions per bath mode. In addition, since each tier is coupled only to its adjacent neighbors, the matrix representation of the system-bath Hamiltonian in this new vibrational basis has a symmetric block-tridiagonal form, with each block being very sparse. This favors the combination of the tier-model with iterative Krylov techniques, such as the Lanczos algorithm, to solve the time-dependent Schrödinger equation for the full Hamiltonian. To illustrate the method, we study vibrational relaxation of a D-Si bending mode, coupled via two- and (mainly) one-phonon interactions to a fully D-covered Si(100)-(2 × 1) surface, using a recent first-principles system-bath Hamiltonian. The results of the tier model are compared with those obtained by the Lindblad formalism of the reduced density matrix. We find that the tier model provides much more information and insight into mechanisms of vibration-phonon couplings at surfaces, and gives more reliable estimates of the adsorbate vibrational lifetimes. Moreover, the tier model might also serve as a benchmark for other approximate quantum-dynamics methods, such as multiconfiguration wavefunction approaches.

The development and optimization of an innovative piezoelectric energy harvester on the basis of vapor-induced vibrations

• Optimization for harvester based on the vibration induced by vapor flow. • The vapor flows over the harvester resulted in 60 Hz of periodicity vibration. • GA method used to optimize harvester dimensions for achieving 60 Hz. • The optimized and simulated results were verified by experiment. • Maximum output power occurred at resonance of vortex vibration and harvester. Various energy harvesters were developed by several energy sources. In the heat pipe, the vapor momentum can be used to drive a mechanical structure to generate electricity. To bridge this gap, this study experimentally designed an energy harvester on the basis of a vapor-induced vibration for the innovative heat pipe application. The energy harvester, comprising a cantilever beam and polyvinylidene fluoride (PVDF), was designed using finite element method and the genetic algorithm (GA) to reach the resonance point. Copper, aluminum, and polyethylene (PE) were used as the material of the cantilever beam for the energy harvester. The optimized energy harvester was examined using a shocker, and obtained the output voltage. The output power of the harvester was affected by the vapor velocity, cantilever beam material, and natural frequency. The output voltages of the PVDF with the cantilever beam are better than the one of PVDF without the cantilever beam and it increased 367%, 393%, and 470%ascantilever beam is copper, aluminum, and polyethylene, respectively. The theoretical and practical implication, limitations of the present study for future studies are presented and studied.

Combined photoluminescence and Raman microscopy for the identification of modern pigments: explanatory examples on cross-sections from Russian avant-garde paintings

In conservation science, the identification of painting materials is fundamental for the study of artists’ palettes, for dating and for understanding on-going degradation phenomena. For these purposes, the study of stratigraphic micro-samples provides unique information on the complex heterogeneity of the pictorial artworks. In this context, we propose a combined-microscopy approach based on the application of time-resolved photoluminescence (TRPL) micro-imaging and micro-Raman spectroscopy. The TRPL device is based on pulsed laser excitation (excitation wavelength = 355 nm, 1 ns pulse width) and time-gated detection, and it is suitable for the detection of photoluminescent emissions with lifetime from few nanoseconds to hundreds of microseconds. In this work, the technique is beneficially applied for identifying different luminescent semiconductor and mineral pigments, on the basis of their spectral and decay kinetic emission properties. The spatial heterogeneities, detected in the micro-sample, are investigated with Raman spectroscopy (785-nm in CW mode) for a further identification of the paint composition on basis of the molecular vibrations associated with the crystal structure. The effectiveness and limits of the proposed combined method is discussed through analysis of a corpus of stratigraphic micro-samples from Russian Avant-garde modern paintings. In the selected samples, the method allows the identification of modern inorganic pigments such as cadmium-based pigments, zinc white, titanium white, chrome yellow, ultramarine and cinnabar.

Possible low-energy isomers of OHn(H2O)4 (n = 0, ±1) clusters via the particle swarm optimization algorithm: An ab initio study

The possible low-energy structures of the anionic, neutral, and cationic water clusters OHn(H2O)4 (n = 0, ±1) were investigated using the particle swarm optimization algorithm together with ab initio calculations. Geometry optimization and vibrational analysis for possible low-lying water clusters were conducted at the MP2/aug-cc-pVDZ level and further verified at the CCSD(T)/aug-cc-pVTZ level. The results revealed obvious structural differences between the OH+(H2O)4, OH(H2O)4, and OH−(H2O)4 clusters. We found that correcting for the zero-point vibrational energies and basis set superposition error exerted a substantial influence on the order of relative energies for the OH−(H2O)4 and OH+(H2O)4 clusters. Topological analysis revealed that both the number and strength of hydrogen bonds were greater for the OH−(H2O)4 cluster compared with the OH+(H2O)4 and OH(H2O)4 clusters. The highest occupied molecular orbitals (HOMOs) of the anionic OH−(H2O)4 cluster were mainly located on the OH− ion and the HOMO-1s and HOMO-2s levels were mainly located on the H2O molecules, whereas in the neutral OH(H2O)4 and cationic OH+(H2O)4 clusters, the singly occupied molecular orbitals mainly originated from the water molecules.

Analysis of Vibration During Turning Process of Different Materials

In this article, we would like to introduce the problems caused by vibrations in case of polymer turning processes. Nowadays there is a lot of research in this topic, to avoid the unnecessary phenomena of vibrations. The two most common methods are the Spindle Speed Variation (SSV), and the Vibration Assisted Machining (VAM). In case of SSV, the CNC machine can increase and decrease the speed of spindle continuously during turning which can significantly reduce the effects of chatter. This method is beneficial for longer workpieces when there is not any support except the chuck. Vibration-assisted machining can be used to minimise the problems caused by vibrations. VAM combines precision machining with small-amplitude tool vibration to improve the fabrication process. It has been applied to some processes ranging from turning, drilling to grinding. Based on the enumerated above we made some trial measurements about the basic vibrations of the turning tool shank. The tests were done on an NCT EUROturn-12B CNC machine which can found in the workshop of our institute. The tested material was Polyamide 6 because this is the most commonly used polymer in the industry. In the future, we would like to test some other basic and composite polymer materials too. The equipment was served by a specialist from SPM Budapest Kft. With these tests, our goal was to make sure that the equipment and the measuring setup are suitable for our future research.

A four-dimensional Numerov approach and its application to the vibrational eigenstates of linear triatomic molecules – The interplay between anharmonicity and inter-mode coupling

An adapted formulation of the grid-based Numerov approach to solve Schrödinger’s equation has been extended to four-dimensional systems and applied to problems in vibrational spectroscopy. The advantage of this novel implementation is that no approximations or assumptions with respect to the wavefunctions are required and the achieved accuracy at a given stencil size is only limited by the selected grid-spacing. To validate this approach the vibrational eigenstates and the corresponding wavenumbers of the linear molecules CO2, BeH2 and HCN were investigated. Based on a potential energy grid at CCSD(T)/cc-pVnZ (n = T, Q) level all fundamental wavenumbers could be reproduced with deviations of less than 1% of the experimental values. Furthermore, the hierarchical application of a one- to four-dimensional Numerov treatment provides detailed information about the increasing influence of inter-mode coupling in addition to the inherent account for anharmonic contributions. The associated vibrational states are eigenfunctions of the Numerov matrix eigenvalue problem. Since no vibrational basis functions have to be applied in this approach, the respective eigenstates are characterized using isosurfaces of the wavefunctions in the hyperplane x4=0. This enables the direct examination of the individual wavefunctions via suitable visualization tools and the assignment of the respective vibrational quantum numbers.

CHF3…H2O complex revisited: a matrix isolation and ab initio study

The structural and spectroscopic features of the CHF3…H2O complex have been investigated using high-level ab initio calculations and IR matrix isolation spectroscopy. In contrast to previous findings, the computations at the CCSD(T)/L3a_3 and MP2/L3a_3 levels of theory revealed only one structure of the complex stabilized by two C-H…O and O-H…F hydrogen bonds. The interaction energy extrapolated to a complete basis set with ZPVE and BSSE corrections is 2.73 kcal/mol at the CCSD(T) level, taking into account the zero-point vibrational energy (ZPVE) and basis set superposition error (BSSE) corrections. According to Bader’s analysis, complex exhibits a cyclic structure, which confirms the existence of ring critical point as well as bond critical points in the system. The calculated complexation-induced shifts of the fluoroform fundamentals are in good agreement with the matrix isolation results. In addition to previously reported IR absorptions of the complex, the feature corresponding to the C-F bending mode of CHF3…H2O was first observed, in good correlation with the computational predictions.

Study on the broadband piezoelectric ceramic transducer based on radial enhanced composite structure

A new type of broadband piezoelectric ceramic transducer is developed and analyzed. The transducer is composed of two radial enhanced composite vibrators with different resonance frequencies stacked along the axial direction. Each vibrator consists of a piezoelectric ceramic stack polarized in the thickness direction and a metal tube, and they are connected and excited to vibrate in the radial direction. On the basis of the radial vibrations of the piezoelectric ceramic thin ring and the metal tube, the electromechanical equivalent circuit of the transducer is derived and the input impedance of the transducer is obtained. The relationship between the resonance frequency and the geometrical dimensions of the transducer is analyzed. The new type of transducer is simulated using the ANSYS software. The simulated resonance frequencies of the transducer are in good agreement with the theoretical results. The transducer exhibits broadband characteristics because of the double stacking of vibrators with different resonance frequencies, and the transducer can be driven under high power because of its radial enhanced composite structure.

Application of the finite segment method to stabilisation of the force in a riser connection with a wellhead

This paper presents a spatial model of riser dynamics formulated using the segment method and its applications. The model has been validated by comparison of the authors’ own results with those obtained from experimental measurements and Abaqus on the basis of forced vibration with large amplitude for the riser submerged in water. The influence of the sea environment is considered. Correctness and numerical effectiveness of the model enable us to formulate and solve the force stabilisation problem. A dynamic optimisation problem is formulated and solved. As a result vertical courses of movement of the upper end of the riser are obtained which compensate the horizontal movement of the base and stabilise the force in the connection of the riser with a wellhead.

Symmetry analysis of trimers rovibrational spectra: the case of Ne3

An approximate method to assign the symmetry to the rovibrational spectrum of homonuclear trimers based on the solution of the rotational Hamiltonian by means of a purely vibrational basis combined with standard rotational functions is applied on Ne3. The neon trimer constitutes an ideal test between heavier systems such as Ar3 for which the method proves to be an extremely useful technique and some other previously investigated cases such as H3+ where some limitations were observed. Comparisons of the calculated rovibrational energy levels are established with results from different calculations reported in the literature.

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem.

Quantum mechanical calculations of ro-vibrational energies of CH4, CHD3, CH3D, and CH3F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH3. Euler angles specifying the orientation of a frame attached to CH3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH4, CHD3, and CH3D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH3F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

Size-dependent piezoelectric energy-harvesting analysis of micro/nano bridges subjected to random ambient excitations

The construction of self-powered micro-electro-mechanical units by converting the mechanical energy of the systems into electrical power has attracted much attention in recent years. While power harvesting from deterministic external excitations is state of the art, it has been much more difficult to derive mathematical models for scavenging electrical energy from ambient random vibrations, due to the stochastic nature of the excitations. The current research concerns analytical modeling of micro-bridge energy harvesters based on random vibration theory. Since classical elasticity fails to accurately predict the mechanical behavior of micro-structures, strain gradient theory is employed as a powerful tool to increase the accuracy of the random vibration modeling of the micro-harvester. Equations of motion of the system in the time domain are derived using the Lagrange approach. These are then utilized to determine the frequency and impulse responses of the structure. Assuming the energy harvester to be subjected to a combination of broadband and limited-band random support motion and transverse loading, closed-form expressions for mean, mean square, correlation and spectral density of the output power are derived. The suggested formulation is further exploited to investigate the effect of the different design parameters, including the geometric properties of the structure as well as the properties of the electrical circuit on the resulting power. Furthermore, the effect of length scale parameters on the harvested energy is investigated in detail. It is observed that the predictions of classical and even simple size-dependent theories (such as couple stress) appreciably differ from the findings of strain gradient theory on the basis of random vibration. This study presents a first-time modeling of micro-scale harvesters under stochastic excitations using a size-dependent approach and can be considered as a reliable foundation for future research in the field of micro/nano harvesters subjected to non-deterministic loads.