Asymmetric Vibration Mode Research Articles

Thermoelastic damping in asymmetric vibrations of nonlocal circular plate resonators with Moore-Gibson-Thompson heat conduction

Precise estimation of the amount of thermoelastic damping (TED) in small-sized resonators is one of the crucial issues in their optimal design. According to several experimental, numerical and theoretical findings, the behavior of structures with such small dimensions in structural and thermal domains does not follow classical elasticity theory and the Fourier law of heat conduction. The objective of this work is to develop a nonclassical formulation for computing TED in asymmetric vibrations of circular nanoplates according to nonlocal theory (NT) and Moore-Gibson-Thompson (MGT) heat transfer model. To do so, first, the coupled equations of motion and heat are derived in the purview of NT and MGT model. Then, the real and imaginary parts of the system frequency are extracted from the frequency equation affected by thermoelastic coupling. Finally, by means of the existing definition for TED, a mathematical expression including nonlocal parameter of NT and nonclassical constants of MGT model is obtained to make an estimate of TED value. In the numerical examples section, to ensure the credibility of the provided formulation, the results obtained through this model are compared with those reported in the literature in the context of simpler models. Then, by presenting various graphical data, the type and extent of the role of different factors in TED changes are appraised. The obtained results indicate that employing NT and MGT model can substantially impact the amount of TED compared to the estimations of the classical formulation. Furthermore, the comparison of results reveals that the magnitude of TED in asymmetric vibration modes surpasses that in symmetric ones, and consequently incorporating asymmetric vibration modes is crucial for thorough analysis of TED in circular nanoplates. Thus, the formulation presented in this article can aid in achieving an optimal design for such plates, particularly in terms of minimizing energy loss.

Exploiting Hydrogen Interaction of Drugs and Biodegradable Scaffolds Using Nanoparticles Loaded Nanofibers

AbstractThis study presents a detailed investigation of the structural and surface modifications of Fe3O4 nanoparticles (NPs). Fourier Transform Infrared (FTIR) spectroscopy was utilized to analyze the distinct characteristic peaks of Fe3O4 NPs and their subsequent modifications with stearic acid (ST) layers. The FTIR analysis revealed characteristic peaks at 580 cm−1, and 441 cm−1, corresponding to the Fe‐O stretching vibrations of the bulk Fe3O4 NPs. The successful loading of stearic acid onto the Fe3O4 NPs was confirmed by the appearance of new peaks at 1413 cm−1 and 2908 cm−1, indicative of the asymmetric CH2 stretch and CH3 umbrella vibration modes of stearic acid. UV‐Vis spectroscopy further corroborated the efficient loading of tetracycline and ibuprofen onto Fe3O4/DST nanoparticles, as evidenced by changes in absorption spectra. N2 adsorption‐desorption isotherms illustrated the presence of micro and meso pores on the surface of Fe3O4 NPs, with alterations in pore volume and diameter post‐surface modification and drug loading. Evaluation of magnetic properties indicated a reduction in saturation magnetization after surface modification and drug loading, attributed to changes in homogeneity and surface moments. Differential Reflectance Spectroscopy (DRS) and Raman spectroscopy elucidated distinctive peaks and shifts in spectra, confirming the composition and structural changes in drug‐loaded nanofibers.

Spontaneous-Symmetry-Breaking Charge Separation Induced by Pseudo-Jahn-Teller Distortion in Organic Photovoltaic Material.

The driving force of charge separation in the initial photovoltaic conversion process is theoretically investigated using ITIC, a nonfullerene acceptor material for organic photovoltaic devices. The density functional theory calculations show that the pseudo-Jahn-Teller (PJT) distortion of the S1 excimer state induces spontaneous symmetry-breaking charge separation between the identical ITIC molecules even without the asymmetry of the surrounding environment. The strong PJT effect arises from the vibronic coupling between the pseudodegenerate S1 and S2 excited states with different irreducible representations (irreps), i.e., Au for S1 and Ag for S2, via the asymmetric vibrational mode with the Au irrep. The vibrational mode responsible for the spontaneous polarization, which is opposite in one ITIC monomer and the other, is the intramolecular C-C stretching vibration between the core IT and terminal IC units. These results suggest that controlling the PJT effect can improve the charge separation efficiency of the initial photovoltaic conversion process.

DFT-Based Calculation of Molecular Hyperpolarizability and SFG Intensity of Symmetric and Asymmetric Stretch Modes of Alkyl Groups.

Vibrational sum frequency generation (SFG) spectroscopy has been extensively used for obtaining structural information of molecular functional groups at two-dimensional (2D) interfaces buried in the gas or liquid medium. Although the SFG experiment can be done elegantly, interpreting the measured intensity in terms of molecular orientation with respect to the lab coordinate is quite complicated. One of the main reasons is the difficulty of determining the hyperpolarizability tensors of even simple molecules that govern their SFG responses. The single-bond polarizability derivative model has been proposed to estimate the relative magnitude of SFG-active hyperpolarizability by assuming that the perturbation associated to each vibration is negligible. In this study, density functional theory was used to calculate the polarizability and dipole derivative tensors of the CH3 stretch mode of CH3I, CH3CH2I, CH3OH, and CH3CH2OH. Then, the hyperpolarizability tensors of symmetric and asymmetric vibration modes were calculated considering the Boltzmann distribution of representative conformers, which allowed us to theoretically calculate their SFG intensities at all polarization combinations as a function of the tilt angle of the CH3 group with respect to the surface normal direction. Then, the ratios of the calculated SFG intensities for the CH3 symmetric and asymmetric stretch peaks used in experimental studies for the CH3 tilt angle determination were compared. This comparison clearly showed that the effect of vibrational coupling among neighboring functional groups is significant and cannot be assumed to be negligible. This study presents new parameters that can be used in determining the average tilt angle of the CH3 group at the 2D interface with SFG measurements as well as limitations of the method.

Causes and evolution of asymmetric polygonal wear of metro train wheelsets

Wheel acoustic roughness of one metro line in China shows that the wheel polygonal wear (WPW) on both sides of the wheelset is asymmetrical. The dominant harmonics of the left and right wheels are 12–13, but with large differences in acoustic roughness levels. To analyse the causes of the asymmetrical WPW (AWPW), an investigation of the acoustic roughness of the wheels and rails and a modal analysis of the wheelset–track system are carried out. In addition, a long-term wear model considering the flexibility of the wheelset and track is established to provide insight into the initiation and evolution of the AWPW. The results of the experiments and simulations show that the natural asymmetric vibration mode in the wheelset–track system with a frequency of 83 Hz is the main cause of WPW, which can be excited on sharp curves. The difference between the lengths of the left and right curved tracks with small radius is the cause of AWPW. The residual WPW after reprofiling and rail corrugation with a wavelength of about 200 mm are the main sources of excitation for the asymmetric natural vibration.

Femtosecond symmetry breaking and coherent relaxation of methane cations via x-ray spectroscopy

Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic-level insight into photochemistry. We performed a time-resolved study of ultrafast molecular symmetry breaking through geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond transient absorption spectroscopy with soft x-rays at the carbon K-edge revealed that the distortion occurred within 10 ± 2 femtoseconds after few-femtosecond strong-field ionization of methane. The distortion activated coherent oscillations in the asymmetric scissoring vibrational mode of the symmetry-broken cation, which were detected in the x-ray signal. These oscillations were damped within 58 ± 13 femtoseconds because vibrational coherence was lost with the energy redistributing into lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation dynamics of this prototypical example and opens avenues for exploring complex systems.

Model of a Micromechanical Modal-Localized Accelerometer with a Sensitive Element in the Form of a Beam with an Initial Deflection

The present study is devoted to mathematical modeling of the proposed new architecture of a microelectromechanical modally localized acceleration sensor (MEMS accelerometer/gravimeter) with a sensitive element in the form of a microbeam pinched at both ends with an initial deflection, made in the form of the first asymmetric mode of free vibrations. The article demonstrates that with an asymmetric form of the initial deflection in the region of positive axial forces, there are zones of proximity of the frequency branches corresponding to the second symmetric and the first asymmetric vibration modes. When the required value of the axial tensile force in the microbeam is provided structurally, this effect can be used, in particular, to measure the axial component of the transfer acceleration according to the principle of amplitude modal localization. The possibility of heating the sensitive element with the help of an electric current flowing through the microbeam, provided in the sensor layout, makes it possible to control the operating point of the oscillation mode and, thus, to vary the range of measured accelerations and the degree of sensor sensitivity within a very wide range. The configuration of the oscillation excitation and output signal pickup electrodes proposed in the article makes it possible, with the help of a feedback loop, to stabilize the oscillation amplitude at the required level in the working (third) symmetrical form and, at the same time, to measure the oscillation amplitude associated with the change in the value of the measured component of the portable acceleration according to the asymmetric form. Thus, a mathematical model of an original modal-localized accelerometer (gravimeter) containing a single sensitive microbeam element and involving the effect of energy exchange between its various modes of vibration is proposed and investigated in the article.

Laser spectroscopic characterization of supersonic jet cooled 2,7-diazaindole.

We report the first gas phase comprehensive study of the electronic spectroscopy of 2,7-diazaindole molecule in the ground and excited states. Single vibronic level fluorescence spectroscopy (SVLF) was performed to determine the ground state vibrations of the molecule, which depicted a large Franck-Condon activity beyond 2600 cm-1. For the excited state characterization, laser-induced fluorescence (LIF) and two-color resonant two-photon ionization spectroscopy (2C-R2PI) were performed. The band origin (000) for S1 ← S0 transition appeared at 33910 ± 1 cm-1 which was red shifted by 718 cm-1 and 1322 cm-1 compared to that of 7-azaindole and indole respectively. The Franck-Condon active vibrational modes in the spectra were seen till the (000) + 1600 cm-1 region. The IR-UV hole burning spectroscopy confirmed the absence of any other isomeric species in the molecular beam. The ionization energy (IE) of the molecule was measured as 8.921 ± 0.001 eV, recorded using photoionization efficiency spectroscopy. The above IE value was significantly higher than that of the related indole derivatives, suggesting the higher photostability of the 27DAI molecule due to N(2) insertion. The ground and excited state N-H stretching frequencies of the molecule were determined using fluorescence-dip infrared spectroscopy (FDIR) and resonant ion-dip infrared spectroscopy (IDIR), and the values are 3523 and 3467 cm-1, respectively. The lower value of νNH in the electronic excited state implied the increased photoacidity of the group. A comparative analysis of the experimental LIF/2C-R2PI spectra was done against Franck-Condon simulated spectra at three different levels of theory. The vibrational frequencies calculated at B3LYP-D4/def2-TZVPP showed the most accurate prediction in comparison with the experimentally detected symmetric modes in the ground state. However, in the excited state, the lower energy asymmetric modes simulated at the B3LYP/def-SVP level of theory provided the best agreement with the experiment. This is most probably due to the distortion observed at the pyrazolyl ring leading to the appearance of asymmetric vibrational modes. The above study highlights the possibility to appropriately tune the excitation wavelengths as well as alter the photostability of the organic chromophores via additional N-insertion in the molecular systems.

Modeling of vibrational excitation dynamics in a nanosecond CO2 discharge

The temporal dynamics of excitation of the asymmetric vibrational mode of CO2 molecules in a nanosecond discharge is simulated. The values of the electric field andthe number density of electrons versus time, calculated for a known experimental dependence of the discharge current on time, are used to evaluate the number densities of the first and second vibrational levels of the asymmetric mode. It is shown that the dynamics of the densities of these levels, calculated using generally accepted values of the vibrational excitation rate constants, is in reasonable agreement with experimental data.

Time-resolved CO2, CO, and N2 vibrational population measurements in Ns pulse discharge plasmas

Time-resolved CO2 and N2 vibrational populations and translational-rotational temperature are measured in a CO2–N2 plasma sustained by a ns pulse discharge burst in plane-to-plane geometry. Time-resolved, absolute number density of CO generated in the plasma is also inferred from the experimental data. CO2 and CO vibrational populations are measured by mid-IR, tunable quantum cascade laser absorption spectroscopy, and N2 vibrational populations are measured by the ns broadband vibrational CARS. Transient excitation of N2 and CO2 asymmetric stretch vibrational energy modes is detected during the discharge burst. The time-resolved rate of CO generation does not correlate with N2 or CO2(ν 3) vibrational temperatures, indicating that CO2 dissociation via the vibrational excitation is insignificant at the present conditions. The rate of CO generation decreases gradually during the discharge burst. The estimated specific energy cost of the CO product is close to that of N atoms in pure nitrogen, measured previously at similar operating conditions. Comparison of the experimental data with the kinetic modeling analysis indicates that CO2 dissociation in collisions with electronically excited N2 molecules is the dominant channel of CO generation at the present conditions, although the inferred CO yield in these processes is significantly lower than 1. The effect of vibrational energy transfer between N2 and CO2 on the plasma chemical processes is insignificant. The kinetic model underpredicts a rapid reduction of the N2 and CO2(ν 3) vibrational temperatures during the later half of the discharge burst and in the afterglow. V–T relaxation of N2 by N and O atoms generated in the ns pulse discharge plasma does not affect the vibrational relaxation rate in a significant way. However, rapid V–T relaxation of CO2 by O atoms has a significant effect on the relaxation rate. The difference between the experimental data and the modeling predictions may be due to the unknown scaling of the CO2–O V–T rates with the vibrational quantum number.

Surface- and nonlocality-dependent vibrational behavior of graphene using atomistic-modal analysis

Classical continuum theories are incapable of accurately describing the behavior of nanostructures due to their size dependence. Size-dependent effects such as surface and non-local are among these phenomena, and their study at the nano-scale is essential. Despite advances in modeling and characterization of graphene's material properties, the surface and nonlocality effects of circular graphene nano-plates have not been calibrated for continuum mechanics theories. Based on a hybrid model that combines the advantages of continuum and atomic models, the present study is primarily focused on developing a method for calculating and estimating the effect of these parameters. A non-local surface elasticity model for graphene has been developed using a modal analysis derived from molecular dynamics simulations based on genetic algorithm optimization. In this research, both asymmetric and axisymmetric linear vibrational modes are studied. The parameters of the model, including surface residual stress, surface elasticity, surface density, and size parameter, are extracted from the results of the atomistic modal. Subsequently, this hybrid atomistic-continuum model has been employed to characterize the vibrational behavior of graphene. Based on the conducted simulations, the surface elasticity model with the nonlocality effect is calibrated with the lowest error for all radii and vibration modes. Moreover, this research suggests using a non-local surface elasticity model for very small radii since its findings are remarkably similar to the molecular dynamics simulations for the same diameters. On the other hand, the error is highest for the continuum model that does not incorporate surface and non-local effects. The findings of this study can be valuable in evaluating the crucial parameters regarding the surface and non-local elasticity of two-dimensional structures.

Classical Intermolecular Hydrogen Bonding Motifs of Heterocyclic rac-2-Amino-3-carbonitrile Derivatives: Linking Hirshfeld Surface Analysis, CT-DNA Binding Affinity, and Molecular Docking

Four 2-amino-4-(aryl)-7,7-dimethyl-5-oxo-5,6,7,8-tetrahydro-4H-chromene-3-carbonitrile (Series I) and three 2-amino-1-phenyl-7,7-dimethyl-5-oxo-4-(aryl)-1,4,5,6,7,8-hexahydroquinoline-3-carbonitrile (Series II) derivatives were formed via multicomponent microwave reactions as racemic mixtures. The solid-state IR spectra revealed bands in the region between 3190 and 3414 cm–1 attributed to the amino functional group’s asymmetric, symmetric, and bending overtone vibration modes. Furthermore, the IR spectra of some of the compounds in each series were similar and this served as an indication of similar structural features in the solid state. This was confirmed via single-crystal X-ray diffraction. A detailed survey of the related 2-amino-3-carbonitrile derivatives in the Cambridge Structural Database revealed 12 classical intermolecular hydrogen-bonding motifs involving the amino functional group. The vast variation in the hydrogen bonding motifs was found to be caused by the type of group bonded to the 4H-pyran (in Series I) or dihydropyridine (in Series II) moiety. In this work, an unprecedented hydrogen bonding motif comprising a non-classical hydrogen bond acceptor was found in one instance. For both Series I and II, the N–H···N and N–H···O hydrogen bonds were investigated using noncovalent interaction (NCI) plots and molecular pairwise energy calculations. The contributions of reciprocal N···H and O···H contacts (attributed to N–H···N and N–H···O, respectively) toward the Hirshfeld surface range between 9.9 and 15.3% in Series I and between 10.8 and 15.0% in Series II. In addition, the compounds showed moderate to good binding affinity to calf thymus DNA (CT-DNA) with intrinsic binding constants (Kb) between 8.00 × 104 and 5.00 × 105 M–1 for Series I compounds and between 6.60 × 104 and 1.45 × 105 M–1 for Series II. A relationship was established between the reciprocal N···H to O···H contributions ratio from the Hirshfeld surface analysis and Kb. Molecular docking studies of each compound’s respective enantiomers into DNA were done using canonical–DNA dodecamer (B-DNA) as a model for CT-DNA. The compounds were found to interact with DNA via a minor groove-binding mode. The S-enantiomer for most of the compounds bound favorably compared to their respective R-enantiomers. The ratio of calculated ΔG for the DNA binding of the R-enantiomer to that of the S-enantiomer (ΔGR/ΔGS) follows the same positive trend as the experimental Kb value for each compound in Series I while a negative trend was observed for Series II. Finally, a relationship between the Hirshfeld surface analysis and calculated ΔG values was also established in this work.

Relationship between the Vibration Acceleration and Stability of a Continuous Girder Bridge during Horizontal Rotation

To ensure the safety of bridges during horizontal rotation, we propose a method through which it is possible to evaluate the stability of structures in real time by measuring the vibration acceleration of the rotating structure. First, the vibration characteristics collected during the horizontal rotation of a typical high-speed railway bridge were compared with the results of a finite element analysis. Second, the analytic formula to calculate the ratio of vibration acceleration and the pier-bottom-section bending moment for the rotating structure was deduced by considering the beam and pier as an infinite-degree-of-freedom rod. Then, the results of the analytical formula were compared with those of the finite element calculation. Overall, the results showed that the bending moment of the pier bottom (which was related to the stability of the rotating bridge) was affected only by the two asymmetrical vibration modes. The analytic formula built by considering the beam and pier as an infinite degree-of-freedom rod with equal cross-section effectively described the relationship between the vibration acceleration and pier-bottom-bending moment. Finally, the vibration of the rotating bridge was simplified to the superposition of the first two asymmetric vibration modes in the facade. Based on our findings, we were able to provide a formula and some check tables to calculate the permissible value of vibration acceleration for typical high-speed railway bridges.

Effect of geometric imperfections and circumferential symmetry on the internal resonances of cylindrical shells

In the present work the resonant response of an imperfect cylindrical shell is investigated using Donnell’s nonlinear shallow shell theory. For this, a reduced order multi degree of freedom model is obtained by discretizing the partial differential equation of motion using the Galerkin procedure and a consistent modal expansion which captures the nonlinear modal interactions and couplings between two asymmetric vibration modes with near commensurable natural frequencies in a 1:2 ratio. As a result of the circumferential symmetry each mode exhibits a 1:1 internal resonance, leading to a possible 1:1:2:2 multiple internal resonances. These modes are coupled through quadratic and cubic nonlinearities arising from the shell curvature and nonlinear strain–displacement relation. The existence and stability of solutions and their bifurcations are investigated using numerical continuation methods for bifurcation analysis and their stability are studied using Floquet theory. It is known that geometric imperfections have a strong influence on the response of thin shell structures. Here, a detailed parametric analysis shows the influence of different forms of geometric imperfections on the shell natural frequencies and bifurcations in the main resonance region. Several branches of solutions due to multiple bifurcations are detected leading to dynamic jumps under increasing and decreasing frequency sweep. Steady-state harmonic and quasi-periodic responses resulting from Neimark–Sacker bifurcations are detected. The reduced order model demonstrates the influence of the geometric imperfection shape and magnitude on the bifurcation scenario and the energy transfer among the four interacting modes.

An effect of extra compactified dimensions of space in the molecule hbox {NO}_{{2}}

The theory of large extra compactified dimensions of space (ADD-model) predicts that gravity may become strong in a compactification space of the size of a molecule and may affect the vibrational motion of a molecule. In triatomic molecules like hbox {NO}_{{2}} nuclear dynamics is strongly coupled to electronic dynamics at the intersection of electronic states (conical intersection). We discuss experimental results on hbox {NO}_{{2}} which reveal that the collision-free molecule optically excited into a symmetric stretch vibration mode of an electronic state with conical intersection undergoes an irreversible non-radiative transition into an asymmetric stretch vibration mode in combination with a change of the electronic state. We suggest ascribing this irreversible non-radiative transition to a gravitational perturbation on the vibrational motion in hbox {NO}_{{2}}. This gravitational perturbation deactivates the upper state of the optical transition. The width of the absorption line is given by the characteristic time of the gravitational perturbation and not by the radiative lifetime of the excited molecular state.Graphical abstract

Nanosecond resolved ro-vibrational CO2 excitation measurement

We report first ns-resolved absorption measurements of the ro-vibrational excitation of CO2. The high temporal resolution of 8 ns is made possible by a fast detector (rise-time 5 ns), sensitive in the mid-infrared region. The resolution is achieved by a slow temperature scan of a quantum cascade laser and a segmented data capturing scheme. A repetitively pulsed ns discharge in 10% CO2 + 90% He at 150 mbar and a repetition rate of 2 kHz is investigated. The evolution of the population densities of the different vibration modes as well as the associated vibrational and rotational temperatures within the discharge pulse of only 150 ns length are simultaneously determined and provide valuable insight into the CO2 excitation dynamics. A preferential excitation in the asymmetric vibrational mode is observed in the discharge phase shortly after the breakdown.

Pseudo Jahn-Teller Origin of the Proton-transfer Energy Barrier in the Hydrogen-bonded [FHF]-System

The results of ab initio calculations of the adiabatic potential energy surfaces for the proton-bound [FHF]- system at different F-F distances have been rationalized in the framework of the vibronic theory. It is shown that the instability of the symmetric D∞h structure at increased F∙∙∙F distances and the proton displacement to one of the fluorine atoms is due to the pseudo Jahn–Teller mixing of the ground 1Σg electronic state with the lowest excited state of 1Σu symmetry through the asymmetric σu vibrational mode.

Angle-independent plasmonic substrates for multi-mode vibrational strong coupling with molecular thin films

Vibrational strong coupling of molecules to optical cavities based on plasmonic resonances has been explored recently because plasmonic near-fields can provide strong coupling in sub-diffraction limited volumes. Such field localization maximizes coupling strength, which is crucial for modifying the vibrational response of molecules and, thereby, manipulating chemical reactions. Here, we demonstrate an angle-independent plasmonic nanodisk substrate that overcomes limitations of traditional Fabry-Pérot optical cavities because the design can strongly couple with all molecules on the surface of the substrate regardless of molecular orientation. We demonstrate that the plasmonic substrate provides strong coupling with the C=O vibrational stretch of deposited films of PMMA. We also show that the large linewidths of the plasmon resonance allow for simultaneous strong coupling to two, orthogonal water symmetric and asymmetric vibrational modes in a thin film of copper sulfate monohydrate deposited on the substrate surface. A three-coupled-oscillator model is developed to analyze the coupling strength of the plasmon resonance with these two water modes. With precise control over the nanodisk diameter, the plasmon resonance is tuned systematically through the modes, with the Rabi splitting from both modes varying as a function of the plasmon frequency and with strong coupling to both modes achieved simultaneously for a range of diameters. This work may aid further studies into manipulation of the ground-state chemical landscape of molecules by perturbing multiple vibrational modes simultaneously and increasing the coupling strength in sub-diffraction limited volumes.

Modification and characterization of chicken eggshell for possible catalytic applications

Researchers have shown considerable interest in finding a sustainable, low cost, and readily available substitute for the commercial calcium oxide (CaO) catalyst. In this work, raw chicken eggshell was modified by boiling and calcination at 900 °C for 3 h. The x-ray diffraction characterization revealed that while the proportion of CaCO3 in the raw and boiled samples was found to be 79.3 % and 99.2 % respectively, the CaCO3 had been converted to 63.8 % CaO and CO2 in the calcined sample. This was due to the thermal decomposition during calcination. The outcome of the infrared spectroscopy showed that the raw and boiled chicken eggshell presented a similar absorption profile with peaks at 1 394 cm−1, 873 cm−1, and 712 cm−1, which were as a result of the presence of asymmetric stretch, out-of-plane bend, and in-plane bend vibration modes. The major peaks presented by the calcined sample at 3642 cm−1 can be attributed to the OAH stretching vibration and bending hydroxyl groups present in Ca(OH)2. The Brunauer-Emmett-Teller surface areas for the raw, boiled and calcined chicken eggshell were found to be 2.33 m2/g, 3.26 m2/g, and 4.6 m2/g respectively, indicating increased catalytic activity of the calcined sample. Overall, boiling was found to have a negligible effect on the chicken eggshell, while high-temperature calcination greatly affected the pore size, surface area, composition, and thermal decomposition profile of the chicken eggshell sample.

Nonlinear vibration of axially moving simply-supported circular cylindrical shell

This paper investigates the nonlinear free and forced vibration of axially moving simply-supported thin circular cylindrical shells in the sub-harmonic region, considering the effect of viscous structure damping. Motion equations of axially moving circular cylindrical shells in cylindrical coordinates are derived with the aid of the Hamilton principle and employing the Donnell–Mushtari nonlinear shells’ theory. Three nonhomogeneous nonlinear partial differential equilibrium equations concerning displacements across the three directions of cylindrical coordinate are reduced to two equations as a result of using the definition of the airy function. The particular and private solution of airy stress function is obtained utilizing the assumption of the form of the displacement in the radial direction based on the simply-supported boundary conditions and combination of axisymmetric and asymmetric driven and companion modes. By gaining the airy function, the third motion equation is discretized using the Galerkin method into the set of coupled nonlinear nonhomogeneous ordinary differential equations. The perturbation method and Runge–Kutta 4th order are employed as a semi-analytical and a numerical solution method, which in practice leads to the prediction of the nonlinear frequencies and amplitudes of various modes of vibration at different velocities and external excitation fluctuation domain and frequency. The bifurcation analysis of the velocity and external excitation parameters in sub-harmonic regions shows the changes in the instability condition of the system. It causes the appearance of the pitchfork bifurcation and the Neimark–Sacker bifurcation points. The accuracy of both, the direct normal form and numerical method results are compared against each other and validated in the particular case in the absence of the velocity with available data. The system would be more stable at a higher speed near 1:1 external resonance due to the activation of more asymmetric vibration modes and the growth of the nonlinear softening characteristic in the absence of companion vibration modes.