Bending Vibration Research Articles

The dynamic behaviour of a finite periodic structure comprising either symmetric or asymmetric exponential- and conical-shaped rods

Periodic structure research is driven by the aim of incorporating them into modern engineering systems to address specific challenges, such as vibration reduction within defined frequency ranges. This paper explores the dynamic behaviour of a periodic structure comprising rods with varying cross-sectional areas. Two specific cases are considered, one in which the unit cell consists of two rods where the cross-sectional area varies exponentially and one where the cross-sectional areas vary conically. The structures are modelled using receptance matrices of a single cell, which are then transformed into transfer matrices. This facilitates a comparison of the two structures and helps to relate the results between finite and infinite structures. An experimental study to validate the approach and some of the results is also presented. It is shown that the structures composed of rods with exponentially or conically varying cross-section areas have similar behaviour. Reasonably good correspondence between the predictions and the experimental results were found. However, some additional features were found in the measured receptances due to bending vibration that was not considered in the theoretical model. Asymmetric cells are found to perform better and have a wider attenuation band when compared to symmetrical cells.

Structural, optical and magnetic characteristics of Mg2+- doped (Ba0.94Sr0.06)(Fe0.80Al0.20-xMgx)O3-ẟ (x = 0–0.20) oxides

Perovskite-type ABO3 oxides have attracted immense attention in recent technologies e.g., gas sensors, solar cells, fuel cells, oxygen-permeable membranes, etc. An attempt has been made here to synthesize (Ba0.94Sr0.06)(Fe0.80Al0.20-xMgx)O3-ẟ (x = 0–0.20) oxides using sol-gel method and characterized with regards to phase, Raman and magnetic properties. X-ray diffraction-cum-Rietveld refinement shows the structural transformation from cubic (Pm3m) to hexagonal (P63/mmc) via cubic (Pm3m) + rhombohedral (R3c) and increase of cubic lattice parameter ac = 4.0369–4.1296 Å with magnesium. FT-IR spectra exhibit different vibrational bands at 548, 555, 638, 667, and 692 cm−1, representing the metal-oxygen (M-O-M) bond vibrations (M - Fe, Mg, Al), deformation of MO6 octahedral, and internal changes in bond lengths. No Raman band was appeared for cubic phase with x=0–0.10. Bands between ∼ 250–450 cm−1 assign the tilting, rotation, and asymmetric bending vibrations of Fe – O, Mg – O and Al – O bonds and asymmetric bending mode of (Fe/Mg/Al)O6 octahedra. Oxygen bending vibration, anti-stretching mode and presence of oxygen vacancies lie in the bands of range ∼498–656 cm−1. Maximum coercivity (Hc ∼ 1081 Oe) and remanent magnetization (Mr ∼ 0.033 emu/g) have been observed for x = 0 and found similar variation with ‘x’. The saturation magnetization (Ms) and anisotropic constant (K1) values lie as Ms = ∼ 0.678 – 0.754 emu/g and K1 = ∼ 1.38× 104 – 1.53× 104 erg/cm3, respectively with magnesium (x). Presence of anion vacancies and high coercivity make the materials suitable for industrial applications.

Higher-order finite strip method (H-FSM) with nonlocal strain gradient theory for analyzing bending and free vibration of orthotropic nanoplates

Higher-order finite strip method (H-FSM) with nonlocal strain gradient theory for analyzing bending and free vibration of orthotropic nanoplates

A Double Fish‐Shaped Metamaterial with Variable Bending Stiffness and Damping under Elastic Tension

The study of bionic metamaterials with unique properties has gained increasing attention in recent years. This article introduces a double fish‐shaped metamaterial (DFSM) and investigates its elasticity and deformation behaviors. The Poisson's ratio of DFSM is derived from the energy principle and Mohr's theorem. The bending deformation behaviors of DFSM under given elastic strains are observed and tested by using the homemade experimental bench, which is further compared with finite element (FE) methods. The FE results show good agreement with experimental results. The bending vibration of DFSM under elastic tension is recorded and analyzed using a homemade prestrain bench in conjunction with a high‐speed camera. The present study proposes a straightforward and valid approach for incorporating the variable bending stiffness and the variable bending damping into DFSM. The revealed mechanical properties of DFSM in this article demonstrate its potential for engineering applications that require multistiffness and multidamping capabilities.

Secondary crystallization of low-isotacticity polypropylene

This study aimed to clarify the secondary crystallization process of low-isotacticity polypropylene (LT-PP). LT-PP demonstrates an exceptionally low crystallization rate at room temperature, which is approximately 1/5000 lower than that of isotactic PP (iPP). During the secondary crystallization of LT-PP at 30 °C, the thickness of lamellar (c-axis) and a- and b-axes of crystallite size remained constant. In addition, no significant change was observed in the CC-C bending vibration. It seems that the direction of the CC-C molecular order is similar to the thickness direction. This vibration mode may be associated with changes in the thickness of the lamellae. To explain the log(t) dependence of crystallinity, the Seto–Frank model was employed.

Near-Infrared Spectroscopic Study of Secondary Minerals in the Oxidation Zones of Copper-Bearing Deposits

This study measured the infrared spectra of secondary minerals in the oxidation zones of three types of copper ores: dioptase, malachite, and azurite, and assigned the peak positions of OH stretching vibrations and the origins of OH combination vibrations. Dioptase contains three types of water molecules with different orientations within its ring channels, which exhibit six kinds of OH stretching vibrations in the 3000–3600 cm−1 range; the bond length range is 2.652 to 2.887 Å. Among them, the 3443 cm−1 band shows strong near-infrared activity and combines with Si–O vibrations or OH bending vibrations in the structure, resulting in five combination vibration peaks in the 4000–5000 cm−1 range. Malachite contains two inequivalent hydroxyls in its structure, leading to two OH stretching vibrations in the high-frequency region located at 3314 and 3402 cm−1, respectively. Azurite contains only one type of hydroxyl, and thus only one characteristic OH stretching vibration is present at 3424 cm−1. The OH stretching vibrations of malachite and azurite mainly combine with [CO3]2− vibrations or OH bending vibrations, leading to six and five combination peaks in the OH combination vibration region, respectively. By analyzing the combination of peak positions at 4341 cm−1 in the near-infrared spectrum, the merged OH bending vibration at 921 cm−1 in azurite was discovered. Spectroscopic research on secondary minerals can better provide a basis for ore exploration and geological remote sensing.

Coupling vibration mechanism of rotating shaft–disc–blade system with blade crack—A systematical investigation on the effect of crack, condition, and structure parameters

Rotating shaft–disc–blade (RSDB) system is one of the most important parts of turbomachinery, such as aero-engine, gas turbine, and power plant. Understating and revealing the coupling vibration mechanism of RSDB system is significant for blade health monitoring and blade crack detection. However, the multi-structure, multi-vibration source, and multi-stress coupling makes it a very tough task. This study aims to reveal the coupling vibration mechanism of RSDB system by systematically investigating the steady-state vibration responses under the influences of different blade crack, operation condition, and structure parameters. First and foremost, a coupling vibration model of RSDB system that comprehensively considers the multi-structure, multi-vibration source, and multi-stress coupling effects is presented. And then, a novel condition indicator for blade health monitoring, called blade–blade distance, is proposed to better characterize and analyse the coupling vibration of RSDB system with blade crack. At last, the comprehensive effects of blade crack, operating condition, and structure parameters on the coupling vibration mechanism of the RSDB system with blade crack are systematically studied. The comparative results demonstrate the effectiveness of blade–blade distance and super-harmonic components of shaft torsional vibration and blade bending vibration for indicating the presence of blade crack and tracking the crack severity. Another observation should be noted is that the vibration behaviour including the blade–blade distance, super-harmonic components of shaft torsional vibration and blade bending vibration, the combination frequency components of shaft bending vibration are co-affected by blade crack, operating condition, and structure parameters. It is indicated that the blade health monitoring and crack detection of rotating blade should comprehensively consider different indicators to obtain a more robust and accurate results.

Microstructure and corrosion properties of Al1-xWxN coatings for potential use in gas turbine blades

Herein, a numerical approach of Al1-xWxN thin film coatings on Inconel 738LC superalloys for thermal barrier applications has been studied and the experimental analysis includes deposition of Al1-xWxN films on Si (100), glass and transparent quartz substrates at 40 % N2 flow rate using a dual target DC reactive magnetron sputtering technique to investigate the morphology, microstructure, chemical bonding and corrosion behaviour. AFM analysis revealed the rms roughness, Sq and average roughness, Sa increased with the increasing W content from 22 to 70 at.%. It was found that Al1-xWxN films tend to form tiny valleys on the film surface because the values of surface skewness, Ssk lie below zero. The TEM image showed a branched snowflake structure for the specimen of Al0.58W0.42N films with discrete spots in the SAED pattern, confirming the microcrystalline nature. The blue-shifting of Ecorr towards positive potential confirmed the lower corrosion resistance of WN films than those of AlN. XRD spectra of Al0.58W0.42N films showed an amorphous nature devoid of peaks, which is also confirmed by the SAED pattern. The quasi-passive oxide layer formation was spontaneous for WN films compared to the AlN films. The bending vibrations of AlN and WN showed the coordination environment of the metal centre in the Al1-xWxN films. The computational results indicated that the thermal barrier properties of Al1-xWxN films decreased with the increasing W content, i.e., AIN > Al0.58 W0.42N > WN.

Open-slit circular tube piezoelectric ultrasonic transducer with longitudinal bending mode conversion

Abstract A new type of longitudinal bending mode conversion ultrasonic transducer is designed by compounding a sandwich type piezoelectric ultrasonic transducer, amplitude transformer and Open-slit circular tube radiator. The radiator is made of a circular tube cut into a number of curved plates along the axis, and the two ends are thin disc end caps. The electromechanical equivalent circuit model of the transducer is established and its frequency equation is derived. The vibration performance of the transducer is studied by using the equivalent circuit method and the finite element method. The results show that: the new structure design and the longitudinal vibration sandwich piezoelectric ultrasonic transducer can effectively stimulate the two ends of the slit circular tube radiator to produce first-order bending vibration, and the curved plate to produce high-order bending vibration, so as to achieve high efficiency, uniform and all-round ultrasonic radiation. The research results are expected to be applied in ultrasonic treatment of large volume liquid such as ultrasonic wastewater treatment, ultrasonic algae removal and ultrasonic chemical reaction.

Novel poly(2-ethyl-2-oxazoline) and poly(diallyldimethylammonium chloride) polymer functionalized montmorillonite: Physicochemical aspects and near-IR study of hydration properties

The novel functionalized montmorillonites (Mts) with non-ionic poly(2-ethyl-2-oxazoline) (PEtOx) and cationic poly(diallyldimethylammonium) (PDDA) were created via an intercalation method with different loading ratio of both polymers. A comprehensive investigation into their physicochemical properties was conducted using Carbon analysis (CA), Powder X-ray diffraction (PXRD), Fourier-transform infrared spectroscopy (FTIR), Simultaneous thermal analysis (TGA/DSC) and BET-N2 adsorption analysis. The impact of hydration on PEtOx-Mts and PDDA-Mts was assessed through gravimetric analysis and near-infrared spectroscopy (NIR) spectroscopy. PXRD analysis revealed a significant increase in 001 diffraction of PDDA-Mt corresponding to a PDDA interlayer with a basal spacing ranging from 1.47 to 1.49 nm. Conversely, the basal spacing exceeding 2 nm for PEtOx suggested, that the PEtOx polymer was intercalated in a larger amount and packed in a less compact manner compared to PDDA. After modification of Na-Mt with PEtOx polymer, FTIR spectroscopy confirmed the presence of the carbonyl CO group (3265 and 1641 cm-1) and the stretching (2982, 2942 and 2883 cm-1) and bending (1480–1200 cm-1) vibrations of the CH2 and CH3 groups. The vibrations of CH groups were further verified following PDDA modification. NIR spectroscopy also confirmed the vibrational bands attributed to both modifiers after intercalation of PEtOx and PDDA. The results of BET-N2 adsorption revealed a significant decrease in the specific surface area (SSA) after intercalation with a non-ionic PEtOx polymer. On the contrary, in the case of saturation of Na-Mt with polycation PDDA, SSA increased slightly in two instances. TGA analysis confirmed greater weight loss for PEtOx-Mts compared to PDDA-Mts. Derivative thermogravimetry (DTG) revealed the release of physisorbed bound water around 100 °C, decomposition of the organic phase within the 250–550 °C range and dehydroxylation of OH groups around 550–800 °C in both cases. The results obtained from the gravimetry and NIR analysis indicated a greater hydrophobic nature for PEtOx-Mts compared to PDDA-Mts. These findings hold substantial potential for enhancing the properties of novel organo-montmorillonites, thereby facilitating their application as adsorbents for pollutants, surface coatings, biodegradable materials, fillers in polymer nanocomposites, drug carriers, anticancer agents and various other significant applications.

Mass Minimization of Axially Functionally Graded Euler–Bernoulli Beams with Coupled Bending and Axial Vibrations

Mass Minimization of Axially Functionally Graded Euler–Bernoulli Beams with Coupled Bending and Axial Vibrations

Finite element analysis of a Helmholtz transducer jointly driven by a trilaminar ring and a piezoelectric circular tube

Abstract Crosswell seismic survey can image the crosswell geological anomalies with high resolution in 3D. To effectively conduct crosswell seismic survey, it is necessary to use a seismic source capable of transmitting low-frequency and high-power signals in a compact size. In this paper, a novel Helmholtz transducer is proposed, which utilizes both the bending vibrations of the trilaminar ring and the radial vibrations of the piezoelectric circular tube to simultaneously drive the vibration of the Helmholtz liquid cavity. This design reduces the resonant frequency of the liquid cavity while enhancing the transmitting voltage response at the liquid cavity resonant frequency. The influence of the inner radius of the trilaminar ring, the outer radius of the ceramic ring and the length of the piezoelectric circular tube on the liquid cavity resonant frequency and the transmitting voltage response at the liquid cavity resonant frequency is simulated using the finite element method. The simulation results provide a theoretical foundation for optimizing the design of such transducers.

Research on Iron Gallium Dipole Logging Transducers

Abstract Orthogonal dipole acoustic logging is an indispensable means to study the mechanical properties of formation rocks, estimate formation porosity and permeability, and carry out out-of-hole remote detection, and the broadband high-power dipole acoustic logging transducer is one of its core components, which is an urgent and unsolved international problem in actual logging. Therefore, it is of great application background and important academic significance to study the new dipole acoustic logging transducer and overcome the related scientific problems. On the basis of full investigation and study of the characteristics of iron gallium materials, this project first designed the iron gallium bending beam oscillator to verify the feasibility of iron gallium bending vibration, and then designed the iron gallium dipole acoustic logging transducer, optimized the driving magnetic circuit, simulated the driving performance of the transducer, and preliminarily verified the feasibility of the design.

Drying kinetics of CeO2-ZrO2 ceramic powders under microwave heating based on a thin-layer drying model

Volume change of ZrO2 during martensitic phase transformation can cause cracking of material and limit the application of ZrO2.Agglomeration of CeO2-ZrO2 ceramic powders can be effectively reduced by choosing the correct drying method. Microwave drying of CeO2-ZrO2 powder can effectively reduce the cracking of zirconia materials and improve powder uniformity. Microwave heating is used to dry CeO2-ZrO2 ceramic powders, and results demonstrate that Modified Page fits experimental data rather well. FT-IR spectra revealed a remarkable decrease in the intensity of the -OH bond's stretching vibration peak, and H-O-H bond's bending vibration. Utilizing Fick's second law, the diffusion coefficient of water molecules in CeO2-ZrO2 ceramic powders with a mass of 20 g and a moisture content of 6.6 % is calculated to be 5.820 × 10−15 m2/s under microwave power of 400 W. Experimental results prove that microwave heating has low activation energy, improves drying efficiency, and realizes fast and efficient drying.

Dynamic characteristics analysis and vibration control of coupled bending-torsional system for axial flow hydraulic generating set

Aiming at the vibration problems of shaft system for axial flow hydraulic generating sets caused by complex excitations, the coupled bending-torsional dynamic equations of rotor-runner system are established considering multi-effect including hydraulic, mechanical, electrical and other external vibration sources. Whether taking the torsional degree of freedom into account, the stability and disparate destabilization laws of system periodic solutions are analyzed using the shooting method combined with Floquet theory. On this basis, the influence of coupling bending-torsional effect on system dynamic behaviors is discussed through bifurcation diagrams, Poincaré maps, trajectories, time domains and frequency spectrums. Furthermore, in order to alleviate the unsteady vibration of rotor as well as runner, the magnetorheological fluid damper is introduced into the shaft system, and numerical simulations are performed on models of coupled bending-torsional systems with or without the magnetorheological fluid damper. The analyses indicate that the interaction between bending and torsional vibration of the shaft system will expand the chaotic sustained range for rotor. Meanwhile, the amplitude of the rotor-runner system is magnified owing to the torsional vibration, which leads to local rubbing faults of the system under specific operating conditions, while the intervention of the magnetorheological fluid damper can significantly suppress the nonlinear motion of rotor and runner, reduce the amplitude of system vibration, so as to avoid the occurrence of friction defects effectively. The above research results can provide conducive references for fault diagnosis, optimized design, and vibration control of axial flow hydraulic generating sets.

Enhanced dielectric, magnetic, and photocatalytic properties of sol-gel synthesized Eu-Cr codoped BiFeO3 nanoparticles

A series of polycrystalline Eu-Cr co-doped BiFeO3 nanoparticles were synthesized using the sol–gel method. The obtained samples were characterized by employing the XRD, FTIR, FESEM, UV–vis, LCR meter, and SQUID techniques. XRD analysis confirmed rhombohedral phase formation for all samples, and the crystallite sizes decreased with higher Cr3+ doping concentrations. The stretching and bending vibrations of Fe-O bonds in FeO6 octahedra and the formation of perovskite nature were confirmed by the FTIR analysis. From microstructural studies, a decrease in crystallite size with increased doping concentration was observed, corroborating the XRD results. The magnetic studies revealed an enhanced magnetization, probably caused by the distorted cycloid spin structure of the codoped nanoparticles with size ≤62 nm. The lower value of the squareness ratio of the M-H loop indicated strong magnetostatic interaction between grains, which might have played a great role in the enhancement of the maximum magnetization of the doped samples. The dielectric constant and loss tangent were evaluated as a function of frequency at room temperature. The photocatalytic activities of all the samples were evaluated by measuring the degradation of RhB dye under sunlight irradiation. The highest photocatalytic degradation efficiency of 94% was achieved with the substitution of Cr3+ (3%) and Eu3+ (4%) ions in BiFeO3 nanoparticles.

Coupling vibration mechanism of multistage blisk-rotor system with blade crack

This study aims to address the issue of vibration modeling and coupling vibration mechanism analysis of multistage blisk-rotor (MBR) systems with blade cracks. First, a comprehensive coupling vibration model of the MRB system containing the flexibility of shaft and blade, the swing motion of offset blisk structure, and the nonlinear effect of blade breathing crack is developed. Then, the coupling vibration mechanism of the MRB system is systematically investigated through analytical and numerical analysis, based on which the vibration indicators for the presence of blade cracks are extracted. At last, the effects of blade crack and operating condition parameters on the coupling vibration of the MRB system are comprehensively analyzed. The comparative results indicate that the crack depth and aerodynamic force may significantly affect the crack indicators in shaft bending and torsional vibrations, while the disc unbalance mainly affects the crack indicators in shaft bending vibrations. It is also suggested that the BHM and crack detection of rotating blades should comprehensively consider different crack indicators and perform continuous condition monitoring to obtain more robust and accurate results.

Structural and antibacterial assessment of two distinct dihydroxy biphenyls encapsulated with β-cyclodextrin supramolecular complex

β-Cyclodextrin plays a vital role in biological application because it can enhance the stability and solubility of the guest molecules in the supramolecular inclusion complexes. Moreover, the β-Cyclodextrin inclusion complex has control-releasing behavior and lower toxicity than bare guest molecules. To improve the solubility and stability properties of two structurally different fluorescent guest molecules, namely 2,2′-dihydroxy biphenyl and 3,3′-dihydroxy biphenyls, they involve the β-Cyclodextrin inclusion complex process. Optical measurements clearly described the efficient binding through the changes in the absorbance and emission intensities of guest molecules in the presence of β-Cyclodextrin. The Job's plot from absorbance measurements reveals the 1:1 stochiometric ratio of binding of guests and the β-Cyclodextrin host. The FT-IR spectra of the solid complex show the characteristic stretching and bending vibrations from both the guests and the host molecule. The 1HNMR spectra of the inclusion complex promote downfield shifting of guest molecule protons upon binding with the β-Cyclodextrin host. The solid complex prepared using the solution method exhibits superior antibacterial activity against both gram-positive and gram-negative bacteria compared to the kneading and physical mixing methods.

Unusual Vibrational Coupling of the Schiff Base in the Retinal Chromophore of Sodium Ion-Pumping Rhodopsins.

A Schiff base in the retinal chromophore of microbial rhodopsin is crucial to its ion transport mechanism. Here, we discovered an unprecedented isotope effect on the C═N stretching frequency of the Schiff base in sodium ion-pumping rhodopsins, showing an unusual interaction of the Schiff base. No amino acid residue attributable to the unprecedented isotope effect was identified, suggesting that the H-O-H bending vibration of a water molecule near the Schiff base was coupled with the C═N stretching vibration. A twist in the polyene chain in the chromophore for the sodium ion-pumping rhodopsins enabled this unusual interaction of the Schiff base. The present discovery provides new insights into the interaction network of the retinal chromophore in microbial rhodopsins.

Thermally stable and anti-corrosive polydimethyl siloxane composite coatings based on nanoforms of boron nitride

Coating technology has been emerged as a recognized and cost-effective approach in regard to mitigating issues that are linked to corrosion. We employed in-house synthesized boron nitride nanosheets (BNNS-CVD) and commercially available nanosized boron nitride (BN-nano) as fillers in this study to fabricate composite coatings with enhanced thermal stability and corrosion resistance. These fillers were dispersed in polydimethylsiloxane (PDMS) resin to develop composite coatings. The Fourier-transform infrared spectroscopy (FTIR), UV–visible spectroscopy, field emission scanning electron microscopy (FESEM), thermogravimetric analysis (TGA), and electrochemical impedance spectroscopy (EIS) were employed to characterize the prepared composite coatings. The FTIR analysis revealed a prominent absorption band around 1350 cm−1 that is indication of the distinctive B-N in-plane bending vibrations characteristic of boron nitride (BN). The FESEM images simultaneously confirmed the sheet-like morphology of both BN-nano and BNNS-CVD, which both found to be uniformly dispersed in the PDMS matrix. The EIS revealed that the composite films based on BNNS-CVD exhibited superior corrosion resistance compared to those based on BN-nano when exposed to a 3.5 wt% NaCl solution. Further, TGA profiles indicated that the composite films maintained their structural integrity up to 200 ℃ without degradation. Therefore, thermally stable and corrosion resistant coatings can be valuable for various new technology applications that involve corrosion issues.