Antisymmetric Vibration Research Articles

Anti-Symmetric Mode Vibration of Electrostatically Actuated Clamped-Clamped Microbeams for Mass Sensing.

This paper details study of the anti-symmetric response to the symmetrical electrostatic excitation of a Micro-electro-mechanical-systems (MEMS) resonant mass sensor. Under higher order mode excitation, two nonlinear coupled flexural modes to describe MEMS mass sensors are obtained by using Hamilton’s principle and Galerkin method. Static analysis is introduced to investigate the effect of added mass on the natural frequency of the resonant sensor. Then, the perturbation method is applied to determine the response and stability of the system for small amplitude vibration. Through bifurcation analysis, the physical conditions of the anti-symmetric mode vibration are obtained. The corresponding stability analysis is carried out. Results show that the added mass can change the bifurcation behaviors of the anti-symmetric mode and affect the voltage and frequency of the bifurcation jump point. Typically, we propose a mass parameter identification method based on the dynamic jump motion of the anti-symmetric mode. Numerical studies are introduced to verify the validity of mass detection method. Finally, the influence of physical parameters on the sensitivity of mass sensor is analyzed. It is found that the DC voltage and mass adsorption position are critical to the sensitivity of the sensor. The results of this paper can be potentially useful in nonlinear mass sensors.

Conceptual Design of Oblong Ring Vibrators

Abstract An oblong ring-type structure is composed by two straight segments (length L) and two semicircular segments (radius R). It can be used to generate traveling waves, being applied to build linear piezoelectric motors and linear conveyor systems. The traveling waves to such applications occur at specific frequencies, generated by simultaneous symmetric and antisymmetric flexural vibration modes which, in general, have distinct natural frequencies. However, for specific designs, they may coincide or be very close. This may be achieved by finding the appropriate L/R ratio. For preliminary design, an analytical model is very desirable, due to its computational efficiency and the absence of a computational automatic identification of symmetric and antisymmetric flexural vibration modes among numerical solutions. Therefore, the objective of this work is to propose an analytical and practical model to determine classes of vibration modes of interest for producing traveling waves in oblong ring-type structures, being employed for conceptual design such that the L/R ratio is determined in an efficient way. The oblong ring is considered as a beam-like structure composed by straight and curved segments, employing Timoshenko and Euler–Bernoulli kinematic assumptions. A design method is proposed by solving sequentially and systematically distinct geometric proposals of oblong ring-type designs and, for each one, evaluating the candidates to produce the flexural traveling waves. Later, the strong-candidates are analyzed by finite element models to test the quality of the design with less assumptions. We show that the methodology provides convenient results as a design method for oblong ring-type structures.

Strain-dependent structure and Raman behaviours in the heavy-ion irradiated manganite at extreme low dose

The microstrains in heavy-ion irradiated manganite LaMnO3 can be managed in linear response of irradiation dose, and the corresponding internal pressure up to 8 GPa can be induced by varying doses. The response of structure under stress is studied by means of Density Functional Theory and Lattice Dynamic Calculation. All obtained Raman scattering lines are discussed in details to shed light onto structural changes during ion implantation. There appears new resonance peak at around 550 cm−1, which splits from broad features in the spectra, and attributes to the anti-symmetric vibrations of O6 cages. The blue shift of this peak scales to ~2.4 cm−1 per 1 GPa of stress. Another strong feature showing considerable blue shift is seen in the vicinity of 640 cm−1 and corresponds to one of rhombohedral distortion related soft modes. A weak mode, not frequently reported, is seen at around 420 cm−1 and corresponds to translation-like motions of fixed O6 cages.

Cooperative Capture of Uranyl Ions by a Carbonyl-Bearing Hierarchical-Porous Cu-Organic Framework.

To efficiently capture the toxic uranyl ions (UO2 2+ ), a new hierarchical micro-macroporous metal-organic framework was prepared under template-free conditions, featuring interconnected multi-nanocages bearing carbonyl groups derived from a semi-rigid ligand. The material exhibits an unusually high UO2 2+ sorption capacity of 562 mg g-1 , which occurs in an intriguing two-steps process, on the macropore-based crystal surface and in the inner nanocages. Notably, the latter is attributed to the cooperative interplay of the shrinkage of the host porous framework induced by uranyl accommodation and the free carbonyl coordination sites, as shown by both single-crystal X-ray diffraction and a red-shift of the infrared [O=UVI =O]2+ antisymmetric vibration band.

Cooperative Capture of Uranyl Ions by a Carbonyl‐Bearing Hierarchical‐Porous Cu–Organic Framework

AbstractTo efficiently capture the toxic uranyl ions (UO22+), a new hierarchical micro‐macroporous metal–organic framework was prepared under template‐free conditions, featuring interconnected multi‐nanocages bearing carbonyl groups derived from a semi‐rigid ligand. The material exhibits an unusually high UO22+ sorption capacity of 562 mg g−1, which occurs in an intriguing two‐steps process, on the macropore‐based crystal surface and in the inner nanocages. Notably, the latter is attributed to the cooperative interplay of the shrinkage of the host porous framework induced by uranyl accommodation and the free carbonyl coordination sites, as shown by both single‐crystal X‐ray diffraction and a red‐shift of the infrared [O=UVI=O]2+ antisymmetric vibration band.

Aerostatic instability mode analysis of three-tower suspension bridges via strain energy and dynamic characteristics

Multispan suspension bridges make a good alternative to single-span ones if the crossed strait or river width exceeds 2-3 km. However, multispan three-tower suspension bridges are found to be very sensitive to the wind load due to the lack of effective longitudinal constraint at their central tower. Moreover, at certain critical wind speed values, the aerostatic instability with sharply deteriorating dynamic characteristics may occur with catastrophic consequences. An attempt of an in-depth study on the aerostatic stability mode and damage mechanism of three-tower suspension bridges is made in this paper based on the assessment of strain energy and dynamic characteristics of three particular three-tower suspension bridges in China under different wind speeds and their further integration into the aerostatic stability analysis. The results obtained on the three bridges under study strongly suggest that their aerostatic instability mode is controlled by the coupled action of the anti-symmetric torsion and vertical bending of the two main-spans\' deck, together with the longitudinal bending of the towers, which can be regarded as the first-order torsion vibration mode coupled with the first-order vertical bending vibration mode. The growth rates of the torsional and vertical bending strain energy of the deck after the aerostatic instability are higher than those of the lateral bending. The bending and torsion frequencies decrease rapidly when the wind speed approaches the critical value, while the frequencies of the anti-symmetric vibration modes drop more sharply than those of the symmetric ones. The obtained dependences between the critical wind speed, strain energy, and dynamic characteristics of the bridge components under the aerostatic instability modes are considered instrumental in strength and integrity calculation of three-tower suspension bridges.

Symmetric and anti-symmetric vibrations in micropolar thermoelastic materials plate with voids

• Dispersion relation for symmetric and anti-symmetric vibrations. • Frequency equations for plate, flexural and Rayleigh’s waves. • Two modes of solution of frequency equations for surface waves. • Velocity ratios of first mode of solutions are greater than second mode. The problem of symmetric and anti-symmetric vibrations in micropolar thermoelastic plate with voids has been investigated. The dispersive frequency equations are obtained for different surface waves propagating in the plate. The velocity curves are depicted for the symmetric and anti-symmetric vibrations, plate, Rayleigh and flexural waves . It is found that there exist two modes in the solution of frequency equation for the surface waves in micropolar thermoelastic plate with voids. We have observed that the first modes of velocity ratios of corresponding surface waves are lesser than those of second mode of vibration .

Deformation and vibration of a buckled beam constrained by springy walls

In this paper we study the deformation and vibration of a pinned-pinned buckled beam constrained by a pair of springy walls of the Winkler type. Small deformation theory is adopted. Static analysis shows that the buckled beam contacts the springy wall in one segment first and then evolves to two-segment contact before the edge thrust reaches a maximum. This is different from the conventional case of rigid wall, in which only one-segment contact is possible before secondary buckling. The two-segment contact deformations before and after reaching the peak thrust are significantly different. Before reaching the peak, the free-of-contact segment in the middle stays close to the wall. After passing the peak, the free-of-contact segment moves away from the wall until the midpoint touches the opposite wall. In vibration analysis, both load control and displacement control are considered. For anti-symmetric vibration modes, the natural frequencies are the same for load and displacement controls. For symmetric modes, the natural frequencies of displacement control are in general higher than the corresponding ones in load control.

Vibrational Spectroscopy of N3- in the Gas and Condensed Phase.

Azido-derivatized amino acids are potentially useful, positionally resolved spectroscopic probes for studying the structural dynamics of proteins and macromolecules in solution. To this end, a computational model for the vibrational modes of N3- based on accurate electronic structure calculations and a reproducing kernel Hilbert space representation of the potential energy surface for the internal degrees of freedom is developed. Fully dimensional quantum bound state calculations yield the antisymmetric stretch vibration at 1974 cm-1 compared with 1986 cm-1 from experiment. This mode shifts by 64 cm-1 (from the frequency distribution) and 74 cm-1 (from the IR line shape) to the blue, respectively, compared with 61 cm-1 from experiment for N3- in water. The decay time of the frequency fluctuation correlation function is 1.1 ps, which is in good agreement with experiment (1.2-1.3 ps) and the full width at half maximum of the asymmetric stretch in solution is 18.5 cm-1 compared with 25.2 cm-1 from experiment. A computationally more efficient analysis based on instantaneous normal modes is shown to provide comparable, albeit somewhat less quantitative results compared to solving the three-dimensional Schrödinger equation for the fundamental vibrations.

Inertial mass damper for vibration control of cable with sag

It has been theoretically predicted that superior supplemental damping can be generated for a taut cable with an inertial mass damper. This paper extends previous studies to investigate the effect of the cable sag on the efficiency of an inertial mass damper. The general dynamic characteristics of an inclined sag cable with an inertial mass damper installed close to the cable end are theoretically investigated. The parametric analysis of the inertial mass and the damping coefficient of the inertial mass damper are conducted to evaluate the control performance of the cable with different sags. The results show that the inertial mass damper can alleviate the negative effect induced by the cable sag, and the cable sag can even increase modal damping ratios provided by the inertial mass damper. Sags of stay cables used in actual bridges only affect nearly symmetric vibrations of cables, while having little impact on nearly antisymmetric vibrations. The effect of cable sags will reduce the optimal damping coefficient and inertial mass of the inertial mass damper for the first symmetric mode of the cable.

Structural studies of transition metal ions doped in biomass ash as silica source for glass production in Thailand

(55-x)SiO2-13B2O3-1.0Al2O3-4.5BaO-6.3CaO-0.2Sb2O3-20Na2O-XMO (X = 0.0, 0.1, 0.2, 0.4, 0.6, 0.8, 1.0 and M = NiO, CoO, CuO and Fe2O3) were prepared by conventional melt quenching technique. In this research, glass productions from rice husk ash (RHA) and the effect of CoO, CuO, NiO, and Fe2O3 on structural properties were investigated. The local RHA in Nakhon Pathom Province, Thailand was used as a silica source for glass matrices. FTIR and RAMAN analysis were performed. FTIR reveled Si—O—Si antisymmetric vibrations of bridging oxygens for all transition ion doped glasses. Vibrations of transitional metal ions were observed in the lower wavenumber (˂1000cm−1) region in RAMAN spectra.

Stretch Vibrations of CH2 as a Measure of Conformational and Lateral Orders in Fatty Acid and Phospholipid Layers

The intensity of the line of antisymmetric vibrations of CH2 in the Raman spectrum of molecular layers of fatty acids and phospholipids is sensitive both to the molecular order in the layer (lateral order) and to the conformational order of the hydrocarbon chain of the molecule. Though the intensity of this line is widely used as an indicator of order in molecular layers containing hydrocarbon tails, the nature of sensitivity of the line of antisymmetric vibrations to the order is still disputable. This issue has been experimentally studied, and it has been demonstrated that disordering leads to redistribution of vibrational modes and to changes in polarizability of antisymmetric vibrations. A hypothesis is proposed that the intensity of the line of the Raman scattering of antisymmetric vibrations of CH2 is determined to a large extent by their interaction with electron excitation of the hydrocarbon chain.

Symmetric and antisymmetric vibration in elastic plate with voids immersed in a liquid

The problem of the symmetric and antisymmetric vibrations are attempted for the elastic plate with voids immersed in a liquid. The frequency equations are derived and deduced for the cases of plate wave, flexural and Rayleigh waves. It is also derived the cases when the liquid is replaced by vacuum/air. The two modes of vibration for the modified symmetric, antisymmetric, plate, flexural and Rayleigh waves in the considered medium are discussed. Numerically and analytically, the phase speeds and attenuations of symmetric and antisymmetric vibration, plate wave, flexural and Rayleigh waves are computed for a particular model. The effects of voids parameters on the phase speeds are also discussed.

Explicit Vibration Formulas Applicable to Timber Plates with Free and Simply Supported Edges

Advances in research and development have led to the application of high-strength timber plates to flooring-slab construction. It is envisaged that floors built from timber plates will have different vibration behavior from conventional joisted floors. In this paper, explicit formulas are developed based on a matrix formulation that links both the symmetric and antisymmetric vibration modes of orthotropic plates. The developed solution can be used for the dynamic analyses of orthotropic timber floor slabs. The solution presented in this paper overcomes limitations associated with previous solutions by eliminating the need for approximate series expansions for solving the characteristic equations. Its application is demonstrated by considering responses of plates with all or two simply supported edges. The new solutions agree closely with classical and Finite-Element Method (FEM) solutions, as well as with the experimental results for Cross-Laminated Timber (CLT) plates. The advantage of the new approach versus alternatives is a combination of accuracy and computational efficiency.

Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate

Anti-plane dynamic shear of a strongly inhomogeneous dynamic laminate with traction-free faces is analysed. Two types of contrast are considered, including those for composite structures with thick or thin stiff outer layers. In both cases, the value of the cut-off frequency corresponding to the lowest antisymmetric vibration mode tends to zero. For this mode, the shortened dispersion relations and the associated formulae for displacement and stresses are obtained. The latter motivate the choice of appropriate settings, supporting the limiting forms of the original anti-plane problem. The asymptotic equation derived for a three-layered plate with thick faces is valid over the whole low-frequency range, whereas the range of validity of its counterpart for another type of contrast is restricted to a narrow vicinity of the cut-off frequency.

Elimination of Nonstationary Oscillations of an Elastic System at the Stopping Time after Finite Rotation by the Given Law via the Tuning of Eigenfrequencies

The article deals with an arbitrary elastic 3D-system (body) that performs a controlled finite rotation with respect to some fixed axis and small nonstationary oscillations. The system oscillations occur due to external load (power control) or inertial load of the rotational transportation of the carrying body (kinematic control). The linear equations of oscillations are used in normal coordinates, in which motion is represented by eigenmodes of vibrations for system that is free in the rotation angle (including system rotation as a solid body in the case of power control) and for system fixed in rotation angle in the case of kinematic control. It is assumed that the (power or inertial)load acting on the system is proportional to some controlling finite time function from a certain class. The purpose of this article is to solve the problem of system rotation for a certain time from one rest position to another at a given finite angle using the given control function and to eliminate the elastic oscillations on the several lowest eigenmodes at the stopping time. The relations between the time of the system rotation under the action of a given control function and the eigenmodes frequencies for oscillations being eliminated are obtained on the basis of the exact solutions of the equations in normal coordinates. These relations satisfy the zero initial and final conditions. They are “tuned” by minimizing the positive definite quadratic form written for them by varying the system parameters to fulfill these relations simultaneously for several eigenfrequencies. As an example, the calculations for a model of a symmetrical spacecraft with two identical elastic solar cell panels consisting of four planar non-deformable sections connected by elastic hinges are carried out for comparison and analysis of the results accuracy. The finite rolling motion of the system with the damping at the stopping time of rotation for several (from one to three) lowest eigenmodes of antisymmetric vibrations is considered. The comparisons of the initial equations of motion for the system in generalized coordinates using several simple control functions and the found parameters of the “tuned” system with numerical solutions are accomplished.

Structural and photoluminescence properties of thermally stable Eu3+activated CaWO4 nanophosphor via Li+ incorporation

In the present paper, we have reported the variation of CaWO4:Eu3+ nano phosphors with different compositions of Li+, (LEC) (Li+ = 2, 5, 7 and 10 at%). The as-prepared (ASP) samples are annealed at 900 °C to eliminate unwanted organic moieties present in the sample and to improve crystallinity. These nanoparticles are characterized by X-ray diffraction (XRD), Thermogravimetric Analysis (TGA), X-ray photoelectron spectroscopy (XPS), Fourier transform IR spectroscopy (FTIR), Raman spectroscopy, photoluminescence studies. FTIR gives the absorption band at ~832 cm−1, which corresponds to antisymmetric vibrations due to O-W-O band in the WO42- tetrahedron. This is also confirmed by the Raman Spectroscopy. CaWO4 has a crystal of the Scheelite type having C4 h point group symmetry and I41/a space group symmetry. The surface/ particle morphology of 900 °C annealed samples studied using Transmission Electron Microscopy (TEM) and Scanning Electron Microscopy (SEM) and show the formation of nanosheet like structure. Annealed samples of lithium co-doped CaWO4:Eu3+nanoparticles have shown the red luminescence which is attributed due to the strong host contribution and different energy transfers from Li+ ions to host matrix under 392 nm excitations. Li+ ion improves the crystallinity and radiative transition rate and these materials may be potential candidates for white light emitting diodes and may be widely used as optoelectronic materials.

A novel additive manufactured three-dimensional piezoelectric transducer: Systematic modeling and experimental validation

Abstract Sandwich piezoelectric transducers are widely used in many industrial applications due to their attractive advantages of compact structure, no electromagnetic interference, and excellent output performance. V-shaped piezoelectric transducers, a typical design, have been adopted as the stator of ultrasonic motors and the machining tool of elliptical vibration surface manufacturing. However, traditional V-shaped piezoelectric transducers were designed with one contact interface to output effective vibration, limiting their applications. To achieve multi contact areas with synchronous actuation function, a novel three-dimensional sandwich piezoelectric transducer is proposed in this study, expecting to drive wheels of a robotic mobile system. Two orthogonal Langevin transducers are adopted to vertically couple in a cylinder, producing two bending vibrations with a spatial phase difference of π/2 in the cylinder. Therefore, elliptical motion is generated at surface points of two driving parts placed at both ends of the cylinder. Due to the fact that two front-end blocks of the two Langevin transducers and the cylinder form a three-dimensional configuration which hard to be manufactured by traditional machining methods, this part is printed using laser additive manufacturing. To analyze the dynamic behavior of the proposed three-dimensional transducer, an analytical model is carried out utilizing the transfer matrix method for providing systematic modeling. This developed transfer matrix model is not only capable of greatly reducing computation efforts, and it is maybe suitable for the analysis of traditional V-shaped transducers. To validate this developed transfer matrix model and confirm the feasibility of the transducer design, experimental investigations are conducted to measure the vibration characteristics of the proposed transducer prototype using a 3D laser Doppler vibrometer and are compared to the calculation results. The measured and computed resonant frequencies of the transducer are 19.975 kHz and 20.045 kHz for the symmetrical vibration mode, and 20.07 kHz and 20.06 kHz for the anti-symmetrical vibration mode, respectively. Comparisons show that calculation results match well with the experimental results, demonstrating the effectiveness of the developed transfer matrix model and the feasibility of the three-dimensional transducer design.

Role of Hydrogen-Bond Interactions in CO2 Capture by Wet Phosphonium Formate Ionic Liquid: A Raman Spectroscopic Study.

The mechanism of CO2 absorption by a formate ionic liquid, [P4444 ]HCOO, was studied by Raman spectroscopy. The band area for the symmetric CO2 stretching of the formate anion linearly decreases with the CO2 loading. From the slope of the decrease, 1 : 1 stoichiometry is proven between CO2 and the formate anion. The result favors the mechanism we proposed in a preceding work [J. Chem. Eng. Data 61, 837 (2016)]: HCOO- +CO2 +H2 O→HCOOH+HCO3- →[HCOOH…HCO3- ]. Further support for the mechanism is obtained by the observation of antisymmetric vibration of CO for the proposed hydrogen-bonded complex between HCOOH and HCO3- . The bands appeared as a doublet (1677 and 1730 cm-1 ) as this complex has two carbonyl groups. Based on DFT calculations, the [HCOOH…HCO3- ] complex is supposed to be the most abundant form of chemisorbed CO2 .

Boundary control of anti-symmetric vibration of satellite with flexible appendages in planar motion with exponential stability

In this research, we have investigated the planar maneuver of a flexible satellite with appendages anti-symmetric vibration. The hybrid governing equations are comprised of coupled partial and ordinary differential equations which are derived by employing Hamilton's principle. In this paper, control goals are the tracking desired pitch angle along with the flexible appendages vibration suppression simultaneously by using only one control torque which is applied to the central hub. The boundary control is proposed to fulfill these control aims; furthermore, this boundary control ensures that spillover instability phenomenon is eliminated, and in-domain sensors and actuators implement are excluded. Indeed, the proposed boundary control is able to stabilize an infinite number of vibration modes, which is one of the important benefits of the proposed control when it is considered that different factors including external disturbances and even the satellite maneuver can excite the various vibration modes of the flexible appendages and consequently the excitement of the high order vibration modes will be possible. Lyapunov's direct method is used to prove the exponential stability; moreover, this Proof is achieved in absence of any damping effect in modeling the vibrations of flexible appendages. In addition, the procedure for finding the boundary control coefficients which ensures the exponential stability is provided. Eventually, numerical simulations are presented to illustrate the effectiveness of the proposed boundary control.