Vibration Of Sphere Research Articles

Unlocking multidirectional and broadband wind energy harvesting with triboelectric nanogenerator and vortex-induced vibration of sphere

Unlocking multidirectional and broadband wind energy harvesting with triboelectric nanogenerator and vortex-induced vibration of sphere

Analytical modeling and experimental verification of a multi-DOF spherical pendulum electromagnetic energy harvester

Low-frequency vibration energy harvesting is a promising technology for providing floating buoys and small marine robots with sustainable energy from ocean waves. A spherical vibration energy harvester with multiple degrees of freedom has the advantages of good multi-directional adaptability and compact structure. However, its magnetic field distribution in three-dimension space is much more complex due to the combined effect of a series of cylindrical permanent magnets mounted on the surface of a gimbaled pendulum. The traditional finite element method is too time-consuming to perform efficient parameter design and optimization. To solve this problem, this work develops an analytical electromagnetic model for the spherical vibration energy harvester based on Biot-Savart Law. This model can be used to predict spatial magnetic flux distribution and electromotive force for given magnet and coil parameters. The accuracy and computational cost of the analytical model is verified by the comparison with the finite element method. Furthermore, the optimization of electromagnetic parameters is implemented to achieve maximum energy conversion efficiency. Finally, an optimized prototype is fabricated and tested in both laboratory and real sea. The resonant frequency and energy conversion efficiency of the prototype reaches 1.0 Hz and 25.45 %, respectively. It is shown that the experimental results are in good accordance with the analytical results.

Sound scattering and radiation suppression by pressurized spherical shells.

Thin-shell models offer important insights into the complex process of sound-structure interaction but are found to be inconsistent with the rigorous thick-shell theory for fluid-loaded spherical shells. Here, linearized equations of motion of fluid-loaded, thin, spherical shells are re-derived from the first principles. The shell may be prestressed due to the difference in the static pressures in the internal and external fluids. Differences in the fluid-loading terms from previously proposed ad hoc models are identified and their significance is analyzed. Analytic solutions are derived of the problems of spherical sound wave scattering by a fluid-filled, prestressed spherical shell and resonant vibrations of the shell. The results reduce to a number of known exact and asymptotic solutions in appropriate limiting cases. The mathematical model of the shell vibrations is applied to characterize the influence of the shell's material properties and the prestress on passive suppression of low-frequency underwater sound radiation due to diffraction on an acoustically compliant sphere, such as an encapsulated gas bubble. Using soft rubber as the encapsulating membrane is found to preserve the sound suppression qualities of the free gas bubble.

Nuclear Shape-Phase Transition From Spherical U(5) to Deformed gamma-Unstable O(6) Dynamical Symmetries of Interacting Boson Model Applied to Ru, Pd, and Xe Isotopic Chains

The shape transition from spherical vibrator U(5) to gamma-unstable deformed rotor O(6) in even-even Ru, Pd, and Xe isotopic chains are studied in framework of sd interacting boson model (IBM1) using the coherent state formalism to obtain the potential energy surfaces (PES’s). The location of critical points in the transition are identified by analysis the PES’s in terms of the deformation parameter beta and by using the catastrophe theory in terms of the two essential parameters (r_1, r_2). By using the most general IBM1 Hamiltonian in Casimir form with neglecting the U(5) and SU(3) quadratic Casimir operators and introducing only one control parameter the PES leads to the same energy surface as the Q-consistent IBM Hamiltonian at gamma =0. For the studied isotopic chains, the chi ^2-test is used to perform the fitting between the experimental and the corresponding calculated IBM for some selected energy levels and electric quadrupole transition probabilities B(E2) values using a simulated search program. A good agreement is produced for both energies and B(E2) transition rates. The present model calculations suggest that ^{100}Ru, ^{102}Pd and ^{130}Xe nuclei are good candidates for the E(5) critical point symmetry.

Spectral features of vibrational Te isotopes

The variation of collective vibrational spectra with varying $N$ displayed by the $Z=52$ Te isotopes, for less than $N=82$ closed shell, are of special interest. The spectral features of the ground band and the two and three phonon excited multiplets in $^{118--128}\mathrm{Te}$, are studied here empirically. The state energy $E({2}_{1}{}^{+})$ increases, and the energy ratio ${R}_{4/2}$ decreases with increasing neutron number $N$. Also the ${0}_{2}{}^{+}$ state rises up sharply, and the ${0}_{3}{}^{+}$ state follows it, unlike their relation in the E(5) symmetry. It is shown that $^{120}\mathrm{Te}$ isotope displays the weakly deformed status, and the heavier isotopes move towards the spherical harmonic vibrator status. The interacting boson model (IBM-1) is used to reproduce these spectral features of $^{118--124}\mathrm{Te}$, with use of slight variation of boson energy \ensuremath{\epsilon} and of the quadrupole interaction strength. In the microscopic approach, the dynamic pairing plus quadrupole model of Kumar and Baranger also reproduces these basic spectral features.

Extended analytical solutions of the Bohr Hamiltonian with the sextic oscillator: Pt-Os isotopes

The sextic oscillator adapted to the Bohr Hamiltonian has been used to describe even Pt and Os isotopes from A = 188 to 198 and A = 186 to 192, respectively. The purpose of this study was to investigate the possible transition from the γ-unstable to the spherical vibrator shape phases. In this setup the potential appearing in the Bohr Hamiltonian is independent from the γ shape variable, and the physical observables (energy eigenvalues, B(E2)) can be obtained in closed analytical form within the quasi-exactly solvable formalism for the model space containing 30 of the lowest-lying levels. Experimental energy levels have been associated with the theoretical ones. The available electric quadrupole transition data (B(E2), decay preferences) have been taken into account in matching the experimental and theoretical levels. Special attention has been paid to transitions from the first two excited 0+ levels to the and levels, as these indicate the change of shape phases with spherical and deformed potential minimum. The three parameters of the Hamiltonian have been determined by a weighted least square fit procedure. Trends in the location of states belonging to the ground-state, the K π = 2+ and two excited K π = 0+ bands have been analysed. The trajectory determined by the fitted parameters in the two-dimensional phase space has also been plotted, and it has been found that all the nuclei are characterized by a deformed potential minimum, except for the heaviest Pt isotope (198Pt), for which the transition to the spherical shape phase is realised. Although the spectroscopic information on the next isotopes of the chains (200Pt and 194Os) is far less complete, there are indications that these nuclei are also close to or fall within the domain of spherical potential minimum.

Inelastic light scattering from a dielectric sphere with a time-varying radius

This work reports on light scattering by a homogeneous dielectric sphere with a periodically time-varying radius. The off-shell inelastic scattering $T$ matrix, which describes the dynamically changing particle, is evaluated using the Floquet method, and some remarkable phenomena, emerging in the strong- and weak-coupling regimes, are discussed. In particular, the limits of validity of the approximate quasistatic solution are established through comparison with the results of fully dynamic calculations, and the scattering in the strong-coupling regime is analyzed in terms of the general behavior of parametrically driven oscillators. Additionally, the influence of damping of the sphere vibrations on the optical spectra is also investigated.

Computational method of underwater acoustic radiation from a spherical shell coupled with nonlinear systems

During the continuous research and practical application of nonlinear vibration isolation systems, new problems arise for the vibro-acoustic calculation of underwater targets. The present frequency-domain analysis method can only deal with linear problems, so the acoustic radiation calculation of underwater targets coupled with nonlinear systems can only be performed in the time domain. When it comes to the real-time calculation, the huge computation cost will definitely bring challenges to the practical application. To solve this problem, a new calculation method is established for the underwater vibro-acoustic problems of structures coupled with nonlinear systems, taking elastic spherical shells as research objects in this paper. This method realizes the time-frequency domain conversion of the fluid-structure coupled vibration equation of an elastic spherical shell through the Fourier transform. The explicit difference method is further used to calculate the vibration response of the spherical shell, while the Newmark method is used to calculate the vibration response of the internal nonlinear system. An efficient integrated calculation of the two coupling parts is then achieved by considering boundary conditions at the connection point. Without the time-domain acoustic field solution, this method is able to calculate the vibration response of both the internal nonlinear system and the spherical shell, as well as the radiated acoustic power generated by the spherical shell vibration in real time. The calculation complexity and efficiency are radically improved. The nonlinear system discussed in this paper is a nonlinear mass-spring oscillator system installed at the bottom of a spherical shell. Finally, the correctness of the method described in this paper is verified through specific numerical examples, and a series of calculations and analyzes are carried out to explore the influence of nonlinear effects on the acoustic radiation of underwater structures. The calculation method described in this article is not limited to spherical shells, and is still applicable to general underwater targets.

Study on Multidegree-of-Freedom Ultrasonic Motor Using Vibration Mode Rotation of Metal Spherical Stator

Most of the multidegree-of-freedom ultrasonic motors (MDOF-USMs) use a spherical rotor, and the design of the stator is restricted due to the use of the resonance mode. (1) Therefore, there is almost impossible to freely design the overall shape, resulting in a complicated structure. (2) To solve such an inconvenience, an MDOF-USM using a metal spherical stator was proposed. The vibration mode rotation on the stator was designed by theoretical analysis of spherical vibration and finite element method analysis. Multilayer piezoelectric actuators (MPAs) were embedded in the sphere to excite the vibration mode. Cylindrical projections were attached to the surface of the stator to magnify the vibration displacement and worked as the driving part. Their effects were evaluated using an electronic circuit simulator method of performance analysis. (3) As a result, two types of vibration mode rotation methods for the 3-DOF rotation were confirmed. It was also confirmed that the rotor covering the outside stator rotates around three axes. However, tiny torque, low power factor, and slow speed were obtained. (4) An MDOF-USM using a spherical stator was realized according to the operating principle. However, since the cause of such a low performance is the excitation method of the sphere and the rotor structure, research for improvement is required in the future.

Dynamical Backaction Magnomechanics

Dynamical backaction resulting from radiation pressure forces in optomechanical systems has proven to be a versatile tool for manipulating mechanical vibrations. Notably, dynamical backaction has resulted in the cooling of a mechanical resonator to its ground-state, driving phonon lasing, the generation of entangled states, and observation of the optical-spring effect. In certain magnetic materials, mechanical vibrations can interact with magnetic excitations (magnons) via the magnetostrictive interaction, resulting in an analogous magnon-induced dynamical backaction. In this article, we directly observe the impact of magnon-induced dynamical backaction on a spherical magnetic sample's mechanical vibrations. Moreover, dynamical backaction effects play a crucial role in many recent theoretical proposals; thus, our work provides the foundation for future experimental work pursuing many of these theoretical proposals.

Experimental evidence of exact E(5) symmetry in Kr82

The low-lying positive-parity structures of $^{82}\mathrm{Kr}$ have been investigated following their population in the $^{76}\mathrm{Ge}(^{9}\mathrm{Be},3n)$ reaction at ${\mathrm{E}}_{\mathrm{lab}}\ensuremath{\approx}31\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and using a large array of Compton suppressed HPGe clovers as the detection setup. Apart from other spectroscopic measurements, level lifetimes of the states have been extracted using the Doppler shift attenuation method. The level energies and the associated transition probabilities exhibit superlative overlap with the calculations in the framework of the interaction boson approximation and the E(5) model. The $^{82}\mathrm{Kr}$ nucleus, thus, exemplifies the critical point of phase (shape) transition from the U(5) (spherical vibrator) to the O(6) ($\ensuremath{\gamma}$-soft rotor) paradigms of nuclear structure.

Adapting H-infinity controller for the desired reference tracking of the sphere position in the maglev process

The Maglev process consists in a magnetic field geerated by the modulation of a coil current which yields the sphere levitation. Foucault current is the current transmitted from the coil to a sphere in the Maglev process which yields the undesired sphere vibrations. In this study, an adapting H-infinity controller is introduced as the combination of the adapting and H-infinity strategies for the desired reference tracking of the sphere position in the Maglev process. The adapting strategy is used for the unknown dynamics estimation, and the H-infinity strategy is used for the desired reference tracking. The Lyapunov technique is used to satisfy the error convergence and the H-infinity criterion. Two simulations show the effectiveness of the considered method for the desired reference tracking of the sphere position in the Maglev process.

Vibration reduction of a sphere through shear-layer control

To date, it has been shown that the vibration response of an elastically mounted sphere undergoing vortex-induced vibration (VIV) can be controlled by imposing rotary oscillations at frequencies close to the vibration frequency. Here, we demonstrate that rotary oscillations imposed at significantly higher frequencies can be used to directly influence shear-layer vortex shedding and consequently reduce vibration. This approach contrasts with aiming to directly target the large-scale wake structures, using lower frequency perturbations. The oscillation frequencies imposed were between 5 and 35 times the natural frequency of the system and the amplitude of the rotational velocities were only 10% of the free-stream velocity. The effects of the rotary oscillations were found to vary significantly across sphere vibration modes. In the mode III transition regime significant attenuation of the vibration response was observed for a narrow band of rotary oscillation frequencies. Time-resolved particle image velocimetry revealed that the shear-layer vortex structures locked to the forcing frequency, where suppression of the vibration response occurred. Optimal tuning of the oscillation frequency reduced the vibration amplitude in the mode III transition regime by 84%, with a rotational velocity amplitude of only 10% of freestream. These results show low-amplitude shear-layer forcing is a promising method of more efficiently suppressing VIV of three-dimensional geometries.

DEM simulations of vibrated sphere packings in slender prismatic containers

Discrete Element Method (DEM) simulations are carried out to investigate the packing structure of the vibrated mono-sized and polydisperse particle assemblies in slender prismatic containers. Quantities like void fraction distributions, coordination number distribution, Voronoi packing fraction distributions were analyzed. DEM simulations show excellent agreement with the experimental data. The transient response of the packing structure during the vibration of mono-sized spheres reveals that the crystallization starts at the walls. The packing structure's crystallinity enhances during vibration, increasing the packing density of the assembly. Vertical vibration is found to be more effective compared to lateral vibration. The packing structure is found to be independent of the container's orientation during the filling process. The influence of the ratio of the container dimensions to mean particle diameter (X/dm) and polydispersity (λ) on the packing structure is analyzed. The results showed that the increase of X/dm ratio or λ, increases the random arrangement of particles.

Circular motion of submillimeter-sized acoustic bubbles attached to a boundary by high-speed image analysis

The circular motion of submillimeter-sized bubbles attached to a boundary in an 18.5 kHz ultrasonic field are investigated experimentally by high-speed photography and image analysis. It is found that the vibration of gas bubbles with diameters of 0.2–0.4 mm is between spherical radial vibration and regular surface fluctuation. Different from the circular motion of suspended bubbles in water, the circular motion of gas bubbles attached to a boundary presents some new characteristics. These bubbles attached to a boundary (wandering bubbles) will rotate around a fixed bubble array (holding bubbles). Both the wondering bubbles and holding bubbles are “degas” bubbles. The primary Bjerknes force acting on wandering bubbles in the acoustic wave field and the secondary Bjerknes force between the wandering bubbles and the holding bubbles strongly affects the circular motion. The circling and residence behavior of gas bubbles is described and analyzed in detail, which is helpful to understand and improve industrial applications such as ultrasonic cleaning, sonochemical treatment, aeration and cavitation reduction.

Dilatation gradient elasticity theory

A simplified version of the strain gradient elasticity theory, in which all gradient effects are related to the first scalar invariant of the infinitesimal strain tensor, i.e., to the dilatation, is developed. Two variants of the theory with different forms of boundary conditions are derived using the variational approach. The first variant is derived taking into account independence of the dilatation variation on the body surface and it has simplified traction boundary conditions formulated only with respect to the total stress tensor. The second variant is derived following a general procedure exploiting the surface divergence theorem which results in a more complex form of boundary conditions on the body surfaces and edges. Correctness of the presented formulations of the theory is discussed. Examples of analytical solutions for the problems of pure bending, pressurized sphere and radial vibrations of sphere are obtained and compared for both variants of the theory.

An analytical method for shallow spherical shell free vibration on two-parameter foundation

The free vibration control differential equation of shallow spherical shell on two-parameter foundation is a four order differential equation. Using the intermediate variable, the four order differential equation is reduced to two lower order differential equations. The first lower order differential equation is a Helmholtz equation. A new method of two-dimensional Helmholtz operator is proposed as shown in the paper in which the Bessel function included in Helmholtz equation needs to be treated appropriately to eliminate singularity. The first lower order differential equation is transformed into the integral equation using the proposed method in the paper. The second lower order differential equation which is a Laplace equation is transformed into the integral equation by existing methods. Then the two integral equations are discretized according to the middle rectangle formula, and the corresponding solutions can be obtained by MATLAB programming. In this paper, the R-function theory is used to select the appropriate boundary equation to eliminate the singularity. Based on the properties of R-function, the combined method of Helmholtz equation and Laplace equation can solve the free vibration problem of irregular shallow spherical shell on two-parameter foundation. Five examples are given to verify the feasibility of the method.

Quasi-exact solutions for the Bohr Hamiltonian with sextic oscillator potential

A discussion on the quasi-exact solution of the Bohr Hamiltonian with sextic oscillator potential is made by attracting the attention on some recent results of its application to the phase transition from spherical vibrator to a γ-unstable system. More precisely, it is underlined the importance of the solvability order on the structure of the states, especially in the critical point, respectively, in the deformed region of the phase transition.

A collective description of the unusually low ratio B4/2 = B(E2; → )/B(E2; → )

The unusually low value of the ratio along the yrast band is described in the interacting boson model-1. Two three-body interactions with SU(3) symmetry are additionally introduced into the usual Hamiltonian describing the transitional behaviors from the spherical vibration to the ellipsoidal rotation. In the SU(3) limit, the energy of the state in the irrep can be lower than the one of the state in the irrep (2N, 0), which causes the anomaly.

Nuclear shape transition between the limiting symmetries U(5) and SU(3) of interacting boson model applied to double even Hafnium isotopic chain

The shape structure of even-even Hafnium isotopic chain 160–180Hf is investigated within the framework of sd-version of interacting boson model (IBM1) using coherent state formalism, the Hamiltonian operator of the model contains Casimir operators of the dynamical symmetries U(5) and SU(3) of the IBM1 besides the Casimir operator of the subgroup O(3). The potential energy surfaces (PES's) are calculated by diagonalizing the Hamiltonian between the coherent states. The PES's are analyzed in terms of the shape variables β, γ and the essential parameters r1, r2 and the locus of the critical points are identified. The model parameters for each nucleus are adjusted so as to reproduce some selected low lying energy levels and reduced electric quadrupole transition probabilities B(E2) with corresponding experimental data.For each nucleus the calculations are performed using the computer codes PHINT, BEFM besides a simulated fitting search program to give best fit between IBM and experimental values. The characteristic of energy ratios and B(E2) values are studied and analyzed with respect to increasing of the total number of bosons.It is concluded that the Hf isotopes lies in shape transition U(5) – SU(3) region of the IBM1 such that lighter isotopes comes very close to spherical vibrator limit U(5), while the heavier isotopes tends to be near the deformed rotator limit SU(3).