Rigid Oscillator Research Articles

Thermodynamic properties of crystalline and gaseous lower niobium chlorides

Thermodynamic functions of crystalline and gaseous niobium chlorides in lower state of oxidation are presented. The thermodynamic properties of solid niobium chlorides including their clusters Nb3Cl8 (NbCl2.67) and Nb6Cl14 (NbCl2.33) in the temperature range from 298 to 1300 K were calculated using experimental low temperature isobaric heat capacity measurements, thermogravimetric and tensimetric data on the process of their thermal decomposition and mass-spectrometric determination of vapor phase composition during this process.The thermodynamic properties of gaseous lower niobium chlorides in the temperature range 298-2000 K were calculated using vibration frequencies of these molecules. The latter were obtained using suggested molecular structures by a method involving the application of the force constants estimated on the basis of vibration frequencies of vapors of titanium, zirconium and vanadium tetrachlorides in terms of modified valence force field.The vibration frequencies were used to calculate the thermodynamic functions of gaseous niobium lower chlorides in terms of the rigid rotator-harmonic oscillator approximation.The obtained thermodynamic data allowed us to calculate the composition of the vapor phase in the system Nb=NbCl5 (vapor) in the temperature range from 700 to 2000 K for pressures 10−6 and 1 atm. The mechanism of thermal decomposition of niobium cluster Nb6Cl14 (NbCl2.33) was determined under pressure of 1 atm and in vacuum.

Simultaneous streamwise and cross-stream oscillations of a diamond oscillator at low Reynolds numbers

A two-dimensional stabilized space-time finite-element-based in-house solver is used to explore flow around an elastically mounted rigid diamond oscillator undergoing undamped vortex-induced vibrations in transverse and stream-wise directions simultaneously. The computations are carried over a reduced velocity (U*) range of 1–12 keeping the Reynolds number (Re) and the mass ratio (m*) fixed at 100 and 10, respectively. In the current investigation, a five-branch response behavior with the presence of an “upper branch” is identified, which is absent for transverse-only oscillations. A shift in normalized time-averaged phase difference (ϕ/π) from 0 to 1 is related to the transition from the upper to the lower branch. The non-dimensional oscillation frequencies in both streamwise and cross-stream directions (Fx and Fy, respectively) collapse on the upper branch, matching the oscillator's non-dimensional natural frequency (FN). This leads to periodic single-looped “raindrop-shaped” cylinder trajectories. On this branch, the vortex-shedding mode is asymmetric, and the mean lift is non-zero (Clavg≠0). For all other response branches, Clavg≈0 and the vortex-shedding modes are symmetric. The presence of multiple frequencies in the in-line oscillations makes the initial branch quasi-periodic, whereas all other response branches are periodic. The addition of in-line motion modifies the fluid loading on the oscillator significantly.

Acoustic Waves Radiated From Two Degrees-of-Freedom Nonlinear Rigid Oscillator Systems Immersed in Unbounded Compressible Fluid

Abstract This paper is concerned with the nonlinear behaviors of acoustic waves produced by two degrees-of-freedom rigid oscillators containing nonlinearities and immersed in infinite fluid medium. The vibrations of the oscillators are computed by both the harmonic balance method (HBM) and the direct-time integration scheme, whereas the linearized Euler equations (LEEs) of the acoustic fluid are discretized by a fourth-order dispersion-relation-preserving (DRP) scheme in space and a four-level explicit time marching scheme in time. A constrained moving least-squares (CMLS) immersed boundary method (IBM) is used to enforce the boundary conditions on the common interfaces of the rigid oscillators and the Cartesian grid of the acoustic fluid. A serially staggered procedure is adopted to solve the governing equations of the oscillators and the acoustic fluid as a coupled system. The perfectly matched layer (PML) technique is utilized to damp out the out-going acoustic waves on the boundaries of the truncated computational domain to approximate the nonreflecting wave conditions. Physical insights into the mechanism of the nonlinear acoustic waves induced by super-harmonic resonances, principal resonances, internal resonances, and combination resonances of two degrees-of-freedom nonlinear oscillator systems are provided. The interference fringes of the acoustic waves due to the nonlinear vibration of the system are also discussed. Numerical results show that the sound fields radiated from the vibration system with the above nonlinear behaviors exhibit more complicated interference phenomena since the high-order harmonic components are introduced.

A coupled closed-form/Doubly Asymptotic Approximation approach for the response of orthotropic plates subjected to an underwater explosion

ABSTRACT A closed-form analytical solution procedure is proposed to solve the coupled fluid-structure interaction (FSI) equations that involve the first-order Doubly Asymptotic Approximation (DAA1) formulation. An efficient method comprised of the nonstandard finite difference (NSFD) scheme is applied. First of all, analytical equations are developed to analyze the response of a rigid mass-spring oscillator in an air-backed condition when it is subjected to a plane shock exponential wave coming from a far-field underwater explosion. After validating the results with LS-DYNA/USA (DAA1), these equations are extended to determine the response of a two-dimensional, simply-supported rectangular plate, and then tested on the isotropic and orthotropic plates within a small deflection regime. Parametric studies are also performed by varying the load decay times, peak pressures, as well as the aspect ratios of the plate. Finally, the advantages and limitations of the proposed formulae are exposed along with suggestions for the future work.

Transition of VIV-only motion of a square cylinder to combined VIV and galloping at low Reynolds numbers

Abstract A rigid oscillator of square cross-section at zero incidence is susceptible to galloping motion. Depending on the mass ratio, m ∗ of the oscillator, the oscillations may be vortex-induced (VIV) or alternately, vortex-induced at low Reynolds numbers, R e and galloping at higher R e . For R e ≤ 250 , the mass ratio at which the motion turns from VIV-only to the one with combined VIV and galloping is determined via space–time finite-element computations in two-dimensions for 3 ≤ m ∗ ≤ 4 . This choice of m ∗ range is driven by the conclusion drawn by Sen and Mittal (2015) that the value of transition mass ratio lies between 1 and 5. For free undamped vibrations of a square cylinder simultaneously along and across the flow, the transition occurs when the value of m ∗ equals 3.4. There exists an essential interdependence between the onset of galloping and presence of secondary hysteresis at m ∗ = 3 . 4 .

Reinvestigation of the rotation effect in solid He4 with a rigid torsional oscillator

The irrotational nature of superfluid helium was discovered through its decoupling from the container under rotation. Similarly, the resonant period drop of a torsional oscillator (TO) containing solid helium was first interpreted as the decoupling of solid from the TO and appearance of supersolid. However, the resonant period can be changed by mechanisms other than supersolid, such as the elastic stiffening of solid helium that is widely accepted as the reason for the TO response. To demonstrate the irrotational nature more directly, the previous experiments superimposed the dc rotation onto the TO and revealed strong suppression on the TO response without affecting the shear modulus. This result is inconsistent with the simple temperature-dependent elasticity model and supports the supersolid scenario. Here, we re-examine the rotational effect on solid helium with a two-frequency rigid TO to clarify the conflicting observations. Surprisingly, most of the result of previous rotation experiments were not reproduced. Instead, we found a very interesting superfluid-like irrotational response that cannot be explained by elastic models.

Comparison between cyclic and dynamic rocking behavior for embedded shallow foundation using centrifuge tests

Designs allowing the rocking behavior of the foundation during earthquake have been introduced to reduce the seismic load on the superstructure and the ductility demand on the structural column. In addition, several studies have been conducted on rocking foundation based on the slow cyclic and dynamic tests by assuming the structure as a rigid oscillator. However, when structural bending is included, the rocking behaviors of the foundation for the slow cyclic and dynamic tests are different. Therefore, a clear description of each method and how each behavior is different should be investigated by considering structural bending motion. To fill the gap between cyclic and dynamic rocking behaviors, embedded foundation models with various slenderness ratios of the systems were investigated using horizontal slow cyclic tests and dynamic tests in a centrifuge. Test results show that the rocking foundation was affected by structural bending. The overturning moment in the dynamic test determined by the conventional method was different compared with results obtained from the slow cyclic test due to the structural bending motion. Finally, the overturning moment was re-evaluated by considering structural net displacement, and the re-evaluated dynamic overturning moment matched the results from the slow cyclic tests.

Bifurcation Analysis of a Rigid Impact Oscillator with Bilinear Damping

This paper studies a rigid impact oscillator with bilinear damping developed as the mechanical model of an impulsive switched system. The stability and the bifurcation of periodic orbits in the impact oscillator are determined by using the mapping methods. One‐parameter bifurcation analyses under variation of forcing frequency and amplitude of external excitation are carried out. Coexisting attractors and various types of bifurcations, such as grazing, period‐doubling, and saddle‐node, are observed, which show the complex phenomena inhered in this impact oscillator.

Is rocking motion predictable?

SummaryAn argument of engineers and researchers against the use of rocking as a seismic response modification technique is that the rocking motion of a structure is chaotic and the existing models are incapable of predicting it well. This argument is supported by the documented inability of rocking models to predict the motion of a specimen excited by a single ground motion. A statistical comparison of the experimental and the numerical responses of a rigid rocking oscillator not to a specific ground motion, but to ensembles of ground motions that have the same statistical properties, is presented. It is shown that the simple analytical model proposed by Housner in 1963 is capable of predicting the statistics of seismic response of a rigid rocking oscillator.

Plasticity in the Period of the Circadian Pacemaker Induced by Phase Dispersion of Its Constituent Cellular Clocks.

The mammalian circadian pacemaker is commonly thought to be a rigid oscillator that generates output under a variety of circumstances that differ only in phase, period, and/or amplitude. Yet the pacemaker is composed of many cells that each can respond to varying circumstances in different ways. Computer simulations demonstrate that networks of such pacemaker cells behave differently under a light-dark cycle compared with constant darkness. The differences demonstrate that the circadian pacemaker is plastic: The pacemaker shapes its properties in response to the circumstances. A consequence is that properties of a pacemaker under a light-dark cycle cannot be derived from studies of the same system in constant darkness. In this paper we show that the dispersion of phase in a network of coupled oscillators can influence ensemble period: For the considered type of coupling, it is demonstrated that the more synchronous the cells are, the longer is the ensemble period. This is consistent with various data sets obtained in mammals, and even with a data set from fruit flies, in which circadian variation in behavior is regulated in a distinctly differently way from that in mammals. We conclude that environmental circumstances such as photoperiod and exposure to light pulses in otherwise darkness modify the phase distribution of the network and, thereby, the period of the ensemble. Our study supports the view that such properties as circadian period are not solely determined by clock genes but are also determined by the genes that regulate the communication in cellular networks.

A study of the electronic structure and properties of the propargyl radical

By means of B3LYP/6-311++G(3df,3pd) the electron density distribution in the propargyl radical CH2CCH is obtained. Within the Quantum Theory of Atoms in Molecules the phenomenon of conjugation and the spin density distribution of the unpaired electron in CH2CCH are studied at the qualitative level. Characteristics of the electronic structure of CH2CCH and its parent molecules CH3–C≡CH and CH2=C=CH2 are compared. With the use of the rigid rotator-anharmonic oscillator model the thermodynamic properties of the propargyl radical and enthalpies of bond cleavage in propyne and allene are calculated in the temperature range 298-1500 K. The relationship between the electronic and thermodynamic properties of CH2CCH is considered and its conjugation energy is calculated.

Thermodynamic properties of dimethylene urethane

Enthalpies of the combustion and formation of crystalline dimethylene urethane (oxazolidin-2-one) are determined via combustion calorimetry. The enthalpy of sublimation is determined via the transpiration method, and the enthalpy of fusion is found by means of differential scanning calorimetry. The temperature dependence of the saturated vapor pressure is measured in the range of 323–353 K. Thermodynamic functions in the ideal gas state are calculated using the rigid rotator-anharmonic oscillator model in the range of T = 298.15–1500 K.

Use of Ricker motions as an alternative to pushover testing

When undertaking centrifuge studies on seismic soil–structure interaction, it is useful to be able to define the pseudo-static ‘pushover’ response of the structure. Normally, this requires separate centrifuge experiments with horizontal actuators. This paper describes an alternative procedure, using Ricker ground motions to obtain the pushover response, thereby allowing both this and the response to seismic shaking to be determined using a centrifuge-mounted shaker. The paper presents an application of this technique to a 1:50 scale model bridge pier with two different shallow foundations, as part of a study on seismic protection using rocking isolation. The moment–rotation (‘backbone’) behaviour of the footings was accurately determined in the centrifuge to large rotations, as verified through independent three-dimensional dynamic non-linear finite-element modelling. Ricker wavelet ground motions are therefore shown to be a useful tool for the identification of pushover response without requiring additional actuators. Furthermore, a simplified analytical methodology is developed, which allows one to predict the maximum foundation rotation induced by a specific Ricker pulse. This methodology may be useful in predicting the characteristics (frequency and acceleration magnitude) of the Ricker pulse required to describe the pushover response of any (practically) rigid oscillator supported on shallow foundations.

Neutron-rich hypernuclei in the chiral soliton model

The binding energies of neutron-rich strangeness S = −1 hypernuclei are estimated in the chiral soliton approach using the bound state rigid oscillator version of the SU(3) quantization model. Additional binding of strange hypernuclei in comparison with nonstrange neutron-rich nuclei takes place at not large values of atomic (baryon) numbers, A = B ≤ ∼10. This effect becomes stronger with increasing isospin of nuclides, and for the “nuclear variant” of the model with rescaled Skyrme constant e. Binding energies of Λ 8 He and recently discovered Λ 6 H satisfactorily agree with data. Hypernuclei Λ 7 H, Λ 9 He are predicted to be bound stronger in comparison with their nonstrange analogues 7H, 9He; hypernuclei Λ 10 Li, Λ 11 LI, Λ 12 Be, Λ 13 Be, etc. are bound stronger in the nuclear variant of the model.

Anharmonicity in the V2O3 molecule and thermodynamic properties of V2O3 in the gas phase

A quantum-mechanical calculation of the relative stability, structural parameters, and vibrational frequencies of V2O3 molecule isomers for different spin states was carried out using the BPW91/6-311+G(d, p) method. It was shown that the isomer with the Cs structure (nonplanar VOVO rectangle with an O atom attached to it) in the X5A″ electronic state possesses the maximum stability. The energy of the C2v symmetry structure was higher than the lowest energy by just 23 cm−1. It definitely indicated the impossibility of usage of the harmonic model in order to calculate the thermodynamic functions of V2O3 (g). A model is proposed based on which the energy levels and vibrational sums of states for this type of motion were calculated for the Cs → C2v → Cs transition coordinate. These data, as well as results obtained from quantum-mechanical calculations, were used to calculate the thermodynamic functions of V2O3 (g) in the temperature range of T = 100–6000 K. The calculations were performed with the five excited electronic states with energies from 1000 to 9000 cm−1 taken into account. A comparison with the data calculated in the “rigid rotator-harmonic oscillator” approximation was performed.

A uniform semiclassical representation of transition probabilities derived from factorization formulas

Factorization formulas are used to derive a uniform semiclassical approximation of transition probabilities. The latter are determined in the analytical form where the basis transition probabilities are set by the analytical formula. As an example, we consider the rigid rotor, harmonic oscillator, and Morse oscillator in collisions with structureless particles.

Examination of quantized multiskyrmions as possible nuclear bound states of antikaons

The spectrum of strange multibaryons is considered within the chiral soliton model using one of several possible SU(3$ quantization models (the bound state rigid oscillator version). The states with energy below that of antikaon and corresponding nucleus can be interpreted as antikaon-nucleus bound states. In the formal limit of small kaon mass the number of such states becomes large, for real value of this mass there are at least several states. For large values of binding energies interpretation of such states just as antikaon-nuclear bound states becomes more ambiguous.

Complex equilibria in unsaturated vapor over AlBr3

Unsaturated AlBr 3 vapor pressure was measured over the temperature and pressure ranges 560–845 K and 54–145 torr by the static method using a quartz diaphragm pressure gauge with increased sensitivity (the confidence interval of pressure, including thermal drift of zero pressure gauge point, was 0.3 torr, and that of temperature, 0.3 K). Two equilibrium models were considered, one including AlBr3 and Al2Br6 and the other, AlBr3, Al2Br6, and Al3Br9. The molecular constants of all vapor constituents were determined using density functional theory at the B3LYP/6-31G(d,p) level. The thermodynamic functions of all bromides were calculated in the rigid rotator-harmonic oscillator approximation. The enthalpies of independent equilibria for each model were determined by minimizing the residual sum of the squares of pressure discrepancies. According to the first model, 0.5Al2Br6 = AlBr3, ΔHo(298.15) = 13629.1 ± 9 cal/mol. According to the second model, 0.5Al2Br6 = AlBr3, ΔHo(298.15) = 13638.8 ± 8 cal/mol, and 1.5Al2Br6 = Al3Br9, ΔHo(298.15) = −8528 ± 800 cal/mol. The second model, for which the variance of pressure differs insignificantly from the experimental variance of pressure, should be given preference.

The thermodynamic properties of 4f metal trifluorides

The experimental low-temperature heat capacities of some solid 4f metal trifluorides were used to reveal the trends in the behavior of variable parameters in the equation that described the lattice heat capacity component in the quasi-harmonic approximation for the whole series of LnF3 (Ln = La, … Lu) compounds. The results were used to describe the temperature dependences of heat capacity over the temperature range from 0 K to the melting point T m. The measured high-temperature enthalpy increments were used to determine corrections to the quasi-harmonic description of heat capacities at T > ∼0.5T m. The reduced Gibbs energies were calculated over the temperature range 298.15–2000 K. The thermodynamic functions of LnF3 in the gaseous state were determined over the same temperature range in the rigid rotator-harmonic oscillator approximation. All calculations were performed taking into account excited electronic states whose energies did not exceed 10000 cm−1. The reliability of the thermodynamic functions obtained was proved by the convergence of the enthalpies of sublimation calculated by the second and third laws of thermodynamics from the experimental data on saturated vapor pressures. The complete set of the consistent thermodynamic properties of these compounds is described.

Thermodynamic properties of some lanthanum and lanthanide halides: II. Thermodynamic functions of gaseous molecules LnX (Ln = Ce−Lu, X = F, Cl)

The molecular constants of LnF (Ln = Ce−Lu) for the ground state have been estimated based on the available spectroscopic characteristics of lanthanum and lanthanide monofluorides. These constants have been used for calculating the reduced Gibbs energy (−[G 0(T) − H 0(0)]/T) of the compounds in the ideal gas state in the range 298.15–3000 K at the standard pressure p 0 = 0.1 MPa. The rigid rotator-harmonic oscillator approximation with additional inclusion of the anharmonicity of oscillations (by the method of Mayer and Goeppert-Mayer) and correction for centrifugal stretching have been used. The contribution made by electronic excitation has been calculated by two methods: based on the energies of the excited states of molecules and based on the electronic excitation energy of the free Ln+ ion. Analogous data are reported for lanthanide monochlorides.