Torsional vibration of crankshaft in an engine–propeller nonlinear dynamical system

Theoretical and experimental studies on torsional vibration of an aircraft engine–propeller system are presented in this paper. Two system models—a rigid body model and a flexible body model, are developed for predicting torsional vibrations of the crankshaft under different engine powers and propeller pitch settings. In the flexible body model, the distributed torsional flexibility and mass moment of inertia of the crankshaft are considered using the finite element method. The nonlinear autonomous equations of motion for the engine–propeller dynamical system are established using the augmented Lagrange equations, and solved using the Runge–Kutta method after a degrees of freedom reduction scheme is applied. Experiments are carried out on a three-cylinder four-stroke engine. Both theoretical and experimental studies reveal that the crankshaft flexibility has significant influence on the system dynamical behavior.     

High-sensitivity CRDS absorption spectroscopy of acetylene between 5851 and 6341 cm−1

The absorption spectrum of acetylene has been recorded at room temperature (297 K) using high-sensitivity cavity ring-down spectroscopy (α_min ～ 5×10^?11 cm^?1) in the 5851 and 6341 cm^?1 interval corresponding to a region of very weak absorption. A list of about 10,700 absorption features with estimated absolute line intensities was constructed. The smallest intensities are of the order of 5×10^?29 cm molecule^?1. The line list includes about 2500 absorption lines of ethylene present at the ppm level in the acetylene sample and identified on the basis of a high-resolution Fourier transform spectrum specifically recorded. A total of more than 2700 lines of ¹²C₂H₂ were rovibrationally assigned in comparison with accurate predictions provided by a global effective operator model. Overall, the present effort adds about 2260 new assignments to the set of about 500 assigned transitions available in the literature. The new assignments correspond to 45 new bands and 17 already-known bands, for which additional J lines were assigned. Spectroscopic parameters were derived for the upper vibrational levels from a band by band fit of the line positions (typical root mean square deviation values are of the order of 0.001 cm^?1). A few of the analysed bands were found to be affected by rovibrational perturbations, which are discussed. The new data will be valuable to refine the parameters of the global effective Hamiltonian and dipole moments of ¹²C₂H₂.     

The far infrared spectrum of trans-formic acid: An extension up to 175 cm−1

The far infrared spectrum of HCOOH was recorded at a high resolution (0.0009 cm^?1) and long path length (72 m) at the far-infrared beamline, Canadian Light Source. Spectra were recorded in the region 62–300 cm^?1, showing transitions from the trans-isomer.Ground state rotational transitions with K_a up to 30, were identified up to 175 cm^?1, extending the observation reported in the literature. A total of 3321 transitions were assigned and fitted together with previous (4149) published data. An improved set of rotational parameters was obtained adopting the symmetric top (A) reduction of the rotational Hamiltonian in the I^r representation. The newly measured far infrared transitions allowed the determination of all diagonal and off diagonal 8th order parameters L and of some of the diagonal 10th order parameters P.     

Laser infrared spectroscopy of vinyl fluoride in the 1280–1400 cm−1 region

The infrared spectra of CH₂=CHF have been investigated in the ν₅ and ν₆ band regions between 1280 and 1400?cm^?1, at a resolution of about 0.002?cm^?1, using a tunable diode laser spectrometer. These vibrations of symmetry species A′ give rise to a/b-hybrid bands with different contributions from both the components. Spectral analysis resulted in the identification of 1565 (J≤46, K _a ≤11) and 1651 (J≤48, K _a ≤15) transitions of the ν₅ and ν₆ fundamentals, respectively. Both bands are perturbed by the nearby states ν₈?+?ν₉ and ν₉?+?ν₁₁ through different Coriolis resonances and an anharmonic interaction. Using Watson's A-reduction Hamiltonian in the I^r representation and perturbation operators almost all the transitions have been fitted simultaneously to a model including six resonances within the tetrad ν₅/ν₆/ν₈?+?ν₉/ν₉?+?ν₁₁. A set of spectroscopic constants for the ν₅ and ν₆ bands, as well as parameters for the dark states ν₈?+?ν₉ and ν₉?+?ν₁₁ and coupling constants, have been determined. From spectral simulations the dipole moment ratio |Δμ _a /Δμ _b | was estimated to be 0.6?±?0.1 and 2.0±0.3 for the ν₅ and ν₆ bands, respectively.     

Spectral Study of Some Samarium Complexes in the Region 750–250 cm−1

Abstract

Rare earth β -diketonates and diketo-ester complexes are promising laser materials due to narrow line width of the internal 4fⁿ transitions and weak crystal-field interactions¹. The electronic energy states², spectral intensities^3–5, bonding^6,7 and infrared spectra^8–11 of some of these complexes have been recently reported by the authors. However, little information regarding their structure and strengths of various bonds are available. The infrared spectra of rare earth complexes in the spectral region 4000 – 750 cm^?1 are characteristic of the ligand, while those in the region 750 – 250 cm^?1 characterize the metal-ligand bonding. The present communication reports the values of force constants computed from the observed infrared absorption spectra of four ethyl 1-methyl acetoacetate (EMA) and ethylbenzoylacetate (EBA) complexes of trivalent samarium in the region 750 – 250 cm^?1.     

Global Multi-isotopologue fit of measured rotation and vibration–rotation line positions of CO in X1Σ+ state and new set of mass-independent Dunham coefficients

A set of mass-independent U_mj and Δ_mj parameters globally describing vibration–rotation energy levels of the CO molecule in the X¹Σ⁺ ground electronic state was fitted to more than 19,000 transitions of ¹²C¹⁶O, ¹³C¹⁶O, ¹⁴C¹⁶O, ¹²C¹⁷O, ¹³C¹⁷O, ¹²C¹⁸O, and ¹³C¹⁸O isotopologues collected from the literature. The maximal values of the vibrational V and the rotational J quantum numbers included in the fit was 41 and 128, respectively. The weighted standard deviation of the fit is .66. Fitted parameters were used for calculation of Dunham coefficients Y_mj for nine isotopologues ¹²C¹⁶O, ¹³C¹⁶O, ¹⁴C¹⁶O, ¹²C¹⁷O, ¹³C¹⁷O, ¹⁴C¹⁷O, ¹²C¹⁸O, ¹³C¹⁸O, and ¹⁴C¹⁸O. Calculated transition frequencies based on the fitted parameters were compared with previously reported. A critical analysis of the CO HITRAN and HITEMP data is also presented.     

The infrared spectrum of DCCF in the 320–850 cm−1 region: bending states up to υ4+υ5 = 3

Infrared spectra of deuterated monofluoroacetylene, DCCF, have been recorded in the region between 320 and 850 cm^?1 at an effective resolution ranging from 0.0024 to 0.0031 cm^?1. In total, 6650 rotation vibration transitions were assigned to 37 bands involving the bending states with v₄ + v₅ and |l₄+l₅|, respectively, up to 3, allowing the characterisation of the ground state and of 18 vibrationally excited states. The vν₅ bending fundamental has been studied for the first time. In addition, the difference band v₃ ← v₄ has been detected and analysed. All the assigned transitions have been fitted simultaneously by adopting a model Hamiltonian that takes into account the vibration and rotation l?type resonances. Rotational transitions in the ground and in bending excited states reported in the literature have been included in the global analysis. The set of 57 derived spectroscopic parameters reproduces 6130 infrared and 90 microwave and millimetre?wave transitions satisfactorily with root mean square values of 5.3 × 10^?4 cm^?1 and 77 kHz, respectively.     

The high-resolution infrared spectrum of ethylene in the 1800–2350 cm−1 spectral region

Fourier transform spectra of ethylene (C₂H₄) have been recorded in the 1800–2350?cm^?1 (4.3–5.6?µm) spectral region using a Bruker IFS125HR spectrometer at a resolution of 0.004?cm^?1 leading to the observation of six vibrational bands, ν ₇?+?ν ₈, ν ₄?+?ν ₈, ν ₆?+?ν ₁₀, ν ₆?+?ν ₇, ν ₄?+?ν ₆ and ν ₃?+?ν ₁₀. The corresponding upper state ro-vibrational levels were fit using a Hamiltonian matrix accounting for numerous interactions. A satisfactory fit could be obtained using a polyad of nine interacting states {8¹10¹,?7¹8¹,?4¹8¹,?8¹12¹,?6¹10¹,?6¹7¹,?4¹6¹,?3¹10¹,?3¹7¹} of which three (8¹10¹, 8¹12¹ and 3¹7¹) are unobserved dark states. As a result a much more accurate and extended set of Hamiltonian constants were obtained than previously derived. The following band centers were determined: ν ₀(ν ₇?+?ν ₈)?=?1888.9783(20)?cm^?1, ν ₀(ν ₄?+?ν ₈)?=?1958.2850(20)?cm^?1, ν ₀(ν ₆?+?ν ₁₀)?=?2047.7589(20)?cm^?1, ν ₀(ν ₆?+?ν ₇)?=?2178.011(60)?cm^?1, ν ₀(ν ₄?+?ν ₆)?=?2252.8026(24)?cm^?1 and ν ₀(ν ₃?+?ν ₁₀)?=?2171.2397(20)?cm^?1. Finally, a synthetic spectrum that could be useful for ethylene detection in planetary atmospheres was generated.     

The absorption spectrum of 12C2H2 IV. The regions 7600–9200 cm−1 and 10600–11500 cm−1

The absorption spectrum of ¹²C₂H₂ has been recorded by intracavity laser absorption spectroscopy (ICLAS) in the 10600–11 500 cm^?1 spectral region, where no absorption bands were previously reported. Fifteen bands starting from the vibrational ground state are observed and rotationally analysed. All corresponding excited vibrational levels were assigned using the polyad model, the so-called cluster model (El Idrissi, M.I., Liévin, J., Campargue, A., and Herman, M., 1999, J. chem. Phys., 110, 2074) which allows vibrational energies, rotational B_v constants and, to some respect, relative band intensities to be predicted. Additional data and constants are also provided in the range 7600–9200cm^?1, whenever improving the literature results, from spectra recorded previously at ULB using Fourier transform spectroscopy. The assignment procedure in the range recorded by ICLAS is detailed, leading to a deeper understanding of vibration-rotation and intensity features of the absorption bands within the frame of the cluster model.     

The refractive index of isotropic and orientated polyethyleneterephtalate in the 40–300 cm−1 range

In the far-infrared region channelled spectra of isotropic and orientated polyethylene-terephtalate were taken with polarized light. From the positions of maxima and minima, the refractive index could be computed. A brief discussion of the results is given.     

LED-based Fourier-transform spectroscopy of H2 18O in the range 15000–15700 cm−1

The spectrum of H₂ ¹⁸O in the range 15000–15700 cm^?1 has been recorded for the first time on a Fourier-transform spectrometer using a high-brightness light-emitting diode as a radiation source. The measurements have been conducted at room temperature with a resolution of 0.05 cm^?1. A threshold sensitivity in absorption of 2 × 10^?7 cm^?1 has been achieved due to both the use of a light-emitting diode and optimization of the multipass cell with a base length of 60 cm, which ensured a 19.2-m length of the absorbing layer. A high signal-to-noise ratio (S/N = 2000–10000) made it possible to record about 670 water-vapor lines with intensities of 1.0 × 10^?26–2.2 × 10^–24 cm/mol at 296 K. The energies of 265 vibrational-rotational levels of the H₂ ¹⁸O molecule are determined and attributed to seven vibrational states, namely, (033), (113), (212), (231), (311), (330), and (410).     

Spectra of carbon disulphide in the 3400–4400 cm−1 region by Fourier transform spectroscopy

Fourier transform spectra have been recorded for carbon disulphide (CS₂) in the region between 3400 cm^?1 and 4400 cm^?1. A data analysis has determined new molecular constants: 14 bands were observed for the main isotopic form ¹²C³²S₂, two bands for the isotopomer ¹²C³²S³⁴S and one each for ¹²C³²S³³S and ¹³C³²S₂.     

The infrared spectrum of 13C2H2 in the 60–2600 cm−1 region: bending states up to v 4 + v 5 = 4

The vibration–rotation spectra of ¹³C substituted acetylene, ¹³C₂H₂, have been recorded in the region between 60 and 2600?cm^?1 at an effective resolution ranging from 0.001 to 0.006?cm^?1. Three different instruments were used to collect the experimental data in the extended spectral interval investigated. In total 9529 rotation vibration transitions have been assigned to 101 bands involving the bending states up to v _tot?=?v ₄?+?v ₅?=?4, allowing the characterization of the ground state and of 33 vibrationally excited states. All the bands involving states up to v _tot?=?3 have been analyzed simultaneously by adopting a model Hamiltonian which takes into account the vibration and rotation l-type resonances. The derived spectroscopic parameters reproduce the transition wavenumbers with a RMS value of the order of the experimental uncertainty. Using the same model, larger discrepancies between observed and calculated values have been obtained for transitions involving states with v _tot?=?4. These could be satisfactorily reproduced only by adopting a set of effective constants for each vibrational manifold, in addition to the previously determined parameters, which were constrained in the analysis.     

The VoTe Room Temperature H216O Line List up to 25 000 cm–1

Optics and Spectroscopy - A new line list transition for the water molecule is presented. The line lists is created on the basis of VoTe calculations using cutoff values of 25 000 cm–1...     

Role of Intermolecular Interactions in Forming the Vibrational Spectra of Carbohydrate Nitrate Crystals in the Region 1600–1700 cm−1

To elucidate the role of intermolecular interactions in forming the vibrational spectra of the crystals of carbohydrate nitrates in the region 1600–1700 cm^–1, theoretical calculations are performed (in the approximation of an additive model of interatomic interactions with the use of the Green's functions) for the density of vibrational states and the intensity of absorption bands in the IR spectrum of a methyl--D-glucopyranoside tetranitrate molecule in a crystal. It is shown that the splitting of absorption bands in the IR spectral region under consideration relates to the crystal effect.     

Symmetry and Fourier analysis of the ab initio-determined torsional variation of structural and Hessian-related quantities for application to vibration–torsion–rotation interactions in CH3OH

The aim of the present paper is to investigate the use of quantum chemistry calculations to obtain the torsional dependence of various structural and vibrational-force-field-related quantities that could help in estimating the vibration–torsion–rotation interaction terms needed to treat perturbations observed in the spectra of methanol-like molecules. We begin by using the Gaussian suite of programs to determine the steepest-descent path from a stationary point at the top of the internal rotation potential barrier in methanol to the equilibrium structure at the bottom of the barrier. This procedure requires determining the gradient ?V of the potential (as calculated in mass-weighted Cartesian coordinates) along the internal rotation path. In addition, we use the Gaussian suite to calculate the Hessian ??V along this path and to generate from these second derivatives the 3N ? 7 small-amplitude vibrational frequencies and the 3N Cartesian vibrational displacements for each of these vibrations. We then symmetrize the internal coordinates used in presenting the structures, gradients, Hessians and vibrational displacements along the path to take into account the periodic variation of the behavior of the three methyl hydrogen atoms H_i as they pass in turn through the C_s-plane of the HOC frame. The symmetrized linear combinations of the CH_i stretches, of the OCH_i bends, and of the HOCH_i dihedral angles of the methyl group depend on the internal rotation angle γ and they are determined by considering coordinate transformations from the G₆ permutation-inversion group appropriate for internally rotating methanol. This symmetrization procedure permits us to explore the feasibility of expressing the structures, gradients, Hessians, and vibrational displacement vectors along the internal rotation path as short Fourier series in γ, which is one of the main goals of this paper. In summary, we find that the symmetrized structures, gradients, and Hessians, as well as nine of the 11 projected vibrational frequencies and the vibrational displacement vectors for the three vibrations occurring primarily in the HOC frame can be expressed by short Fourier series expansions to their precision in the Gaussian output, and that these series involve only sin 3nγ or only cos 3nγ terms, as required by G₆ symmetry considerations. A preliminary discussion is given of why short Fourier expansions fail for the projected frequencies of the two methyl asymmetric stretches, and for the vibrational displacement vectors of the methyl group vibrational modes. Looking more closely at the symmetrized and projected 3N × 3N Hessian, we find algebraically that only elements in the (3N ? 7) × (3N ? 7) small-amplitude-vibrational block of the Hessian are useful for spectroscopic problems. Non-zero elements in the rest of the 3N × 3N symmetrized and projected Hessian cannot be converted into quantities needed for perturbation studies.