VIBRATIONAL ENERGIES OF MEMBERS IN STRUCTURAL NETWORKS FITTED WITH TUNED VIBRATION ABSORBERS

2006 ◽  
Vol 06 (02) ◽  
pp. 269-284 ◽  
Author(s):  
SUNNY K. GEORGE ◽  
K. SHANKAR
Keyword(s):  
Energy Level ◽  
Vibrational Energy ◽  
General Structure ◽  
Energy Levels ◽  
Complex Structure ◽  
Input Power ◽  
Vibration Absorbers ◽  
Tuned Vibration Absorbers ◽  
Vibrational Energies ◽  
Structural Networks

The distribution of vibrational energy in members of a complex structure with tuned absorbers attached at the joints and subjected to dynamic loading is studied. The concept of power flows through the structure is used to determine the time-averaged energy levels of each member in the structure. The power flows are calculated using the time-averaged product of force and velocity at the input and coupling points (joints) of a general structure made of axially vibrating rods. The receptance approach is used to calculate the coupling forces and velocities in the structure. By balancing the input power against the dissipated powers, the time-averaged energy levels in members are determined. The main criteria studied here is the reduction in the frequency-averaged vibrational energy level of a member when an absorber is attached, expressed as a percentage compared to the case where there are no absorbers. The concept is first illustrated with a simple model of 2 axially vibrating rods with an absorber attached to the joint. Next, a more complex structure comprising 8 rods with arbitrary orientations and several absorbers attached to junctions is studied. The effect of activating absorbers at various locations on reducing the energy levels of certain members is examined. It is possible to estimate the usefulness of the absorber with respect to any member by determining the percentage reduction of energy level for that member.

Promoting and inhibiting tunneling via nuclear motions

2016 ◽  
Vol 18 (2) ◽  
pp. 1092-1104 ◽  
Author(s):  
Attila G. Császár ◽  
Tibor Furtenbacher
Keyword(s):  
Energy Level ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Tunneling Splittings ◽  
Vibrational Energy Levels

Accurate, experimental rotational–vibrational energy levels determined via the MARVEL algorithm and published recently for the 14NH3 molecule in J. Quant. Spectrosc. Radiat. Transfer, 2015, 116, 117–130 are analyzed to unravel the promoting and inhibiting effects of vibrations and rotations on the tunneling splittings of the corresponding symmetric (s) and antisymmetric (a) rovibrational energy level pairs.

Vibrational energies of H3+ and Li3+ based on the diatomics-in-molecules potentials

1986 ◽  
Vol 51 (10) ◽  
pp. 2057-2062 ◽  
Author(s):  
Jan Vojtík ◽  
Vladimír Špirko ◽  
Per Jensen
Keyword(s):  
Potential Energy ◽  
Ab Initio ◽  
Potential Energy Surfaces ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Vibrational Motion ◽  
Variational Calculations ◽  
Vibrational Energies ◽  
Vibrational Energy Levels ◽  
Energy Surfaces

The present publication reports variational calculations of the vibrational energy levels for H3+, D3+, 6Li3+, and 7Li3+, starting from potential energy surfaces generated by the DIM scheme. The vibrational energies obtained agree semiquantitatively with those based on the best ab initio potentials available. The results seem to indicate that an analogous approach might be useful in describing the vibrational motion of heavier alkali cluster cations A3+.

scholarly journals Penentuan Tingkat-Tingkat Energi Vibrasi Molekul Hidrogen Pada Keadaan Elektronik Dasar Menggunakan Potensial Morse

Wahana Fisika ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 1-9
Author(s):  
Redi Kristian Pingak ◽  
Albert Zicko Johannes
Keyword(s):  
Morse Potential ◽  
Hydrogen Molecule ◽  
Vibrational Energy ◽  
Classical Method ◽  
Energy Levels ◽  
Vibrational Levels ◽  
Oppenheimer Approximation ◽  
False Position ◽  
Vibrational Energies ◽  
Vibrational Energy Levels

Pendekatan Born-Oppenheimer diterapkan untuk menghitung tingkat energi vibrasi keadaan dasar molekul hidrogen. Persamaan Schrodinger untuk inti atom diselesaikan dengan menggunakan metode semi-klasik, di mana inti atom diasumsikan bergerak secara klasik dalam sumur potensial dan energi vibrasi ditentukan dengan menerapkan aturan kuantisasi kuantum. Potensial yang digunakan pada penelitian adalah potensial Morse. Dalam penelitian ini, tingkat energi vibrasi dihitung dengan metode numerik, yaitu metode integrasi Simpson dan metode regula falsi. 15 Tingkat energi vibrasi dari molekul H2 diperoleh dan dibandingkan dengan data hasil eksperimen. Perbandingan ini mengindikasikan pendekatan yang digunakan pada penelitian ini memberikan hasil yang sangat akurat pada tingkat energi vibrasi yang relatif rendah (0≤n≤4), dengan kesalahan kurang dari 0,7%, dan untuk 5≤n≤8 dengan kesalahan maksimum 7,3%. Keakuratan menurun ketika tingkat energi vibrasi meningkat. Secara khusus, untuk n = 13 dan n = 14, kesalahan meningkat secara signifikan, menunjukkan gagalnya pendekatan ini untuk tingkat energi vibrasi yang relatif tinggi, khususnya untuk dua tingkat energi ini. Born-Oppenheimer approximation was applied to calculate vibrational energy levels of ground state of Hydrogen molecule. The Schrodinger equation for the nuclei was solved using a semi-classical method, in which the nuclei are assumed to move classically in a potential well and the vibrational energies are determined by applying the quantum mechanical quantization rules. Potential used in this research was the Morse potential. Here, vibrational energy levels of the molecule were calculated using numerical methods, i.e. Simpson integration method and false position method. 15 Vibrational energy levels of the H2 molecule were obtained and compared to the corresponding results from experiments. The comparison indicated that the approximation used in this research yielded very accurate results for relatively low vibrational levels (0≤n≤4), with errors being less than 0.7% and for 5≤n≤8 with maximum of 7.3% errors. The accuracy decreased as the vibrational levels increased, as expected. In particular, for n=13 and n=14, errors significantly increased, indicating the breakdown of the approximation for relatively high vibrational levels, in particular for these two energy levels.           Keywords: Hydrogen Molecule; Morse Potential; Born-Oppenheimer Approximation; Simpson Method; False Position Method

Master Equation for the Dissociation of a Dilute Diatomic Gas. V. Effect of Energy-level Spacing

1971 ◽  
Vol 49 (23) ◽  
pp. 3915-3917 ◽  
Author(s):  
D. L. S. Mcelwain ◽  
H. O. Pritchard
Keyword(s):  
Energy Level ◽  
Master Equation ◽  
Temperature Coefficient ◽  
Numerical Experiments ◽  
Vibrational Energy ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Level Spacing ◽  
Vibrational Energy Levels ◽  
Arrhenius Temperature

Our previous vibration–dissociation coupling calculations for H2 have been repeated for D2. Closer spacing of the vibrational energy levels in D2 leads to increased translation–vibration transition probabilities, and the effect of this is to increase the rate of recombination by the vibrational mechanism at all temperatures. These numerical experiments also clarify two other issues: (i) that the position of the bottleneck does not necessarily occur at that level above which direct collisional dissociation can take place rapidly, and (ii) that there is no simple correspondence between the position of the bottleneck and the Arrhenius temperature coefficient for dissociation.

High-lying vibrational energies and analytical potential energy functions for some electronic states of diatomic ions

2016 ◽  
Vol 15 (02) ◽  
pp. 1650014 ◽  
Author(s):  
Chun Guo Zhang ◽  
Qun Chao Fan ◽  
Zhi Xiang Fan ◽  
Hui Dong Li ◽  
Jia Fu
Keyword(s):  
Potential Energy ◽  
Electronic State ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Electronic States ◽  
Algebraic Method ◽  
Potential Energy Function ◽  
Spectroscopic Constants ◽  
Analytical Potential ◽  
Vibrational Energies

The full vibrational spectra especially those high-lying vibrational energies in the dissociation region of the electronic state [Formula: see text] of [Formula: see text], the [Formula: see text] state of [Formula: see text], the [Formula: see text] and [Formula: see text] states of [Formula: see text] are obtained using the variational algebraic method (VAM). Then, an analytical potential energy function (APEF) with adjustable parameter [Formula: see text] for each electronic state is determined by the 4-terms variational algebraic energy consistent method (VAECM(4)) based on the VAM vibrational energies. The full vibrational energies, the vibrational spectroscopic constants, the force constants [Formula: see text], and the expansion coefficients [Formula: see text] of the potential are tabulated. Compared with experimental and other calculated results, accurate APEFs, vibrational energy levels and spectroscopic parameters are obtained with the VAECM(4) for the four electronic states of diatomic ions. The results show that the VAECM(4) method also applies to diatomic ion systems.

scholarly journals Experimental energy levels of 12C14N through marvel analysis

2020 ◽  
Vol 499 (1) ◽  
pp. 25-39
Author(s):  
Anna-Maree Syme ◽  
Laura K McKemmish
Keyword(s):  
Experimental Data ◽  
Partition Function ◽  
Energy Level ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Line List ◽  
Level Data ◽  
Vibrational Energy Levels ◽  
Cyano Radical ◽  
Current Energy

ABSTRACT The cyano radical (CN) is a key molecule across many different factions of astronomy and chemistry. Accurate, empirical rovibronic energy levels with uncertainties are determined for eight doublet states of CN using the marvel (Measured Active Rotational-Vibrational Energy Levels) algorithm. 40 333 transitions were validated from 22 different published sources to generate 8083 spin-rovibronic energy levels. The empirical energy levels obtained from the marvel analysis are compared to current energy levels from the mollist line list. The mollist transition frequencies are updated with marvel energy level data which brings the frequencies obtained through experimental data up to 77.3 per cent from the original 11.3 per cent, with 92.6 per cent of the transitions with intensities over 10−23 cm molecule−1 at 1000 K now known from experimental data. At 2000 K, 100.0 per cent of the partition function is recovered using only marvel energy levels, while 98.2 per cent is still recovered at 5000 K.

scholarly journals The ultra-violet spectrum of magnesium hydride. 1.—The band at λ 2430

1929 ◽  
Vol 122 (790) ◽  
pp. 442-455 ◽  
Keyword(s):  
Fine Structure ◽  
General Structure ◽  
Energy Levels ◽  
Visible Region ◽  
Ultra Violet ◽  
Present Theory ◽  
Magnesium Hydride ◽  
Electronic Energy ◽  
Band Spectra ◽  
Electronic Energy Levels

The system of bands in the visible region of the emission spectrum of magnesium hydride is now well known. The bands with heads at λλ 5622, 5211, 4845 were first measured by Prof. A. Fowler, who arranged many of the strongest lines in empirical series for identification with absorption lines in the spectra of sun-spots. Later, Heurlinger rearranged these series in the now familiar form of P, Q and R branches, and considered them, with the OH group, as typical of doublet systems in his classification of the fine structure of bands. More recently, W. W. Watson and P. Rudnick have remeasured these bands, using the second order of a 21-foot concave grating, and have carried out a further investigation of the fine structure in the light of the present theory of band spectra. Their detection of an isotope effect of the right order of magnitude, considered with the general structure of the system, and the experimental work on the production of the spectrum, seems conclusive in assigning these bands to the diatomic molecule MgH. The ultra-violet spectrum of magnesium hydride is not so well known. The band at λ 2430 and the series of double lines in the region λ 2940 to λ 3100, which were recorded by Prof. Fowler in 1909 as accompanying the group of bands in the visible region, appear to have undergone no further investigation. In view of the important part played by hydride band spectra in the correlation of molecular and atomic electronic energy levels, it was thought that a study of these features might prove of interest in yielding further information on the energy states of the MgH molecule. The present paper deals with observations on the band at λ 2430; details of an investigation of the other features of the ultra-violet spectrum will be given in a later communication.

First models for structural energy transmission decoupling in the high frequency regime under aerodynamic excitations

2021 ◽  
pp. 095440622110200
Author(s):  
G Mazzeo ◽  
MN Ichchou ◽  
G Petrone ◽  
O Bareille ◽  
S De Rosa ◽  
...  
Keyword(s):  
Wind Tunnel ◽  
Vibrational Energy ◽  
Complex Structure ◽  
Structural Response ◽  
Test Case ◽  
Analysis Model ◽  
Quick Method ◽  
Vibrational Velocity ◽  
Frequency Regime ◽  
The Difference

In the wind tunnel facility, a test structure is often used for measuring its vibrational response to the aerodynamic excitation. A support is needed to sustaining the structure and it is mandatory that this support does not influence the vibrational energy to be measured. To this aim, the maximum amount of energy decoupling between the structure and the support is desired. This work is focused around a quick method to estimate this decoupling by using simplified models for the Turbulent Boundary Layer (TBL) excitation and for the structural response. Specifically, the Equivalent Rain-on-the-roof excitation is invoked with a Statistical Energy Analysis model for the structure. Some simple design rules are proposed and based on little information leading to foresee the difference of vibrational velocity levels between the two structural systems. A simplified test-case is used for the first investigations and a complex structure is finally conceived thinking to vibroacoustic measurements in a large wind tunnel facility. Although some results are largely expected, the global approach is promising.

scholarly journals Research progress in the effects of terahertz waves on biomacromolecules

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Liu Sun ◽  
Li Zhao ◽  
Rui-Yun Peng
Keyword(s):  
Vibrational Energy ◽  
Rapid Development ◽  
Energy Levels ◽  
Basic Research ◽  
Research Progress ◽  
Biological Macromolecules ◽  
Terahertz Waves ◽  
Terahertz Spectrum ◽  
Biomedical Field ◽  
Vibrational Energy Levels

AbstractWith the rapid development of terahertz technologies, basic research and applications of terahertz waves in biomedicine have attracted increasing attention. The rotation and vibrational energy levels of biomacromolecules fall in the energy range of terahertz waves; thus, terahertz waves might interact with biomacromolecules. Therefore, terahertz waves have been widely applied to explore features of the terahertz spectrum of biomacromolecules. However, the effects of terahertz waves on biomacromolecules are largely unexplored. Although some progress has been reported, there are still numerous technical barriers to clarifying the relation between terahertz waves and biomacromolecules and to realizing the accurate regulation of biological macromolecules by terahertz waves. Therefore, further investigations should be conducted in the future. In this paper, we reviewed terahertz waves and their biomedical research advantages, applications of terahertz waves on biomacromolecules and the effects of terahertz waves on biomacromolecules. These findings will provide novel ideas and methods for the research and application of terahertz waves in the biomedical field.

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