### 5 results for qubit oscillator frequency

Contributors: Kazakevitch, M. I., Volkova, Viktorija

Date: 1997-01-01

In this paper the results of the investigations of the free **oscillations** of the pre-stressed flexible structure elements are presented . Two cases of the central preliminary stress are investigated : without intermediate fastening of the tie to the flexible element and with the intermediate fastening in the middle of the element length. The given physical model can be applied to the flexible sloping shells and arches, membranes, large space antenna fields (besides flexible elements). The peculiarity of these systems is the possibility of the non-adjacent equilibrium form existence at the definite relations of the physical parameters . The transition from one stable equilibrium form to another, non-adjacent form, may be treated as jump. In this case they are called systems with buckling or the systems with two potential «gaps». These systems commenced the new section of the mathematical physics - the theory of chaos and strange attractors. The analysis of the solutions confirms the received for the first time by the author and given in effect of the **oscillation** period doubling of the system during the transition from the «small» **oscillations** relatively center to the >large< relatively all three equilibrium conditions. The character of the **frequency** (period) dependence on the free **oscillation** amplitudes of the non-linear system also confirms the received earlier result of the duality of the system behaviour : >small< **oscillations** possess the qualities of soft system; >large< **oscillations** possess the qualities of rigid system. The >small< **oscillation** natural **frequency** changing, depending on the **oscillation** amplitudes, is in the internal . Here the **frequency** takes zero value at the amplitude values Aa and Ad (or Aa and Ae ); the **frequency** takes maximum value at the amplitude value near point b .The >large< **oscillation** natural **frequency** changes in the interval . Here is also observed . The influence of the tie intermediate fastening doesn't introduce qualitative changes in the behaviour of the investigated system. It only increases ( four times ) the critical value of the preliminary tension force ... In this paper the results of the investigations of the free **oscillations** of the pre-stressed flexible structure elements are presented . Two cases of the central preliminary stress are investigated : without intermediate fastening of the tie to the flexible element and with the intermediate fastening in the middle of the element length. The given physical model can be applied to the flexible sloping shells and arches, membranes, large space antenna fields (besides flexible elements). The peculiarity of these systems is the possibility of the non-adjacent equilibrium form existence at the definite relations of the physical parameters . The transition from one stable equilibrium form to another, non-adjacent form, may be treated as jump. In this case they are called systems with buckling or the systems with two potential «gaps». These systems commenced the new section of the mathematical physics - the theory of chaos and strange attractors. The analysis of the solutions confirms the received for the first time by the author and given in effect of the **oscillation** period doubling of the system during the transition from the «small» **oscillations** relatively center to the >large< relatively all three equilibrium conditions. The character of the **frequency** (period) dependence on the free **oscillation** amplitudes of the non-linear system also confirms the received earlier result of the duality of the system behaviour : >small< **oscillations** possess the qualities of soft system; >large< **oscillations** possess the qualities of rigid system. The >small< **oscillation** natural **frequency** changing, depending on the **oscillation** amplitudes, is in the internal . Here the **frequency** takes zero value at the amplitude values Aa and Ad (or Aa and Ae ); the **frequency** takes maximum value at the amplitude value near point b .The >large< **oscillation** natural **frequency** changes in the interval . Here is also observed . The influence of the tie intermediate fastening doesn't introduce qualitative changes in the behaviour of the investigated system. It only increases ( four times ) the critical value of the preliminary tension force

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Contributors: Ganev, T., Marinov, M.

Date: 1997-01-01

... Thin elastic plates are the basic constructional elements and are very often subjected to dynamic effects especially in the machine-building structures. Their saving design of resonance conditions of operation is an extremely complicated task which cannot be solved analytically. In the present report an efficient and sufficiently general method for optimal design of thin plates is worked out on the basis of energy resonance method of Wilder, the method of the finite elements for dynamic research and the methods of parameter optimization. By means of these methods various limitations and requirements put by the designer to the plates can be taken into account. A programme module for numerical investigation of the weight variation of the plate depending on the taken variable of the designed thickness at different supporting conditions is developed. The reasons for the considerable quantity and quality difference between the obtained optimal designs are also analysed.

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Contributors: Markwardt, Klaus

Date: 2006-01-01

In many applications such as parameter identification of **oscillating** systems in civil enginee-ring, speech processing, image processing and others we are interested in the **frequency** con-tent of a signal locally in time. As a start wavelet analysis provides a time-scale decomposition of signals, but this wavelet transform can be connected with an appropriate time-**frequency** decomposition. For instance in Matlab are defined pseudo-**frequencies** of wavelet scales as **frequency** centers of the corresponding bands. This **frequency** bands overlap more or less which depends on the choice of the biorthogonal wavelet system. Such a definition of **frequency** center is possible and useful, because different **frequencies** predominate at different dyadic scales of a wavelet decomposition or rather at different nodes of a wavelet packet decomposition tree. The goal of this work is to offer better algorithms for characterising **frequency** band behaviour and for calculating **frequency** centers of orthogonal and biorthogonal wavelet systems. This will be done with some product formulas in **frequency** domain. Now the connecting procedu-res are more analytical based, better connected with wavelet theory and more assessable. This procedures doesn’t need any time approximation of the wavelet and scaling functions. The method only works in the case of biorthogonal wavelet systems, where scaling functions and wavelets are defined over discrete filters. But this is the practically essential case, because it is connected with fast algorithms (FWT, Mallat Algorithm). At the end corresponding to the wavelet transform some closed formulas of pure **oscillations** are given. They can generally used to compare the application of different wavelets in the FWT regarding it’s **frequency** behaviour. ... In many applications such as parameter identification of **oscillating** systems in civil enginee-ring, speech processing, image processing and others we are interested in the **frequency** con-tent of a signal locally in time. As a start wavelet analysis provides a time-scale decomposition of signals, but this wavelet transform can be connected with an appropriate time-**frequency** decomposition. For instance in Matlab are defined pseudo-**frequencies** of wavelet scales as **frequency** centers of the corresponding bands. This **frequency** bands overlap more or less which depends on the choice of the biorthogonal wavelet system. Such a definition of **frequency** center is possible and useful, because different **frequencies** predominate at different dyadic scales of a wavelet decomposition or rather at different nodes of a wavelet packet decomposition tree. The goal of this work is to offer better algorithms for characterising **frequency** band behaviour and for calculating **frequency** centers of orthogonal and biorthogonal wavelet systems. This will be done with some product formulas in **frequency** domain. Now the connecting procedu-res are more analytical based, better connected with wavelet theory and more assessable. This procedures doesn’t need any time approximation of the wavelet and scaling functions. The method only works in the case of biorthogonal wavelet systems, where scaling functions and wavelets are defined over discrete filters. But this is the practically essential case, because it is connected with fast algorithms (FWT, Mallat Algorithm). At the end corresponding to the wavelet transform some closed formulas of pure **oscillations** are given. They can generally used to compare the application of different wavelets in the FWT regarding it’s **frequency** behaviour.

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Contributors: Misyura, E, Volkova, Viktorija

Date: 2006-01-01

The paper is devoted to the investigation of dynamical behavior of a cable under influence of various types of excitations. Such element has a low rigidity and is sensitive to dynamic effect. The structural scheme is a cable which ends are located at different level. The analysis of dynamical behavior of the cable under effect of kinematical excitation which is represented by the **oscillations** of the upper part of tower is given. The scheme of cable is accepted such, that lower end of an inclined cable is motionless. The motion of the upper end is assumed only in horizontal direction. The fourth-order Runge-Kutta method was realized in software. The fast Fourier transform was used for spectral analysis. Standard graphical software was adopted for presenting results of investigations. The mathematical model of **oscillations** of a cable was developed by the account of the viscous damping. The analysis of dynamical characteristics of a cable for various parameters of damping and kinematical excitation was carried out. The time series, spectral characteristics and amplitude-**frequencies** characteristics was obtained. The resonance amplitude for different **oscillating** regimes was estimated. It is noted that increasing of the coefficient of the viscous damping and decreasing of the amplitude of tower's **oscillations** reduces the value of the critical **frequency** and the resonant amplitudes. ... The paper is devoted to the investigation of dynamical behavior of a cable under influence of various types of excitations. Such element has a low rigidity and is sensitive to dynamic effect. The structural scheme is a cable which ends are located at different level. The analysis of dynamical behavior of the cable under effect of kinematical excitation which is represented by the **oscillations** of the upper part of tower is given. The scheme of cable is accepted such, that lower end of an inclined cable is motionless. The motion of the upper end is assumed only in horizontal direction. The fourth-order Runge-Kutta method was realized in software. The fast Fourier transform was used for spectral analysis. Standard graphical software was adopted for presenting results of investigations. The mathematical model of **oscillations** of a cable was developed by the account of the viscous damping. The analysis of dynamical characteristics of a cable for various parameters of damping and kinematical excitation was carried out. The time series, spectral characteristics and amplitude-**frequencies** characteristics was obtained. The resonance amplitude for different **oscillating** regimes was estimated. It is noted that increasing of the coefficient of the viscous damping and decreasing of the amplitude of tower's **oscillations** reduces the value of the critical **frequency** and the resonant amplitudes.

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Contributors: Wang, Cuixia

Date: 2018-01-01

Advances in nanotechnology lead to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators with ultra-high resonant **frequencies**. The ultra-high-**frequency** resonators have recently received significant attention for wide-ranging applications such as molecular separation, molecular transportation, ultra-high sensitive sensing, high-**frequency** signal processing, and biological imaging. It is well known that for micrometer length scale, first-principles technique, the most accurate approach, poses serious limitations for comparisons with experimental studies. For such larger size, classical molecular dynamics (MD) simulations are desirable, which require interatomic potentials. Additionally, a mesoscale method such as the coarse-grained (CG) method is another useful method to support simulations for even larger system sizes.
Furthermore, quasi-two-dimensional (Q2D) materials have attracted intensive research interest due to their many novel properties over the past decades. However, the energy dissipation mechanisms of nanomechanical resonators based on several Q2D materials are still unknown. In this work, the addressed main issues include the development of the CG models for molybdenum disulphide (MoS2), investigation of the mechanism effects on black phosphorus (BP) nanoresonators and the application of graphene nanoresonators. The primary coverage and results of the dissertation are as follows:
Method development. Firstly, a two-dimensional (2D) CG model for single layer MoS2 (SLMoS2) is analytically developed. The Stillinger-Weber (SW) potential for this 2D CG model is further parametrized, in which all SW geometrical parameters are determined analytically according to the equilibrium condition for each individual potential term, while the SW energy parameters are derived analytically based on the valence force field model. Next, the 2D CG model is further simplified to one-dimensional (1D) CG model, which describes the 2D SLMoS2 structure using a 1D chain model. This 1D CG model is applied to investigate the relaxed configuration and the resonant **oscillation** of the folded SLMoS2. Owning to the simplicity nature of the 1D CG model, the relaxed configuration of the folded SLMoS2 is determined analytically, and the resonant **oscillation** **frequency** is derived analytically. Considering the increasing interest in studying the properties of other 2D layered materials, and in particular those in the semiconducting transition metal dichalcogenide class like MoS2, the CG models proposed in current work provide valuable simulation approaches.
Mechanism understanding. Two energy dissipation mechanisms of BP nanoresonators are focused exclusively, i.e. mechanical strain effects and defect effects (including vacancy and oxidation). Vacancy defect is intrinsic damping factor for the quality (Q)-factor, while mechanical strain and oxidation are extrinsic damping factors. Intrinsic dissipation (induced by thermal vibrations) in BP resonators (BPRs) is firstly investigated. Specifically, classical MD simulations are performed to examine the temperature dependence for the Q-factor of the single layer BPR (SLBPR) along the armchair and zigzag directions, where two-step fitting procedure is used to extract the **frequency** and Q-factor from the kinetic energy time history. The Q-factors of BPRs are evaluated through comparison with those of graphene and MoS2 nanoresonators. Next, effects of mechanical strain, vacancy and oxidation on BP nanoresonators are investigated in turn. Considering the increasing interest in studying the properties of BP, and in particular the lack of theoretical study for the BPRs, the results in current work provide a useful reference.
Application. A novel application for graphene nanoresonators, using them to self-assemble small nanostructures such as water chains, is proposed. All of the underlying physics enabling this phenomenon is elucidated. In particular, by drawing inspiration from macroscale self-assembly using the higher order resonant modes of Chladni plates, classical MD simulations are used to investigate the self-assembly of water molecules using
graphene nanoresonators. An analytic formula for the critical resonant **frequency** based on the interaction between water molecules and graphene is provided. Furthermore, the properties of the water chains assembled by the graphene nanoresonators are studied. ... Advances in nanotechnology lead to the development of nano-electro-mechanical systems (NEMS) such as nanomechanical resonators with ultra-high resonant **frequencies**. The ultra-high-**frequency** resonators have recently received significant attention for wide-ranging applications such as molecular separation, molecular transportation, ultra-high sensitive sensing, high-**frequency** signal processing, and biological imaging. It is well known that for micrometer length scale, first-principles technique, the most accurate approach, poses serious limitations for comparisons with experimental studies. For such larger size, classical molecular dynamics (MD) simulations are desirable, which require interatomic potentials. Additionally, a mesoscale method such as the coarse-grained (CG) method is another useful method to support simulations for even larger system sizes.
Furthermore, quasi-two-dimensional (Q2D) materials have attracted intensive research interest due to their many novel properties over the past decades. However, the energy dissipation mechanisms of nanomechanical resonators based on several Q2D materials are still unknown. In this work, the addressed main issues include the development of the CG models for molybdenum disulphide (MoS2), investigation of the mechanism effects on black phosphorus (BP) nanoresonators and the application of graphene nanoresonators. The primary coverage and results of the dissertation are as follows:
Method development. Firstly, a two-dimensional (2D) CG model for single layer MoS2 (SLMoS2) is analytically developed. The Stillinger-Weber (SW) potential for this 2D CG model is further parametrized, in which all SW geometrical parameters are determined analytically according to the equilibrium condition for each individual potential term, while the SW energy parameters are derived analytically based on the valence force field model. Next, the 2D CG model is further simplified to one-dimensional (1D) CG model, which describes the 2D SLMoS2 structure using a 1D chain model. This 1D CG model is applied to investigate the relaxed configuration and the resonant **oscillation** of the folded SLMoS2. Owning to the simplicity nature of the 1D CG model, the relaxed configuration of the folded SLMoS2 is determined analytically, and the resonant **oscillation** **frequency** is derived analytically. Considering the increasing interest in studying the properties of other 2D layered materials, and in particular those in the semiconducting transition metal dichalcogenide class like MoS2, the CG models proposed in current work provide valuable simulation approaches.
Mechanism understanding. Two energy dissipation mechanisms of BP nanoresonators are focused exclusively, i.e. mechanical strain effects and defect effects (including vacancy and oxidation). Vacancy defect is intrinsic damping factor for the quality (Q)-factor, while mechanical strain and oxidation are extrinsic damping factors. Intrinsic dissipation (induced by thermal vibrations) in BP resonators (BPRs) is firstly investigated. Specifically, classical MD simulations are performed to examine the temperature dependence for the Q-factor of the single layer BPR (SLBPR) along the armchair and zigzag directions, where two-step fitting procedure is used to extract the **frequency** and Q-factor from the kinetic energy time history. The Q-factors of BPRs are evaluated through comparison with those of graphene and MoS2 nanoresonators. Next, effects of mechanical strain, vacancy and oxidation on BP nanoresonators are investigated in turn. Considering the increasing interest in studying the properties of BP, and in particular the lack of theoretical study for the BPRs, the results in current work provide a useful reference.
Application. A novel application for graphene nanoresonators, using them to self-assemble small nanostructures such as water chains, is proposed. All of the underlying physics enabling this phenomenon is elucidated. In particular, by drawing inspiration from macroscale self-assembly using the higher order resonant modes of Chladni plates, classical MD simulations are used to investigate the self-assembly of water molecules using
graphene nanoresonators. An analytic formula for the critical resonant **frequency** based on the interaction between water molecules and graphene is provided. Furthermore, the properties of the water chains assembled by the graphene nanoresonators are studied.

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