Showing papers on "Normal mode published in 2017"
TL;DR: In this article, the authors derived the frequency range of the locally resonant bandgap in uniform finite metamaterial beams using modal analysis, and showed that the bandgap expression is the same regardless of the type of vibration problem under consideration, depending only on the added mass ratio and target frequency.
151 citations
TL;DR: In this paper, an exact transfer matrix method was developed to analyze the free vibration characteristics of a functionally graded beam, which can be used to produce the natural frequencies and mode shapes for such problems in which material properties such as the elastic modulus and density are assumed to vary continuously along the height direction of the beam cross-section depending on a power-law form.
105 citations
TL;DR: In this paper, a semi-analytical method for linear vibration analysis of carbon nanotube reinforced composite (FG-CNTRC) doubly-curved panels and shells of revolution on with arbitrary boundary conditions is presented.
105 citations
TL;DR: In this article, the authors considered the problem of a two-dimensional thermoelastic half-space in the context of generalized thermo-elastic theory with one relaxation time.
Abstract: In this article, we consider the problem of a two-dimensional thermoelastic half-space in the context of generalized thermoelastic theory with one relaxation time. The surface of the half-space is taken to be traction free and thermally insulated. The solution of the considered physical quantity can be broken down in terms of normal modes. The nonhomogeneous basic equations have been written in the form of a vector-matrix differential equation, which is then solved by an eigenvalue approach. The exact analytical solution is adopted for the temperature, the components of displacement and stresses. The results obtained are presented graphically for the effect of laser pulse to display the phenomena physical meaning. The graphical results indicate that the thermal relaxation time has a great effect on the temperature, the components of displacement and the components of stress.
101 citations
TL;DR: In this article, the authors investigated the free torsional vibration behaviors of tubes made of a bi-directional functionally graded (FG) material, which is composed of two different materials with continuously varying along the radius and length directions.
96 citations
TL;DR: It is demonstrated that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable.
Abstract: We experimentally demonstrate an exploitation of the nonlinear softening, hardening, and veering phenomena (near crossing), where the frequencies of two vibration modes get close to each other, to realize a bandpass filter of sharp roll off from the passband to the stopband. The concept is demonstrated based on an electrothermally tuned and electrostatically driven MEMS arch resonator operated in air. The in-plane resonator is fabricated from a silicon-on-insulator wafer with a deliberate curvature to form an arch shape. A DC current is applied through the resonator to induce heat and modulate its stiffness, and hence its resonance frequencies. We show that the first resonance frequency increases up to twice of the initial value while the third resonance frequency decreases until getting very close to the first resonance frequency. This leads to the phenomenon of veering, where both modes get coupled and exchange energy. We demonstrate that by driving both modes nonlinearly and electrostatically near the veering regime, such that the first and third modes exhibit softening and hardening behavior, respectively, sharp roll off from the passband to the stopband is achievable. We show a flat, wide, and tunable bandwidth and center frequency by controlling the electrothermal actuation voltage.
82 citations
16 Nov 2017
TL;DR: In this paper, the authors show that the character of phonons changes dramatically within the first few percent of impurity concentration, beyond which phonons more closely resemble the modes found in amorphous materials.
Abstract: Current understanding of phonons treats them as plane waves/quasi-particles of atomic vibration that propagate and scatter. The problem is that conceptually, when any level of disorder is introduced, whether compositional or structural, the character of vibrational modes in solids changes, yet nearly all theoretical treatments continue to assume phonons are still waves. For example, the phonon contributions to alloy thermal conductivity (TC) rely on this assumption and are most often computed from the virtual crystal approximation (VCA). Good agreement is obtained in some cases, but there are many instances where it fails—both quantitatively and qualitatively. Here, we show that the conventional theory and understanding of phonons requires revision, because the critical assumption that all phonons/normal modes resemble plane waves with well-defined velocities is no longer valid when disorder is introduced. Here we show, surprisingly, that the character of phonons changes dramatically within the first few percent of impurity concentration, beyond which phonons more closely resemble the modes found in amorphous materials. We then utilize a different theory that can treat modes with any character and experimentally confirm its new insights. In solids, atoms continuously vibrate in collective motions with quantized amplitudes that can be described in terms of quasiparticles known as phonons—which are responsible for heat transfer and sound. Phonons are usually treated as waves that propagate and scatter, but this approach can sometimes fail when dealing with materials with disorder. A team of researchers from the Georgia Institute of Technology, led by Asegun Henry, show that by focussing on phonon correlation rather than scattering, it is possible to more accurately capture the changes in vibrational mode behavior as a function of disorder.
80 citations
TL;DR: In this paper, the amplitude of the signal includes the operational deflected shape data, which can be used to estimate the bridge mode shapes with high resolution and accuracy using a rescaling process.
77 citations
TL;DR: In this article, the authors studied the two-temperature problem with two-dimensional (2D) deformations for a semi-infinite semiconducting medium at the free surface with the influence of mechanical force through a photothermal process.
Abstract: In this investigation, we study the two-temperature problem with two-dimensional (2-D) deformations for a semi-infinite semiconducting medium at the free surface with the influence of mechanical force through a photothermal process. The harmonic wave method (Normal Mode analysis) has been used to get the exact expression of normal displacement, normal force stress, carrier density, and temperature distribution, and also the two-temperature coefficients ratios has been obtained analytically. The effects of several parameters as thermoelastic and thermoelectric coupling parameters and two-temperature parameter of this force on the displacement component, force stress, carrier density, and temperature distribution have been depicted graphically.
73 citations
TL;DR: In this paper, the dynamic properties of skyrmionic states in thin-film FeGe disk samples have been studied, and the eigenvalue and ringdown method has been employed to identify all resonance frequencies and corresponding eigenmodes that can exist in the simulated system.
Abstract: In confined helimagnetic nanostructures, skyrmionic states in the form of incomplete and isolated skyrmion states can emerge as the ground state in absence of both external magnetic field and magnetocrystalline anisotropy. In this work, we study the dynamic properties (resonance frequencies and corresponding eigenmodes) of skyrmionic states in thin film FeGe disk samples. We employ two different methods in finite-element based micromagnetic simulation: eigenvalue and ringdown method. The eigenvalue method allows us to identify all resonance frequencies and corresponding eigenmodes that can exist in the simulated system. However, using a particular experimentally feasible excitation can excite only a limited set of eigenmodes. Because of that, we perform ringdown simulations that resemble the experimental setup using both in-plane and out-of-plane excitations. In addition, we report the nonlinear dependence of resonance frequencies on the external magnetic bias field and disk sample diameter and discuss the possible reversal mode of skyrmionic states. We compare the power spectral densities of incomplete skyrmion and isolated skyrmion states and observe several key differences that can contribute to the experimental identification of the state present in the sample. We measure the FeGe Gilbert damping, and using its value we determine what eigenmodes can be expected to be observed in experiments. Finally, we show that neglecting the demagnetisation energy contribution or ignoring the magnetisation variation in the out-of-film direction -- although not changing the eigenmode's magnetisation dynamics significantly -- changes their resonance frequencies substantially. Apart from contributing to the understanding of skyrmionic states physics, this systematic work can be used as a guide for the experimental identification of skyrmionic states in confined helimagnetic nanostructures.
71 citations
TL;DR: In this paper, the authors derived analytical expressions for the IA-wave dispersion relation in an anisotropic plasma in the framework of gyrokinetics and then compared them to fully kinetic numerical calculations, results from two-fluid theory, and magnetohydrodynamics (MHD).
Abstract: Observations in the solar wind suggest that the compressive component of inertial-range solar-wind turbulence is dominated by slow modes. The low collisionality of the solar wind allows for nonthermal features to survive, which suggests the requirement of a kinetic plasma description. The least-damped kinetic slow mode is associated with the ion-acoustic (IA) wave and a nonpropagating (NP) mode. We derive analytical expressions for the IA-wave dispersion relation in an anisotropic plasma in the framework of gyrokinetics and then compare them to fully kinetic numerical calculations, results from two-fluid theory, and magnetohydrodynamics (MHD). This comparison shows major discrepancies in the predicted wave phase speeds from MHD and kinetic theory at moderate to high β. MHD and kinetic theory also dictate that all plasma normal modes exhibit a unique signature in terms of their polarization. We quantify the relative amplitude of fluctuations in the three lowest particle velocity moments associated with IA and NP modes in the gyrokinetic limit and compare these predictions with MHD results and in situ observations of the solar-wind turbulence. The agreement between the observations of the wave polarization and our MHD predictions is better than the kinetic predictions, which suggests that the plasma behaves more like a fluid in the solar wind than expected.
TL;DR: In this article, a new approach based on Chebyshev polynomials theory is introduced to analyze free vibration of axially functionally graded Euler-Bernoulli and Timoshenko beams with non-uniform cross-sections.
TL;DR: In this paper, a normal mode analysis using density functional theory of thousands of proton-water clusters taken from reactive molecular dynamics trajectories of the latest generation multistate empirical valence bond proton model is applied to obtain a vibrational density of states and IR spectral density, which are decomposed on the basis of solvated proton structure and the frequency dependent mode character.
Abstract: The local environmental sensitivity of infrared (IR) spectroscopy to a hydrogen-bonding structure makes it a powerful tool for investigating the structure and dynamics of excess protons in water. Although of significant interest, the line broadening that results from the ultrafast evolution of different solvated proton-water structures makes the assignment of liquid-phase IR spectra a challenging task. In this work, we apply a normal mode analysis using density functional theory of thousands of proton-water clusters taken from reactive molecular dynamics trajectories of the latest generation multistate empirical valence bond proton model (MS-EVB 3.2). These calculations are used to obtain a vibrational density of states and IR spectral density, which are decomposed on the basis of solvated proton structure and the frequency dependent mode character. Decompositions are presented on the basis of the proton sharing parameter δ, often used to distinguish Eigen and Zundel species, the stretch and bend character of the modes, the mode delocalization, and the vibrational mode symmetry. We find there is a wide distribution of vibrational frequencies spanning 1200-3000 cm-1 for every local proton configuration, with the region 2000-2600 cm-1 being mostly governed by the distorted Eigen-like configuration. We find a continuous red shift of the special-pair O⋯H+⋯O stretching frequency, and an increase in the flanking water bending intensity with decreasing δ. Also, we find that the flanking water stretch mode of the Zundel-like species is strongly mixed with the flanking water bend, and the special pair proton oscillation band is strongly coupled with the bend modes of the central H5O2+moiety.
TL;DR: In this article, an exact solution on the basis of the method of reverberation ray matrix (MRRM) and golden section search (GSS) algorithm is presented to study the exact free in-plane vibration characteristics of rectangular plates with arbitrary boundary conditions.
TL;DR: In this article, the authors report an experimental campaign that aims at measuring the evolution of bridge modal properties during the passage of a vehicle and investigate not only frequency shifts due to various vehicle positions, but also changes in the shape of the modes of vibration.
TL;DR: In this paper, a case study of the sensitivity method in finite element (FE) model updating is presented to the Bergsoysund Bridge, which is a long-span floating pontoon bridge in Norway.
TL;DR: An experimental realization of a quantum absorption refrigerator in a system of three trapped ions, with three of its normal modes of motion coupled by a trilinear Hamiltonian such that heat transfer between two modes refrigerates the third.
Abstract: Thermodynamics is one of the oldest and well-established branches of physics that sets boundaries to what can possibly be achieved in macroscopic systems. While it started as a purely classical theory, it was realized in the early days of quantum mechanics that large quantum devices, such as masers or lasers, can be treated with the thermodynamic formalism. Remarkable progress has been made recently in the miniaturization of heat engines all the way to the single Brownian particle as well as to a single atom. However, despite several theoretical proposals, the implementation of heat machines in the fully quantum regime remains a challenge. Here, we report an experimental realization of a quantum absorption refrigerator in a system of three trapped ions, with three of its normal modes of motion coupled by a trilinear Hamiltonian such that heat transfer between two modes refrigerates the third. We investigate the dynamics and steady-state properties of the refrigerator and compare its cooling capability when only thermal states are involved to the case when squeezing is employed as a quantum resource. We also study the performance of such a refrigerator in the single shot regime, and demonstrate cooling below both the steady-state energy and the benchmark predicted by the classical thermodynamics treatment.
TL;DR: In this article, the vibration performance of sandwich beams with honeycomb-corrugation hybrid cores was investigated, and the method of homogenization was employed to obtain the equivalent macroscopic stiffness of honeycomb and Corrugation Hybrid cores.
TL;DR: In this article, a faster-than-adiabatic two-qubit phase gate with smooth state-dependent forces is proposed. But the forces are designed to leave no final motional excitation, independently of the initial motional state in the harmonic small-oscillations limit.
Abstract: We implement faster-than-adiabatic two-qubit phase gates using smooth state-dependent forces. The forces are designed to leave no final motional excitation, independently of the initial motional state in the harmonic small-oscillations limit. They are simple, explicit functions of time and the desired logical phase of the gate, and are based on quadratic invariants of motion and Lewis-Riesenfeld phases of the normal modes.
TL;DR: In this article, a reduced-order analytical dynamic model for a signal flexible-link flexible-joint (SFF) manipulator is proposed to obtain a reducedorder analytical model for the SFF manipulator.
TL;DR: In this paper, a dynamic modeling approach for flexible spacecraft with multiple solar panels and flexible joints is presented, where the natural frequencies and global mode shapes of the flexible spacecraft are determined, and orthogonality relations of the global mode shape are established.
TL;DR: In this paper, a power-based nonlinear mode indicator function is derived, which is generally applicable, reliable and easy to implement in experiments, and the tuning of the excitation phase is automated by the use of a Phase-Locked-Loop controller.
TL;DR: A new conceptually simple and computationally efficient method for nonlinear normal-mode analysis called NOLB, which relies on the rotations-translations of blocks (RTB) theoretical basis, which produces better structures compared to the standard approach, especially at large deformation amplitudes.
Abstract: We present a new conceptually simple and computationally efficient method for nonlinear normal-mode analysis called NOLB. It relies on the rotations-translations of blocks (RTB) theoretical basis developed by Y.-H. Sanejouand and colleagues [Durand et al. Biopolymers 1994, 34, 759–771. Tama et al. Proteins: Struct., Funct., Bioinf. 2000, 41, 1–7]. We demonstrate how to physically interpret the eigenvalues computed in the RTB basis in terms of angular and linear velocities applied to the rigid blocks and how to construct a nonlinear extrapolation of motion out of these velocities. The key observation of our method is that the angular velocity of a rigid block can be interpreted as the result of an implicit force, such that the motion of the rigid block can be considered as a pure rotation about a certain center. We demonstrate the motions produced with the NOLB method on three different molecular systems and show that some of the lowest frequency normal modes correspond to the biologically relevant motions...
TL;DR: This work studies the nonadiabatic relaxation of photoexcited [Cu(dmp)2]+ (dmp = 2,9-dimethyl-1,10-phenanthroline) using QM/MM Trajectory Surface Hopping (TSH) and identifies the dominant normal modes activated during the excited state decay, which are then used to design the vibronic Hamiltonian for quantum wavepacket dynamics simulations.
Abstract: On-the-fly excited state molecular dynamics is a valuable method for studying non-equilibrium processes in excited states and is beginning to emerge as a mature approach much like its ground state counterparts. In contrast to quantum wavepacket dynamics methods, it negates the need for modelling potential energy surfaces, which usually confine nuclear motion within a reduced number of vibrational modes. In addition, on-the-fly molecular dynamics techniques are easily combined with the atomistic description of the solvents (through the QM/MM approach) making it possible to explicitly address the effect of the environment. Herein, we study the nonadiabatic relaxation of photoexcited [Cu(dmp)2]+ (dmp = 2,9-dimethyl-1,10-phenanthroline) using QM/MM Trajectory Surface Hopping (TSH). We show that the decay of the initially excited singlet state into the lowest singlet (S1) state occurs within 100 fs, in agreement with previous experiments, and is slightly influenced by the solvent. Using a principal component analysis (PCA), we also identify the dominant normal modes activated during the excited state decay, which are then used to design the vibronic Hamiltonian for quantum wavepacket dynamics simulations.
TL;DR: In this article, the free vibration of rotating tap beam was examined and the frequency and mode shape of the Timoshenko beam was determined for a rotating tapered beam with the objective of determining its natural frequencies and mode shapes.
Abstract: Accurate determination of natural frequencies and mode shapes of the rotating tapered Timoshenko beam is important in engineering practice. This paper re-examines the free vibration of rotating tap...
TL;DR: In this article, the linear thermal expansion coefficients (LTEC) of two-dimensional honeycomb structured pure graphene and B/N doped graphene are analyzed using ab initio density functional perturbation theory (DFPT) employed in VASP software under quasiharmonic approximation.
Abstract: Graphene and its derivatives distinguish themselves for their large negative thermal expansion even at temperatures as high as 1000 K. The linear thermal expansion coefficients (LTEC) of two-dimensional honeycomb structured pure graphene and B/N doped graphene are analyzed using ab initio density functional perturbation theory (DFPT) employed in VASP software under quasiharmonic approximation. One of the essential ingredients required is the phonon frequencies for a set of points in the Brillouin zone and their volume dependence. These were obtained from the dynamical matrix which was calculated using VASP code in interface with phonopy code. In particular, the transverse acoustic modes (ZA) behave drastically differently as compared to planer modes and so also their volume dependence. Using this approach firstly thermal expansion for pure graphene is calculated. The results agree with earlier calculations using similar approach. Thereafter we have studied the effect of boron and nitrogen doping on LTEC. The LTEC of graphene is found to be negative in the entire range of temperature under study (0–1000 K) and its value at room temperature (RT) is around −3.26 × 10−6 K−1. The value of LTEC at RT becomes more negative with B/N doping in graphene. In order to get an insight into the cause of negative thermal expansion, we have computed the contribution of individual phonon modes of vibration. We notice that it is principally the ZA modes which are responsible for negative thermal expansion. It has been concluded that transverse mode in 2D hexagonal lattices have an important role to play in many of the thermodynamical properties of 2D structures. We have extended the study to calculate the LTEC of h-BN sheet also.
TL;DR: In this article, analytical solutions for propagation of time-harmonic waves in three-dimensional, transversely isotropic, magnetoelectroelastic and multilayered plates with nonlocal effect are derived.
TL;DR: Based on the modified couple-stress theory, three-dimensional analytical solutions of free vibration of a simply supported, multilayered and anisotropic composite nanoplate are derived by solving an eigenvalue system and using the propagator matrix method as discussed by the authors.
Abstract: Based on the modified couple-stress theory, three-dimensional analytical solutions of free vibration of a simply supported, multilayered and anisotropic composite nanoplate are derived by solving an eigenvalue system and using the propagator matrix method. By expanding the solutions of the extended displacements in terms of two-dimensional Fourier series, the final governing equations of motion with modified couple-stress effect are reduced to an eigenvalue system of ordinary differential equations. Analytical expressions for the natural frequencies and mode shapes of multilayered anisotropic composite plates with modified couple-stress effect are then derived via the propagator matrix method. Numerical examples are carried out for homogeneous thick-plates and sandwich composite plates to show the effect of the non-local parameter in different layers and stacking sequence on the mode shapes. The present solutions can serve as benchmarks to various thick-plate theories and numerical methods, and could be further useful for designing layered composite structures involving small scale.
TL;DR: In this paper, the authors obtained the black brane solution in arbitrary dimensional Gauss-Bonnet-axions (GBA) gravity theory, and then the thermal conductivity of the boundary theory dual to this neutral brane is explored.
TL;DR: In this article, a closed cavity built of an array of elementary harmonic oscillators with negative mutual couplings exhibits a dispersion curve with lower order modes corresponding to higher frequencies, which may help to achieve large mode volumes for boosting sensitivity of the axion searches.