Mode Motions Research Articles

Free vibration analysis of a spinning piezoelectric beam with geometric nonlinearities

The linear and non-linear free vibrations of a spinning piezoelectric beam are studied by considering geometric nonlinearities and electromechanical coupling effect. The non-linear differential equations of the spinning piezoelectric beam governing two transverse vibrations are derived by using transformation of two Euler angles and the extended Hamilton principle, wherein an additional piezoelectric coupling term and different linear terms are present in contrast to the traditional shaft model. Linear frequencies are obtained by solving the standard eigenvalues of the linearized system directly, and the non-linear frequencies and non-linear complex modes are achieved by using the method of multiple scales. For free vibrations analysis of a spinning piezoelectric beam, the non-linear modal motions are investigated as forward and backward precession with different spinning speeds. The responses to the initial conditions for this gyroscopic system are studied and a beat phenomenon is found, which are then validated by numerical simulation. The influences of some parameters such as electrical resistance, rotary inertia and spinning speeds to the non-linear dynamics of a spinning piezoelectric beam are investigated.

LONGITUDINAL NON-STATIONARY MOTIONS OF MAGLEV TRAIN

Purpose. The quality of passenger’s and good’s transportation by a magnetically levitated train (MLT) is a key criterion for evaluating its consumer properties. The dynamics of a train’s electromechanical subsystem (EMS) has a decisive influence on this quality. Non-stationary modes of this subsystem’s motion, such as a speed increase, service and emergency braking, as well as the passage of the tunnel are especially critical. Therefore, the train’s motion in such modes is limited by acceptable safety standards. Based on this, the purpose of this study is to assess the dynamic qualities and load of the train in the above-mentioned non-stationary modes. Methodology. At the present stage, the main and most universal tool for analyzing and synthesizing processes in systems is their mathematical and, in particular, computer modelling. On this basis, the work was done by conducting a series of experiments with computer model of EMS MLT dynamics. This computer model was obtained as a result of the relevant transformation of the corresponding mathematical model into it. The mentioned computer model was programmatically recorded in the input language of the Mathematica computer mathematics system. Findings. The obtained results of modelling are presented in graphical form and reflect the train's motion in the modes of acceleration, the passage through a tunnel, as well as service and emergency braking. The control by the train's electromechanical subsystem in all considered transient modes of motion, with the exception of emergency braking, is carried out by changing the voltage feeding of the linear synchronous motor’s armature’s winding according to one or another law. Therefore, during modelling the train’s motion in each of these modes, frequency, amplitude-frequency, and phase-frequency control options for the motor’s armature’s voltage changing were considered. Analysis of the simulation results made it possible to estimate the MLT’s dynamic qualities in various non-stationary modes of motion and its load in their process. Originality. The research suggests setting the priority of the holistic consideration of non-stationary modes of MLT's EMS's motion. Practical value. The main manifestation of the practical value of the work is the possibility, in the case of using its results, of significant increasing in the efficiency of dynamic studies of MLT while reducing their resource intensity.

Frequency Based Substructuring for Structure with Double Bolted Joints: A Case Study

Adopting dynamic substructuring schemes is a common practice in the field of structural dynamics, where the dynamic behaviour of a structure is predicted by combining the multiple subsystems that are analysed individually. This paper investigated the dynamic behaviour of a structure with doubled bolted joints using the frequency based substructuring (FBS) method. In the attempt, the substructures were combined with the frequency domain that can be numerically derived or experimentally measured. However, the applicability of this method suffered from several issues where most of them were related to the frequency response function (FRF) of the rotational degree of freedom (DOF) at the subsystem’s interface. In some cases, the system’s interface vibrated in the rotary motion of certain modes, for instance, a car side rear view mirror. Therefore, excluding the rotational FRF during the coupling process could lead to a completely different result. This paper presents the use of the FBS method for a structure with double bolted joints by using the equivalent multipoint constraint (EMPC) method through which rotational DOFs can be completely neglected. The actual tested structure for this study was an assembled structure consisting of two substructures: a simple beam and an irregular plate steel structure. The FRFs of both substructures were derived from using the FRF synthesis from finite element models and combined together via the FBS method. This study reveals that the use of the FBS method with the EMPC method for a structure double bolted joints has led to very promising results.

Validation of the Longitudinal Motion Amplitude and Phase for Two Ships with Forward Speed at Close Proximity in Waves

The longitudinal motion amplitude and phase for two ships with forward speed at close proximity in waves are investigated by the frequency-domain potential flow theory, which is based on the mathematical kernel of three-dimension translating-pulsating source. On the foundation of numerical validation for a modified Wigley ship, the frequency-domain method is then extended to the kinematic characteristics for two ships. The two-ship model test is focused on the surge, heave and pitch mode motions. The numerical and experimental results shows that it is applicable to solve the hydrodynamic interaction problem for two advancing ships in waves by the introduction of translating-pulsating source Green function.

Coupled Bending–Bending–Axial–Torsional Vibrations of Rotating Blades

In this paper, the coupled bending–bending–axial–torsional free vibrations of rotating blades are investigated based on the Euler–Bernoulli beam model. The coupled partial differential equations governing flapwise, edgewise, axial and torsional motions are derived by the Hamilton’s principle, wherein three types of velocity-dependent terms, namely static centrifugal terms, dynamic centrifugal terms and gyroscopic coupling terms, are focused. The ordinary differential equations are acquired by the Galerkin truncation, and the natural frequencies in all directions and complex mode shapes of the rotating blades are analyzed in detail. It is revealed that the three types of velocity-dependent terms have different effects on the natural frequencies. The natural frequencies are noticeably dependent on the rotating speed and preset angle, except for the axial vibration, which is almost immune to the preset angle. The complex modal motions are displayed by a series of positions of the central line and free-end cross section for different time instants, showing the coupled vibrations among different directions.

Tympanic membrane surface motions in forward and reverse middle ear transmissions.

Characterization of Tympanic Membrane (TM) surface motions with forward and reverse stimulation is important to understanding how the TM transduces acoustical and mechanical energy in both directions. In this paper, stroboscopic opto-electronic holography is used to quantify motions of the entire TM surface induced by forward sound and reverse mechanical stimulation in human cadaveric ears from 0.25 to 18.4 kHz. The forward sound stimulus was coupled to an anatomically realistic artificial ear canal that allowed optical access to the entire TM surface, and the reverse mechanical stimulus was applied to the body of the incus by a piezo-electric stimulator. The results show clear differences in TM surface motions evoked by the two stimuli. In the forward case, TM motion is dominated by standing-wave-like modal motions that are consistent with a relatively uniform sound-pressure load over the entire TM surface. With reverse mechanical stimulation, the TM surface shows more traveling waves, consistent with a localized mechanical drive applied to the manubrium embedded in the TM. With both stimuli, the manubrium moves less than the rest of the TM, consistent with the TM acting like a compliant membrane rather than a stiff diaphragm, and also consistent with catenary behavior due to the TM's curved shape.

On Travelling Wave Modes of Axially Moving String and Beam

The traditional vibrational standing‐wave modes of beams and strings show static overall contour with finite number of fixed nodes. The travelling wave modes are investigated in this study of axially moving string and beam although the solutions have been obtained in the literature. The travelling wave modes show time‐varying contour instead of static contour. In the model of an axially moving string, only backward travelling wave modes are found and verified by experiments. Although there are n − 1 fixed nodes in the nth order mode, similar to the vibration of traditional static strings, the presence of travelling wave phenomenon is still spotted between any two adjacent nodes. In contrast to the stationary nodes of string modes, the occurrence of galloping nodes of axially moving beams is discovered: the nodes oscillate periodically during modal motions. Both forward and backward travelling wave phenomena are detected for the axially moving beam case. It is found that the ranges of forward travelling wave modes increase with the axially moving speed. It is also concluded that backward travelling wave modes can transform to the forward travelling wave modes as the transport speed surpasses the buckling critical speed.

Vibrational Coupling between Organic and Inorganic Sublattices of Hybrid Perovskites.

The interplay of electronic and nuclear degrees of freedom in semiconductor hybrid organic-inorganic perovskites determines many of their fundamental photophysical properties. For instance, charge carriers are dressed with phonons, that is, form polarons, and combination modes composed of strongly mixed localized vibrations and delocalized phonons can provide pathways for electronic energy relaxation and dissipation. Mixing of the different types of nuclear motion in vibrational combination modes requires their strong coupling. The direct measurement of coupling between the high-frequency N-H stretch modes of the organic methylammonium and formamidinium ions and low-frequency Pb-I phonon modes of the inorganic sub-lattice in hybrid organic-inorganic perovskites is presented. The results reveal direct and substantial coupling between the non-covalently interacting organic and inorganic sub-lattices.

Modal Analysis of Fuel Injection Systems and the Determination of a Transfer Function Between Rail Pressure and Injection Rate

A detailed analysis of a common rail (CR) fuel injection system, equipped with solenoid injectors for Euro 6 diesel engine applications, has been performed in the frequency domain. A lumped parameter numerical model of the high-pressure hydraulic circuit, from the pump delivery to the injector nozzle, has been realized. The model outcomes have been validated through a comparison with frequency values that were obtained by applying the peak-picking technique to the experimental pressure time histories acquired from the pipe that connects the injector to the rail. The eigenvectors associated with the different eigenfrequencies have been calculated and physically interpreted, thus providing a methodology for the modal analysis of hydraulic systems. Three main modal motions have been identified in the considered fuel injection apparatus, and the possible resonances with the external forcing terms, i.e., pump delivered flow rate, injected flow rate, and injector dynamic fuel leakage through the pilot valve, have been discussed. The investigation has shown that the rail is mainly involved in the first two vibration modes. In the first mode, the rail performs a decoupling action between the high-pressure pump and the downstream hydraulic circuit. Consequently, the oscillations generated by the pump flow rates mainly remain confined to the pipe between the pump and the rail. The second mode is centered on the rail and involves a large part of the hydraulic circuit, both upstream and downstream of the rail. Finally, the third mode principally affects the injector and its internal hydraulic circuit. It has also been observed that some geometric features of the injection apparatus can have a significant effect on the system dynamics and can induce hydraulic resonance phenomena. Furthermore, the lumped parameter model has been used to determine a simplified transfer function between rail pressure and injected flow rate. The knowledge obtained from this study can help to guide designers draw up an improved design of this kind of apparatus, because the pressure waves, which are triggered by impulsive events and are typical of injector working, can affect the performance of modern injection systems, especially when digital rate shaping strategies or closely coupled multiple injections are implemented.

Dynamics of a beam with both axial moving and spinning motion: An example of bi-gyroscopic continua

Abstract Classical gyroscopic continua include axially moving materials and spinning structures. The gyroscopic effect of the axially moving material is pronounced via the gyroscopic coupling among the basis functions in the same motional direction. On the other hand, the gyroscopic coupling of the spinning structure acts in the two different directions of motion. In this paper, we study the dynamics of a beam with both axial moving motion and spinning motion as a prototype of bi-gyroscopic continua. The influence of bi-gyroscopic effects on the natural frequencies, modes, and stability is investigated by an analytical method applied to the discretized equations of the axially moving and spinning beam. Distinct bifurcation series of the eigenvalues and corresponding physical interpretations are discussed by numerical display of the modal motions. The complex modes describing both whirling motions and traveling waves are investigated in detail for such bi-gyroscopic system. New interesting phenomena have been analyzed numerically and important conclusions have been drawn for such bi-gyroscopic system.

Wave propagation through mangrove forests in the presence of a viscoelastic bed

The influence of viscoelastic ocean beds on the characteristics of surface waves passing through mangrove forests is analyzed under the assumption of linearized water wave theory in two dimensions. The trunks of the mangroves are assumed to be in the upper-layer inviscid fluid domain, whilst the roots are inside the viscoelastic bed. The associated equation of motion is obtained by coupling the Voigt’s model for flow within the viscoelastic medium with the equation of motion in the presence of mangroves. The modified dynamic conditions are coupled with the kinematic conditions to obtain the boundary condition at the free surface and the interface of the two fluids consisting of the upper layer inviscid fluid and the viscoelastic fluid bed. To understand the effects of bed viscosity as well as elasticity on energy dissipation, the complex dispersion relation associated with the plane progressive wave is derived and analyzed. Effect of physical parameters associated with mangroves and viscoelastic bed on wave motion in surface and internal modes are computed and analyzed to understand their roles in attenuating wave effects. The present model will be useful in the better understanding of wave propagation through mangroves in the coastal zone having muddy seabed.

Transverse free vibration and stability analysis of spinning pipes conveying fluid

In this paper, the transverse free vibration and stability are analyzed for spinning pipes conveying fluid as a typical example of doubly gyroscopic systems. The partial differential equations of motion are derived by the extended Hamilton principle, and are then truncated by the 4-term Galerkin technique. The natural frequencies, complex modal motions and responses to initial conditions are comprehensively investigated to display the essential dynamical properties of such spinning structures conveying fluid. It is indicated that the qualitative stability of the present system mainly depends on the effects of fluid-structure interaction (FSI) and mass ratio, while the spinning speed plays a significant role in determining the quantitative values of the frequency. The critical flow velocities are independent of the spinning speed and mass ratio. Forward and backward whirling motions are found to take place alternatively for the first four modes, and a ‘traveling wave’ with spatial configuration is observed during vibrations. The gyroscopic couplings caused by spin and FSI will yield great impacts on the energy transfers between different general coordinates.

Quantum self-organization and nuclear collectivities

The quantum self-organization is introduced as one of the major underlying mechanisms of the quantum many-body systems. In the case of atomic nuclei as an example, two types of the motion of nucleons, single-particle states and collective modes, dominate the structure of the nucleus. The outcome of the collective mode is determined basically by the balance between the effect of the mode-driving force (e.g., quadrupole force for the ellipsoidal deformation) and the resistance power against it. The single-particle energies are one of the sources to produce such resistance power: a coherent collective motion is more hindered by larger gaps between relevant single particle states. Thus, the single-particle state and the collective mode are “enemies” each other. However, the nuclear forces are demonstrated to be rich enough so as to enhance relevant collective mode by reducing the resistance power by changing singleparticle energies for each eigenstate through monopole interactions. This will be verified with the concrete example taken from Zr isotopes. Thus, when the quantum self-organization occurs, single-particle energies can be self-organized, being enhanced by (i) two quantum liquids, e.g., protons and neutrons, (ii) two major force components, e.g., quadrupole interaction (to drive collective mode) and monopole interaction (to control resistance). In other words, atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naïve Fermi liquid picture. Type II shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger. The quantum self-organization is a general phenomenon, and is expected to be found in other quantum systems.

Waves Perturbation in Rotating Plasma Magnetic Cylinder Surrounded by Plasma Atmosphere with Consideration for Compression

In the cylindrical coordinate system (R, φ, z) the problem of motion of helical modes in a long current carrying plasma cylinder with an azimuthal magnetic field Bφ ~ R/a , where a is the radius of the cylinder, and a constant vertical field Bzi is studied. It is assumed that inside the cylinder plasma moves with velocities Vφ = ΩR/a, Vz = const and outside its boundary a motion of the environment and a magnetic field are absent. It is shown that under certain conditions there occurs the generation of resonance perturbations which can lead to destruction of plasma configuration. It is established that in this case an energy of the cylinder rotational motion changes to an energy of helical perturbations. The work also gives a thorough consideration to helical modes which do not lead to resonant events. The results of the work are applicable to interpretation of data on studying magnetic tubes in the Sun.

Single-particle states vs. collective modes: friends or enemies ?

The quantum self-organization is introduced as one of the major underlying mechanisms of the quantum many-body systems. In the case of atomic nuclei as an example, two types of the motion of nucleons, single-particle states and collective modes, dominate the structure of the nucleus. The collective mode arises as the balance between the effect of the mode-driving force (e.g., quadrupole force for the ellipsoidal deformation) and the resistance power against it. The single-particle energies are one of the sources to produce such resistance power: a coherent collective motion is more hindered by larger spacings between relevant single particle states. Thus, the single-particle state and the collective mode are “enemies” against each other. However, the nuclear forces are rich enough so as to enhance relevant collective mode by reducing the resistance power by changing single-particle energies for each eigenstate through monopole interactions. This will be verified with the concrete example taken from Zr isotopes. Thus, the quantum self-organization occurs: single-particle energies can be self-organized by (i) two quantum liquids, e.g., protons and neutrons, (ii) monopole interaction (to control resistance). In other words, atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naïve Fermi liquid picture. Type II shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger.

Theoretical framework for analyzing structural compliance properties of proteins.

We propose methods for directly analyzing structural compliance (SC) properties of elastic network models of proteins, and we also propose methods for extracting information about motion properties from the SC properties. The analysis of SC properties involves describing the relationships between the applied forces and the deformations. When decomposing the motion according to the magnitude of SC (SC mode decomposition), we can obtain information about the motion properties under the assumption that the lower SC mode motions or the softer motions occur easily. For practical applications, the methods are formulated in a general form. The parts where forces are applied and those where deformations are evaluated are separated from each other for enabling the analyses of allosteric interactions between the specified parts. The parts are specified not only by the points but also by the groups of points (the groups are treated as flexible bodies). In addition, we propose methods for quantitatively evaluating the properties based on the screw theory and the considerations of the algebraic structures of the basic equations expressing the SC properties. These methods enable quantitative discussions about the relationships between the SC mode motions and the motions estimated from two different conformations; they also help identify the key parts that play important roles for the motions by comparing the SC properties with those of partially constrained models. As application examples, lactoferrin and ATCase are analyzed. The results show that we can understand their motion properties through their lower SC mode motions or the softer motions.

Free Vibration Analysis of Pipes Conveying Fluid Based on Linear and Nonlinear Complex Modes Approach

In this paper, linear and nonlinear complex modes are used to analyze the free vibration of pipes conveying fluid involving the gyroscopic properties of the system. The natural frequencies, complex mode functions and time domain responses of the admissible mode functions based on discretized model are obtained using the invariant manifold method and compared with those of the continuous model. A good agreement has been achieved if the admissible mode functions for the static beams are adopted. The energy contributions of different admissible modes to the modal motions are also studied which explores the gyroscopic coupling variation among the admissible modes for different fluid velocities. Nonlinear complex modes are constructed for the nonlinear case and the morphology of the modal motions is demonstrated for different initial energy to show the contribution of the nonlinear terms. ‘Traveling waves’ are found for the transverse vibrations of the pipes conveying fluid due to the gyroscopic effects, contrary to the “standing waves” found for the pipes without moving fluid.

Coupled dynamic analysis of deep-sea mining support vessel with dynamic positioning

ABSTRACTDeep-sea mining (DSM) is an advanced concept. A simulation method of coupled vessel/riser/body system in DSM combined with dynamic positioning (DP) is proposed. Based on the three-dimensional potential flow theory, lumped mass method, and Morison’s equations the dynamic models of the production support vessel, riser and slurry pump are established. A proportion integration differentiation (PID) controller with a nonlinear observer and a thrust allocation unit are used to simulate the DP system. Coupled time domain simulation is implemented with the vessel operated in two DP modes. Results of the vessel and pump motions, riser tension, and thruster forces are obtained. It shows that the pump will be lifted by the riser when the vessel is chasing the next set point. Riser tension is influenced by the wave frequency motions of the vessel in positioning mode and low-frequency motions in tracking mode. The proposed simulation scheme is practical to study the DSM operation.

Markovian Dynamics of Josephson Parametric Amplification

Abstract. In this work, we derive the dynamics of the lossy DC pumped non-degenerate Josephson parametric amplifier (DCPJPA). The main element in a DCPJPA is the superconducting Josephson junction. The DC bias generates the AC Josephson current varying the nonlinear inductance of the junction. By this way the Josephson junction acts as the pump oscillator as well as the time varying reactance of the parametric amplifier. In quantum-limited amplification, losses and noise have an increased impact on the characteristics of an amplifier. We outline the classical model of the lossy DCPJPA and derive the available noise power spectral densities. A classical treatment is not capable of including properties like spontaneous emission which is mandatory in case of amplification at the quantum limit. Thus, we derive a quantum mechanical model of the lossy DCPJPA. Thermal losses are modeled by the quantum Langevin approach, by coupling the quantized system to a photon heat bath in thermodynamic equilibrium. The mode occupation in the bath follows the Bose-Einstein statistics. Based on the second quantization formalism, we derive the Heisenberg equations of motion of both resonator modes. We assume the dynamics of the system to follow the Markovian approximation, i.e. the system only depends on its actual state and is memory-free. We explicitly compute the time evolution of the contributions to the signal mode energy and give numeric examples based on different damping and coupling constants. Our analytic results show, that this model is capable of including thermal noise into the description of the DC pumped non-degenerate Josephson parametric amplifier.

Biomechanical evaluation of different surgical procedures in single-level transforaminal lumbar interbody fusion in vitro

BackgroundsA variety of improved surgical methods were adopted in the transforaminal lumbar interbody fusion. A mechanical stability provides an ideal environment for the formation of a fusion mass and is the basis of their good outcomes. The object of this study is to evaluate the initial similarities and differences of four commonly-used posterior surgical procedures biomechanically. MethodsBiomechanical testing was performed at L3–4 motion segment in 6 fresh-frozen human cadaveric lumbar spines (L2–L5), including the following sequentially tested configurations: 1) intact motion segment; 2) bilateral pedicle screw fixation; 3) unilateral pedicle screw fixation; 4) unilateral pedicle screw plus contralateral translaminar facet joint screw fixation according to the Magerl technique; and 5) bilateral pedicle screw fixation with bilateral facetectomies. The range of motion, neutral zone and stiffness of each method and intact segment were collected and compared. FindingsAll of four methods reduce the range of motion significantly in flexion and extension and lateral bending but not in axial torsion compared with the native segment. There is no significant difference among four procedures about the range of motion in all loading modes. All of methods increase the stiffness of segmental motion compared with intact segment in all loading modes, but only bilateral pedicle screw fixation showed significant increases in stiffness in flexion and extension(p=0.02) and lateral bending(p=0.023). The stiffness offered by instrumented constructs in different methods showed no significant difference in all loading modes. InterpretationThe stiffness offered by four different posterior fixations in single segmental transforaminal lumbar interbody fusion is not significantly different.