Search Results (26)

Fractional-order models provide a powerful framework for capturing memory-dependent and viscoelastic dynamics in mechanical systems, which are often inadequately represented by classical integer-order characterizations. This study addresses the identification of dynamic parameters in both single-degree-of-freedom (1-DOF) and three-degree-of-freedom (3-DOF) Duffing oscillators with fractional damping, modeled using the Grünwald–Letnikov characterization. The 1-DOF system includes a cubic nonlinear restoring force and is excited by a harmonic input to induce steady-state oscillations. For both systems, time domain simulations are conducted to capture long-term responses, followed by Fourier decomposition to extract steady-state displacement, velocity, and acceleration signals. These components are combined with a GL-based fractional derivative approximation to construct structured regressor matrices. System parameters—including mass, stiffness, damping, and fractional-order effects—are then estimated using pseudoinverse techniques. The identified models are validated through a comparison of reconstructed and original trajectories in the phase space, demonstrating high accuracy in capturing the underlying dynamics. The proposed framework provides a consistent and interpretable approach for frequency domain system identification in fractional-order nonlinear systems, with relevance to applications such as mechanical vibration analysis, structural health monitoring, and smart material modeling. Full article

To characterize a phenomenological model of a mechanical oscillator, it is important to know the properties of the envelope of the three main physical motion variables: deviation from equilibrium, velocity, and acceleration. Experimental data show that friction forces restrict the shape of these functions. A linear, exponential, or more abrupt decay can be observed depending on the different physical systems and conditions. This paper aimed to contribute to clarifying the role that some types of friction forces play in these shapes. Three types of friction—constant sliding friction, pressure drag proportional to the square of velocity, and friction drag proportional to velocity—were considered to characterize the line connecting the maxima and minima of displacement for a generic mechanical harmonic oscillator. The ordinary differential equation (ODE), describing the harmonic oscillator simultaneously containing the three types of dissipative forces (constant, viscous, and quadratic), was numerically solved to obtain energy dissipation, and the extrema of both displacement and velocity. The differential equation ruling the behavior of the amplitude, as a function of the friction force coefficients, was obtained from energy considerations. Solving this equation, we obtained analytical functions, parametrized by the force coefficients that describe the oscillator tail. A comparison between these functions and the predicted oscillator ODE extrema was made, and the results were in agreement for all the situations tested. Information from the velocity extrema and nulls was enough to obtain a second function that rules completely the ODE solution. The correlations obtained allow for the reverse operation: from the identified extremum data, it was possible to identify univocally the three friction coefficients fitting used in the model. Motion equations were solved, and some physical properties, namely energy conservation and work of friction forces, were revisited. Full article

Recent studies have identified a near six-year oscillation (SYO) in Global Navigation Satellite Systems (GNSS) surface displacements, with a degree 2, order 2 spherical harmonic (SH) pattern and retrograde motion. The cause is uncertain, with proposals ranging from deep Earth to near-surface sources. This study investigates the SYO and possible causes from surface loading. Considering the irregular spatiotemporal distribution of GNSS data and the variety of contributors to surface displacements, we used synthetic experiments to identify optimal techniques for estimating low degree SH patterns. We confirm a reported retrograde SH degree 2, order 2 displacement using GNSS data from the same 35 stations used in a previous study for the 1995–2015 period. We also note that its amplitude diminished when the time span of observations was extended to 2023, and the retrograde dominance became less significant using a larger 271-station set. Surface loading estimates showed that terrestrial water storage (TWS) loads contributed much more to the GNSS degree 2, order 2 SYO, than atmospheric and oceanic loads, but TWS load estimates were highly variable. Four TWS sources—European Centre for Medium-Range Weather Forecasts Reanalysis 5 (ERA5), Modern-Era Retrospective analysis for Research and Applications (MERRA), Global Land Data Assimilation System (GLDAS), and Gravity Recovery and Climate Experiment (GRACE/GRACE Follow-On)—yielded a wide range (24% to 93%) of predicted TWS contributions with GRACE/GRACE Follow-On being the largest. This suggests that TWS may be largely responsible for SYO variations in GNSS observations. Variations in SYO GNSS amplitudes in the extended period (1995–2023) were also consistent with near surface sources. Full article

This study seeks to improve the performance of a low-temperature differential free-piston Stirling air conditioner (FPSAC). To achieve this, a novel approach is proposed, which replaces the conventional simple harmonic drive with a multi-harmonic drive. This modification aims to optimize the motion of the driving piston, bringing it closer to the ideal movement pattern. The research involves both thermodynamic and dynamic coupling simulations of the FPSAC, complemented by experimental verification of its key performance parameters. A thermodynamic model for the gas medium, employing a quasi-one-dimensional dynamic approach for compressible fluids, and a nonlinear two-dimensional vibration dynamic model for the solid piston are developed, focusing on the low-temperature differential FPSAC physical model. The finite difference method is employed to numerically simulate the entire system, including the electromagnetic thrust of the multi-harmonic-driven linear oscillating motor, fluid transport equations, and the nonlinear dynamic equations of the power and gas control pistons. Variations in displacement, velocity, and pressure for each control volume at any given time are obtained, along with the indicator and temperature–entropy diagrams after the system stabilizes. The simulation results show that, in cooling mode, assuming no heat loss or mechanical friction, the Stirling cooler operates at a frequency of 80 Hz. Using the COP_sin value for the simple harmonic drive as a baseline, performance is improved by altering the driving method. Under the multi-harmonic drive, the COP_c5 increased by 10.03% and COP_c7 by 14.23%. In heating mode, the COP under the multi-harmonic drive improved by 0.51% for COP_h5 and 2.61% for COP_h7. Performance experiments were conducted on the low-temperature differential FPSAC, and the key parameter test results showed good agreement with the simulation outcomes. The maximum deviation at the trough was found to be less than 2.45%, while at the peak, the maximum error did not exceed 3.61%. When compared to the simple harmonic drive, the application of the multi-harmonic drive significantly enhances the overall efficiency of the FPSAC, demonstrating its superior performance. The simulation analysis and experimental results indicate a significant improvement in the coefficient of performance of the Stirling cooler under the multi-harmonic drive at the same power level, demonstrating that the multi-harmonic drive is an effective approach for enhancing FPSAC performance. Furthermore, it should be noted that the method proposed in this study is applicable to other types of low-temperature differential free-piston Stirling air conditioners. Full article

We study two harmonic oscillators with high quality factors, driven by equilibrium and off equilibrium thermal noise, the latter mimicked by establishing a temperature gradient. The two oscillators are coupled via a third reciprocal harmonic interaction. We deepen the case of a weak coupling between the two oscillators, and show the emergence of a “spike” in the displacement variance of the colder oscillator, when the respective elastic constants approach each other. Away from the peak, the displacement variance of each oscillator only reflects the value of the local temperature. We name this phenomenon the variance resonance, or alternatively covariance resonance, in the sense that it comes about as one element of the covariance matrix describing both oscillators. In fact, all of the elements of the covariance matrix show some distinctive behavior. The oscillator at the lower temperature, therefore, oscillates as if driven by a higher temperature, resonating with the other one. By converse, the variance of the hotter oscillator develops a deep dent, or depression, around the same region. We could not reproduce this behavior if either the coupling constant is not small compared to those of the two oscillators, or if the quality factors are not large enough. In fact, in such instances the system tends to resemble one which is in equilibrium at the average temperature, regardless of the relative strengths of the elastic constants of the two oscillators. Our results could have various applications including for example precision measurement systems, when not all parts of the apparatuses are at the same temperature. Full article

We study the nonlinear absorptive and dispersive optical properties of molecular systems immersed in a thermal reservoir interacting with a four-wave mixing (FWM) signal. Residual spin-orbit Hamiltonians are considered in order to take into account the internal structure of the molecule. As system parameters in the dissipation processes, transverse and longitudinal relaxation times are considered for stochastic solute–solvent interaction processes. The intramolecular coupling effects on the optical responses are studied using a molecule model consisting of two coupled harmonic curves of electronic energies with displaced minima in nuclear energies and positions. In this study, the complete frequency space is considered through the pump–probe detuning, without restricting the derivations to only maximums of population oscillations. This approach opens the possibility of studying the behavior of optical responses, which is very useful in experimental design. Our results indicate the sensitivity of the optical responses to parameters of the molecular structure as well as to those derived from the photonic process of FWM signal generation. Full article

This paper conducts a comparative analysis of the global dynamics of a harmonically excited oscillator with geometrical nonlinearities. Static analysis of the oscillatory system shows that adjusting the horizontal distance ratio from 1 to 0 can lead to single, double and quadruple well configurations successively. Intra-well and inter-well resonant responses are deduced analytically. Qualitative and quantitative results both reveal that the oscillator displays the stiffness–softening characteristic in cases of double and quadruple wells and the stiffness–hardening characteristic in the case of a single well. The initial-sensitive phenomenon jump is performed via fractal basins of attraction. Complex dynamical behaviors, including higher-order periodic responses and chaos, are also exhibited. The results demonstrate that the oscillator with a double or quadruple well configuration can achieve the inter-well response with large displacement, thus confirming its desirability in engineering applications of geometrically nonlinear oscillators. Full article

Voicing: requires frequent starts and stops at various sound pressure levels (SPL) and frequencies. Prior investigations using rigid laryngoscopy with oral endoscopy have shown variations in the duration of the vibration delay between normal and abnormal subjects. However, these studies were not physiological because the larynx was viewed using rigid endoscopes. We adapted a method to perform to perform simultaneous high-speed naso-endoscopic video while simultaneously acquiring the sound pressure, fundamental frequency, airflow rate, and subglottic pressure. This study aimed to investigate voice onset patterns in normophonic males and females during the onset of variable SPL and correlate them with acoustic and aerodynamic data. Materials and Methods: Three healthy males and three healthy females were studied by simultaneous high-speed video laryngoscopy and recording with the production of the gesture [pa:pa:] at soft, medium, and loud voices. The fiber optic endoscope was threaded through a pneumotachograph mask for the simultaneous recording and analysis of acoustic and aerodynamic data. Results: The average increase in the sound pressure level (SPL) for the group was 15 dB, from 70 to 85 dB. The fundamental frequency increased by an average of 10 Hz. The flow was increased in two subjects, reduced in two subjects, and remained the same in two subjects as the SPL increased. There was a steady increase in the subglottic pressure from soft to loud phonation. Compared to soft to medium phonation, a significant increase in glottal resistance was observed with medium-to-loud phonation. Videokymogram analysis showed the onset of vibration for all voiced tokens without the need for full glottis closure. In loud phonation, there is a more rapid onset of a larger amplitude and prolonged closure of the glottal cycle; however, more cycles are required to achieve the intended SPL. There was a prolonged closed phase during loud phonation. Fast Fourier transform (FFT) analysis of the kymography waveform signal showed a more significant second- and third-harmonic energy above the fundamental frequency with loud phonation. There was an increase in the adjustments in the pharynx with the base of the tongue tilting, shortening of the vocal folds, and pharyngeal constriction. Conclusion: Voice onset occurs in all modalities, without the need for full glottal closure. There was a more significant increase in glottal resistance with loud phonation than that with soft or middle phonation. Vibration analysis of the voice onset showed that more time was required during loud phonation before the oscillation stabilized to a steady state. With increasing SPL, there were significant variations in vocal tract adjustments. The most apparent change was the increase in tongue tension with posterior displacement of the epiglottis. There was an increase in pre-phonation time during loud phonation. Patterns of muscle tension dysphonia with laryngeal squeezing, shortening of the vocal folds, and epiglottis tilting with increasing loudness are features of loud phonation. These observations show that flexible high-speed video laryngoscopy can reveal observations that cannot be observed with rigid video laryngoscopy. An objective analysis of the digital kymography signal can be conducted in selected cases. Full article

Downhole turbine generators (DHTG) installed within drill-string are susceptible to internal and external excitation during the drilling process, causing significant dynamic loads on bearings, and thereby reducing the bearing’s service life. In this study, a finite element model of an unbalanced rotor-bearing system (RBS) of DHTG with multi-frequency excitations, based on the Lagrangian motion differential equation, is established. The responses of the RBS under different drill-string excitations in terms of time-domain response, whirl orbit, and spectrum are analyzed. For a constant rotor speed, lateral harmonic translational and lateral oscillation both transform the whirl orbit to quasi-periodic, while axial rotation only changes the response amplitude. Changing the duration of pulse excitation leads to different response forms. Then, the dynamic characteristics of the RBS supported by a squeeze film damper (SFD) are investigated. The results indicate that SFD effectively reduces the displacement response amplitude and bearing force near the critical speed. As the axial rotation angular velocity of the drill-string increases, the first critical speed and displacement response decrease, while the variation of lateral oscillation frequency and amplitude has limited impact on them. The established model provides a means for analyzing the dynamic characteristics of DHTG’s RBS under drill-string excitations during the design stage. Full article

In recent years, many works have explored possible advantages of indefinite causal order, with the main focus on its controlled implementation known as quantum switch. In this paper, we tackle advantages in quantum thermodynamics, studying whether quantum switch is capable of activating a passive state, either alone or with extra resources (active control state) and/or operations (measurement of the control system). By disproving the first possibility and confirming the second one, we show that quantum switch is not a thermodynamic resource in the discussed context, though it can facilitate work extraction given external resources. We discuss our findings by considering specific examples: a qubit system subject to rotations around the x and y axes in the Bloch sphere, as well as general unitaries from the $U\left(2\right)$ group; and the system as a quantum harmonic oscillator with displacement operators, as well as with a combination of displacement and squeeze operators. Full article

In 2012, Kim and Hirata derived two generalized Langevin equations (GLEs) for a biomolecule in water, one for the structural fluctuation of the biomolecule and the other for the density fluctuation of water, by projecting all the mechanical variables in phase space onto the two dynamic variables: the structural fluctuation defined by the displacement of atoms from their equilibrium positions, and the solvent density fluctuation. The equation has an expression similar to the classical Langevin equation (CLE) for a harmonic oscillator, possessing terms corresponding to the restoring force proportional to the structural fluctuation, as well as the frictional and random forces. However, there is a distinct difference between the two expressions that touches on the essential physics of the structural fluctuation, that is, the force constant, or Hessian, in the restoring force. In the CLE, this is given by the second derivative of the potential energy among atoms in a protein. So, the quadratic nature or the harmonicity is only valid at the minimum of the potential surface. On the contrary, the linearity of the restoring force in the GLE originates from the projection of the water’s degrees of freedom onto the protein’s degrees of freedom. Taking this into consideration, Kim and Hirata proposed an ansatz for the Hessian matrix. The ansatz is used to equate the Hessian matrix with the second derivative of the free-energy surface or the potential of the mean force of a protein in water, defined by the sum of the potential energy among atoms in a protein and the solvation free energy. Since the free energy can be calculated from the molecular mechanics and the RISM/3D-RISM theory, one can perform an analysis similar to the normal mode analysis (NMA) just by diagonalizing the Hessian matrix of the free energy. This method is referred to as the Generalized Langevin Mode Analysis (GLMA). This theory may be realized to explore a variety of biophysical processes, including protein folding, spectroscopy, and chemical reactions. The present article is devoted to reviewing the development of this theory, and to providing perspective in exploring life phenomena. Full article

The coupling with external mechanical systems such as oscillating masses working as tuned mass dampers, dynamic mass absorbers, elasto-plastic dampers, and rigid walls is an effective method to reduce the displacements and drifts of structures under external loads. An alternative method is provided by the coupling of the structure with an independent, auxiliary elasto-plastic system. This paper investigates the dynamic and seismic behaviour of a structure rigidly coupled with an auxiliary yielding mechanical system under harmonic and seismic ground excitation. A two-degree-of-freedom model is used to describe the dynamic and seismic behaviour of the main structure rigidly coupled to the yielding system, which is described by a one-degree-of-freedom model. The auxiliary system has an elasto-plastic constitutive behaviour that is modelled by a Bouc-Wen model. The equations of motion of the coupled system are obtained by a direct approach. The coupling with the yielding system is considered beneficial if the displacements of the coupled system reduce with respect to those of the stand-alone frame structure. An extensive parametric analysis is performed to point out the role of the mechanical parameters that describe the elasto-plastic constitutive behaviour of the auxiliary system. Results reveal that in large ranges of the parameters’ values, the coupling with the elasto-plastic system improves the performance of the frame structure. Full article

For the displaced harmonic double-well oscillator, the existence of exact polynomial bound states at certain displacements $d$ is revealed. The N-plets of these quasi-exactly solvable (QES) states are constructed in closed form. For non-QES states, the Schrödinger equation can still be considered “non-polynomially exactly solvable” (NES) because the exact left and right parts of the wave function (proportional to confluent hypergeometric function) just have to be matched in the origin. Full article

In recent years, the Tuned Mass Damper with inerter (TMDI) has received significant attention. The inerter is defined to exert a force that is in proportion to the relative acceleration of the two inerter terminals. Here, two TMDI topologies are investigated. The conventional topology is given by the inerter being in parallel to the spring and viscous damper of the TMDI. The other topology is the serial arrangement of spring, inerter and viscous damper being in parallel to the stiffness of the mass spring oscillator of the TMDI. While the first topology intends to increase the inertial force of the TMDI, the second topology aims at producing an additional degree of freedom. The considered TMDI concepts are simulated for harmonic and random excitations, with parameters set according to those described in the literature and with numerically optimized parameters which minimize the primary structure displacement response. The classical TMD is used as a benchmark. The findings are twofold. The conventional TMDI with typical inertance ratio of 1% and the very small value of 0.02% performs significantly worse than the classical TMD with the same mass ratio. In contrast, the TMDI with an additional degree of freedom can improve the mitigation of the primary structure if the inertance ratio is set very small and if the TMDI parameters are numerically optimized. Full article

When a vehicle passes over a bridge, it may jump on the bridge due to a damaged expansion joint. The sudden jump induces a heavy dynamic impact on the bridge and therefore damages the bridge deck and girder. The traditional dynamic amplification factor defined by the current bridge design code shows the amplification of the static effects on the bridge. However, it only concerns the stable moving load induced by the vehicle. The sudden vehicle impact due to a damaged expansion joint sometimes exceeds the allowable design load, so it is important to evaluate the dynamic impact in practice. In fact, the dynamic impact can be approximately considered as a contact force between a damped harmonic oscillator and a beam due to the bilateral symmetry of the vehicle; therefore, a model-based approach using the bridge midspan acceleration is proposed in this study to approximately evaluate the impact force, where it is assumed as an exponentially damped sine function. This is a typical parametric model-based inverse problem. The conjugate direction method is used to determine the unknown parameters and the initial values are determined by a simple global search method. Since only five parameters are included, the proposed method is simpler than the conventional basis function-based methods. Numerical simulations were conducted to validate the proposed method. Generally, the proposed method performs well to identify the dynamic impact. In particular, the displacement measured directly from the bridge is preferred since the displacement obtained from the acceleration has numerical errors; the measurement noise in the range of 1% to 5% shows a slight influence on the proposed method; and the error of frequencies and mode shapes greatly affects the proposed method, especially for the maximum force. Full article