Fundamental Torsional Mode Research Articles

A novel multi-modal analytical method focusing on dynamic mechanism of bridge flutter

A novel three-dimensional (3D) multi-modal analytical method is proposed in the present study for investigating the dynamic mechanism of long-span bridge flutter. The multi-modal coupled flutter differential equations are derived in a practical manner utilizing the principle of virtual work in this method, and the explicit expressions of system damping and stiffness are established through the excitation-feedback mechanism. Consequently, this method can not only conveniently identify the critical point of 3D bridge flutter, but also provide a comprehensive understanding of the underlying mechanism involved in 3D bridge flutter. The well-known coupled aerodynamic damping related to flutter derivatives A1∗ and H3∗, which is principally responsible for the coupled flutter, is further subdivided in this study to reveal the intrinsic coupled mechanism of flutter participating modes: The aerodynamic coupled degree between a certain vertical bending mode and the fundamental torsional mode can be ascertained by evaluating the similarity factor between their mode shapes; the phase angle between a certain vertical bending mode and the fundamental torsional mode, which is largely dominated by the numerical relationship between natural and flutter frequency, determines whether the aerodynamic coupled effect associated with the two modes drives or restrains flutter.

Optomechanical feedback cooling of a 5 mm long torsional mode

We report three orders of magnitude optical cooling of the fundamental torsional mode of a 5 mm long, 550 nm diameter optical nanofiber. The rotation of the nanofiber couples to the polarization of guided laser fields. We use a weak laser probe to monitor the rotation and use feedback to modulate the polarization of an auxiliary drive laser providing torque. Our results present a tool for the optomechanical control of large-scale torsional resonators, with metrological applications and potential implications for studying macroscopic objects in quantum states.

Circumferential Damage Monitoring of Steel Pipe Using a Radar Map Based on Torsional Guided Waves

Ultrasonic guided wave technology has been successfully applied to detect multiple types of defects in pipes. However, the circumferential location and coverage of a defect are less studied because it is difficult to determine. In this study, the fundamental torsional mode T (0, 1) is selected to conduct monitoring of the circumferential defect in pipelines because of its almost non-dispersive property. A radar map of the peak wave signals at 30 circumferential positions is proposed to detect the damage. The circumferential defect of a steel pipe is thoroughly investigated using numerical simulation. First, the circumferential positioning of defects in various areas of the pipe is studied. Second, the results are compared to those based on longitudinal guide waves. Finally, the circumferential coverage of a defect in the pipeline is determined. The waves are excited and received using the pitch–catch approach, and the collected monitoring signals are processed using the Hilbert transformation. According to the findings, the circumferential defect in the pipe can be effectively identified from a ‘T’ shape in the radar image, and the monitoring method by the torsional guided wave is superior to the longitudinal wave method. The results clearly demonstrate the advantages of torsional guided waves in defect monitoring. The proposed method is expected to provide a promising solution to circumferential damage identification in pipelines.

Feedback cooling the fundamental torsional mechanical mode of a tapered optical fiber to 30 mK

Feedback cooling the fundamental torsional mechanical mode of a tapered optical fiber to 30 mK

Three-dimensional nonlinear flutter analysis of long-span bridges by multimode and full-mode approaches

Based on amplitude-dependent flutter derivatives (FDs), the present study established three-dimensional (3D) nonlinear flutter analysis methods, including a multimode and a full-mode approach, for long-span bridges. Then, by adopting the proposed methods, the influences of 3D effects, self-excited drag force, and multimode aerodynamic coupling effects on nonlinear flutter response were investigated. Besides, critical structural modes that have a great impact on nonlinear flutter were identified, their contributions were quantified and roles were clarified. The results show that the 3D effects of structural modes can reduce the system stability mainly by increasing the negative uncoupled aerodynamic damping. Thus, if the 3D effects are ignored, the stable amplitude of nonlinear flutter will be underestimated. For long-span bridges whose foundational symmetric torsional mode couples a minor lateral-bending mode shape, the added aerodynamic damping from self-excited drag force, especially the term of FD P1∗∗1, can improve the stability of the system. Thus, it will overestimate the nonlinear flutter response if the self-excited drag force is ignored. Meanwhile, the aerodynamic coupling effect among different structural modes should be considered, otherwise the nonlinear flutter responses of long-span bridges may be misestimated significantly. For the nonlinear flutter dominated by the fundamental symmetric torsional modal branch, the symmetric vertical bending modes with a frequency lower than the fundamental symmetric torsional mode should be considered. Besides, the other higher-order structural mode coupled with relatively significant fundamental symmetric torsional mode shape is also worth being taken into account. The selection of structural modes is an important and experience-based work in the multimode method. Thus, the full-mode method, which can consider the potential higher-order structural modes that may have contributions to the 3D nonlinear flutter, is also needed, especially when the amplitude is large enough. Otherwise, the nonlinear flutter response may be underestimated by the multimode method.

Observing dominant dual-mode second-harmonic (DMSH) generation in an isotropic nonlinear elastic cylindrical waveguide

Nonlinear ultrasonic techniques have gained much interest owing to their microstructural characterisation capabilities, which can help in early-state defect detection and provide timely maintenance activity calls. Microstructural features such as micro-cracks, precipitates or dislocations can be accessed while studying higher harmonics data via amplitude analysis. A proper understanding of second harmonic modes shall provide clarity and insights into the defect type. This paper studies and analyses the second harmonic wave modes generated while exciting fundamental torsional mode(T(0,1)) in a cylindrical wire waveguide structure. The work presents the presence of a simultaneously propagating dominant dual-mode second-harmonic (DMSH), fundamental longitudinal (l(0,1)) mode and an orthogonal-torsional (t(0,1)┴) mode generated on a cylindrical steel wire waveguide of 1 mm diameter while excited with a T(0,1) mode in a large domain. The presence of two dominant modes at second harmonic frequency is the reason for terming this phenomenon DMSH. The DMSH was observed and analysed using numerical simulations and validated experimentally. This work attempts to extend the study of DMSH generation on thin plates with SH0 mode with the analogy of cylindrical structures for rod waves with T(0,1) mode. However, in the present study of cylindrical waveguides, at primary frequency also, dual flexural modes (F(1,1)-F(1,2)) with approximately similar group velocities to DMSH were observed. These wave modes were identified with Fourier transform methods (STFT and 2D-FFT) and interpreted using dispersion curves. The dual-mode wave packets will separate in the time domain if the travel length exceeds the minimum separation distance of approximately 60 λ, depending on the variation in their respective group velocities. This approach can provide important implications for highly sensitive long-range early-state defect detection and structural health monitoring in cylindrical structures with improved insights into the generated wave modes.

Magnetized neutron star crust within effective relativistic mean-field model

Even though the crystallize nature of the neutron star crust plays a pivotal role in describing various fascinating astrophysical observations, its microscopic structure is not fully understood in the presence of a colossal magnetic field. In the present work, we study the crustal properties of a neutron star within an effective relativistic mean field framework in the presence of magnetic field strength $\sim 10^{17}$G. We calculate the equilibrium composition of the outer crust by minimizing the Gibbs free energy using the most recent atomic mass evaluations. The magnetic field significantly affects the equation of state (EoS) and the properties of the outer crust, such as neutron drip density, pressure, and melting temperature. For the inner crust, we use the compressible liquid drop model for the first time to study the crustal properties in a magnetic environment. The inner crust properties, such as mass and charge number distribution, isospin asymmetry, cluster density, etc., show typical quantum oscillations (De Haas-van Alphen effect) sensitive to the magnetic field's strength. The density-dependent symmetry energy influences the magnetic inner crust like the field-free case. We study the probable modifications in the pasta structures and it is observed that their mass and thickness changes by $\sim 10-15 \%$ depending upon the magnetic field strength. The fundamental torsional oscillation mode frequency is investigated for the magnetized crust in the context of quasiperiodic oscillations (QPO) in soft gamma repeaters. The magnetic field strengths considered in this work influences only the EoS of outer and shallow regions of the inner crust, which results in no significant change in global neutron star properties. However, the outer crust mass and its moment of inertia increase considerably with increase in magnetic field strength.

Influence of periodic structure with a different shape element on the torsional wave

Periodic structure is wildly used in metamaterial design in different fields. It has great potential in NDE and SHM fields due to different features, like focusing, bandgap, direction manipulation, and mode selection. First fundamental torsional mode T(0,1) can be focused by adding periodic structure based on phononic crystals and gradient index refraction. In the present study influence of the periodic structure with different element shape on torsional wave is discussed. Eigenfrequency analysis was performed for different configurations of the periodic structure by using the finite element method and floquet boundary condition. Dispersion curves for the torsional wave were obtained as an analysis result. Propagating wave creates a local resonance which leads to the bandgaps between modes and the first torsional mode T(0,1) becomes dispersive. The influence of the configuration on the dispersion curves is shown. Additionally mentioned that negative group velocity can be achieved.

The strain gradient-based torsional vibration analysis of micro-rotors with nonlinear flexural-torsional coupling

The powerful non-classical continuum theory of strain gradient elasticity is capable of effectively capturing small-scale effects in micro-structures. Based on this theory, a formulation is developed to investigate the coupled torsional-flexural vibrations of micro-rotors in the presence of inertia nonlinearities arising from the eccentricity and gyroscopic motion of the rotors. With the aid of a weighted-residual technique, coupled nonlinear partial differential equations of motion are truncated into a discrete model. Then, the resonance of the fundamental mode of the torsional vibration excited by the flexural vibration is investigated by utilizing the perturbation method of multiple scales. Moreover, a numerical simulation approach is conducted to confirm the validity of the analytical solution proposed by the multiple scales perturbation method. Obtained results for the resonant frequency and amplitude of the fundamental torsional mode indicate that the strain gradient theory can predict far more reliable results than the classical continuum mechanics for micro-rotors with very thin shafts.

Data-Driven Damage Classification Using Guided Waves in Pipe Structures

Damage types are important for structural condition assessment, however, for conventionally guided wave-based inspections, the characteristics extracted from the guided wave packets are usually used to detect, locate and quantify the damages, but not classify them. In this work, the data-driven method is proposed to classify the common damages in the pipe utilizing the guided wave signals obtained from numerous damage detection tests. The fundamental torsional mode T(0,1) is selected to conduct the guided wave-based damage detection to reduce the complexity of signal processing for its almost non-dispersive property. A total of 520 groups of experimental data under different degrees of damage were obtained to verify the proposed method. Finally, with help of a deep neural network (DNN) algorithm, all response data from the damages in the pipes were all clearly classified with quite high probability.

Pasta properties of the neutron star within effective relativistic mean-field model

We study the properties of pasta structures and their influence on the neutron star observables employing the effective relativistic mean-field (E-RMF) model. The compressible liquid drop model is used to incorporate the finite size effects, considering the possibility of nonspherical structures in the inner crust. The unified equation of states are constructed for several E-RMF parameters to study various properties such as pasta mass and thickness in the neutron star's crust. The majority of the pasta properties are sensitive to the symmetry energy in the subsaturation density region. Using the results from Monte Carlo simulations, we estimate the shear modulus of the crust in the context of quasiperiodic oscillations from soft gamma-ray repeaters and calculate the frequency of fundamental torsional oscillation mode in the inner crust. Global properties of the neutron star such as mass-radius profile, the moment of inertia, crustal mass, crustal thickness, and fractional crustal moment of inertia are worked out. The results are consistent with various observational and theoretical constraints.

Controlling the thickness dependence of torsional wave mode in pipe-like structures with the gradient-index phononic crystal lens

The fundamental torsional wave mode, T(0,1), is typically preferred in monitoring defects in long-range pipe-like structures due to non-dispersive and low attenuation characteristics such that the wave packet is not distorted with distance. However, the sensitivity of T(0,1) wave mode depends on the defect type and orientation. While it is highly sensitive to cracks along the axis of pipes, the sensitivity to detect thickness change is low as T(0,1) wave mode generates tangential displacement motion around the pipe circumference. In this study, a gradient-index phononic crystal (GRIN-PC) lens is integrated into a steel pipe to manipulate its dispersion characteristics such that the phase velocity of T(0,1) wave mode is affected by the overall change in pipe thickness. The modified behavior of T(0,1) wave mode within the GRIN-PC lens region increases the damage detection capability of T(0,1) wave mode. Numerical models involving a parametric unit cell study indicate that the phase velocity of T(0,1) wave mode decreases as the thickness of the pipe with the GRIN-PC lens decreases, in contrast with the conventional pipe. The signal difference coefficient (SDC) is applied to the acquired signal from the focal point of GRIN-PC lens to quantify the uniform thickness change. Full-scale wave propagation simulations involving solid mechanics coupled with the piezoelectric actuation demonstrate that the SDC increases as the thickness decreases. The numerical results are validated with experiments using three steel pipes with different wall thicknesses.

Reduction of the squeal noise from an automotive water pump

This paper presents a method to reduce the squeal noise generated by an automotive water pump. The noise and vibration of the water pump were analyzed through experiments, from which it was found that the squeal noise was caused by the torsional vibration of the shaft in the pump rotor system. Therefore, the water pump rotor system was modeled as an equivalent single-degree-of-freedom model for torsional vibration and the stability coefficient was established to assess the possibility of generating the squeal noise. Based on a parametric study, a design strategy was suggested to reduce the possibility of squeal noise. A sensitivity analysis showed how changes in various design parameters of the water pump affected the stability coefficient. We found that the closer the position of the mechanical seal is to the nodal point of the fundamental torsional mode of the water pump shaft, the less squeal noise is generated. It was also found that decreasing the mass moment of inertia of the pulley and increasing that of the impeller to place the seal position close to the nodal point help to suppress the squeal noise. In addition, an optimal design procedure for the water pump was presented to reduce squeal noise generation, and the water pump designed and manufactured according to this design procedure was experimentally verified to confirm that no noise was generated.

Torsional wave focusing in cylindrical structures with the conformal gradient-index phononic crystal lens

We present torsional wave focusing in cylindrical structures integrated with conformal gradient-index phononic crystal (GRIN-PC) lenses. The mechanical lens modifies the refractive characteristics of propagating waves along the axial direction such that the torsional wave energy focuses at a desired point with an increased amplitude. In this paper, our main goal is to exploit the GRIN-PC concept for amplification of the fundamental torsional wave mode, namely, T(0,1), which is especially favorable in the guided wave ultrasonic testing of pipelines and can extend important structural information over long-range pipelines. To this end, we first study d35 piezoelectric transducer arrays through multiphysics simulations coupling piezoelectric and solid mechanics models and determine the optimal number of transducers to achieve the excitation of torsional plane wave. Two-dimensional Fourier transform as well as the tangential displacement histories around the pipe circumference at various axial positions verify the pure T(0,1) excitation, which is validated with experiments. Next, we design, fabricate, and numerically and experimentally study the conformal GRIN-PC for T(0,1) mode focusing in a range of ultrasonic frequencies, from 30 to 50 kHz. Measurements show that the amplitude of the torsional wave mode is amplified by 39% at the focal point with the presence of the GRIN-PC lens.

Simultaneous three-axis torque measurements of micromagnetism

Measurements of magnetic torque are most commonly preformed about a single axis or component of torque. Such measurements are very useful for hysteresis measurements of thin film structures in particular, where high shape anisotropy yields a near-proportionality of in-plane magnetic moment and the magnetic torque along the perpendicular in-plane axis. A technique to measure the full magnetic torque vector (three orthogonal torque components) on micro- and nano-scale magnetic materials is introduced. The method is demonstrated using a modified, single-paddle silicon-on-insulator resonant torque sensor. The mechanical compliances to all three orthogonal torque components are maximized by clamping the sensor at a single point. Mechanically-resonant AC torques are driven by an RF field containing a frequency component for each fundamental torsional mode of the device, and the resulting displacements read out through optical position-sensitive detection. Measurements are compared against micromagnetic simulations of mechanical torque to augment the interpretation of the signals. As an application example, simultaneous observations of hysteresis in the net magnetization along with the field-dependent in-plane anisotropy is highly beneficial for studies of exchange bias.

Giant Enhancement in the Thermal Responsivity of Microelectromechanical Resonators by Internal Mode Coupling

We report on a giant enhancement in the thermal responsivity of the doubly-clamped GaAs microelectromechanical (MEMS) beam resonators by using the internal mode coupling effect. This is achieved by coupling the fundamental bending mode with the fundamental torsional mode of the MEMS beam resonators through the cubic Duffing nonlinearity. In the mode coupling regime, we have found that, when the input heat to the MEMS resonators is modulated at a particular frequency, the resonance frequency shift caused by heating can be enhanced by almost two orders of magnitude. The observed effect is promising for realizing high-sensitivity thermal sensing by using MEMS resonators, such as ultrasensitive terahertz detection at room temperature.

Stress Sensitivity of the T(0,1) Mode Velocity for Cylindrical Waveguides

In this paper, the stress influence in the guided wave velocity of the fundamentaltorsional mode is presented. Two analytical models, based on the Acoustoelasticity effect, tocompute the fundamental torsional mode velocity propagating in a specimen subject to anaxial stress are studied. These models are obtained due to the relation between the T(0, 1)guided wave velocity and the bulk shear velocity. The analytical models to calculate the guidedwave velocity are functions of the stress, second and third order elastic constants. A series ofaxial stress levels applied to a cylindrical waveguide is investigated with numerical simulations(Finite Elements) to estimate variations of the T(0, 1) guided wave velocity. This analysisprovides a criterion to evaluate the practical implementation of a stress monitoring schemebased on velocity variations of the fundamental torsional mode.

Support Stiffness Monitoring of Cylindrical Structures Using Magnetostrictive Transducers and the Torsional Mode T(0,1).

In this paper, a support stiffness monitoring scheme based on torsional guided waves for detecting loss of rigidity in a support of cylindrical structures is presented. Poor support performance in cylindrical specimens such as a pipeline setup located in a sloping terrain may produce a risky operation condition in terms of the installation integrity and the possibility of human casualties. The effects of changing the contact forces between support and the waveguide have been investigated by considering variations in the load between them. Fundamental torsional mode is produced and launched by a magnetostrictive collar in a pitch-catch configuration to study the support effect in the wavepacket propagation. Several scenarios are studied by emulating an abnormal condition in the support of a dedicated test bench. Numerical results revealed ultrasonic energy leakage in the form of bulk waves when a mechanical coupling between the cylindrical waveguide and support is yielded. Experimental results showed that the rate of ultrasonic energy leakage depends on the magnitude of the reaction forces between pipe and support; so different levels of attenuation of mode will be produced with different mechanical contact conditions. Thus, it is possible to relate a measured attenuation to variations in the supports condition. Results of each scenarios are presented and discussed demonstrating the feasibility and potential of tracking of the amplitude of the as an indicator of abnormal conditions in simple supports.

Compensation of nonlinear hardening effect in a nanoelectromechanical torsional resonator

A mechanical resonator based on torsional resonance has been fabricated in our facilities to sense infrared radiation. Actuation and detection are both electrostatic. Reaching phonon noise is highly desirable in order to get low noise uncooled infrared detectors. Therefore a high dynamic range has to be reached to increase as much as possible the overall signal to noise ratio and minimize the contribution of amplitudes noises (thermomechanical or electrical) to frequency noise. The dimensions of resonator body are similar to most clamped-clamped NEMS and our devices are thus also greatly affected by nonlinearities. We present here a nonlinear model for mechanical behavior around fundamental mode resonance taking account of both mechanical and electrostatic nonlinearities. The model correctly reproduces the nonlinear behavior observed for different resonator designs. We experimentally observe on some devices a compensation of hardening effects, allowing a linear operation of torsion angle up to 13°. The model provided in this work allows an engineering strategy in order to design high linear dynamic range for fundamental torsional mode.

On the scattering of torsional waves from axisymmetric defects in buried pipelines.

This article develops a numerical model suitable for analysing elastic wave scattering in buried pipelines. The model is based on a previous so-called hybrid approach, where a nominally infinite length of pipe is split up into uniform and non-uniform regions. The key challenge for buried structures is in enforcing the appropriate boundary conditions in both the axial and radial directions, which must encompass the entire length of the structure, as well as the surrounding material. Accordingly, the focus of this article is on developing a model suitable for accurately applying these boundary conditions, and so the analysis is restricted here to the study of axisymmetric defects and to an incident sound field that consists of the fundamental torsional mode only. It is shown that this problem may be addressed in a numerically efficient way provided one carefully choses a perfectly matched layer for the surrounding material, and then integrates over this layer using a complex co-ordinate stretching function. This enables the use of mode matching to deliver a convergent system of equations that enforce the appropriate axial and radial boundary conditions.