Free Transverse Research Articles

Effect of axial rotation on free transverse vibration analysis of two-phase nanobeams

Effect of axial rotation on free transverse vibration analysis of two-phase nanobeams

Damping properties of some tropical wood species determined by free transverse vibration method

ABSTRACT This article describes a non-destructive method for determining the damping properties of wood. It was based on the analysis of the attenuation of the free transverse vibrations of a fixed support-free specimen following excitation. Cameroonian forests abound important species that were much in demand for structural applications and were often subjected to dynamic loads. However, in the literature and in the available databases, very little information was available on the vibration properties of these wood species. To solve this problem, three specimens of twenty-four wood species with a cross-section of 10 × 20 mm, with a length of 1600 mm were prepared and subjected to a free vibration test in the fixed support-free configuration. The accelerations as a function of time were obtained. By transforming the recorded accelerations into displacements, it was allowed to determine the logarithmic decrement by mean the first twenty-one amplitudinal peaks. Thanks to the interrelationships, the viscous damping ratio, loss factor, quality factor and specific damping ratio were deduced. The results obtained were relatively variable between species. Compared with the data available in the literature for the same species, there was a considerable difference.

The role of reconstructive plastic surgery in the treatment of victims of the 2023 Kahramanmaraş earthquake

Objective: As a result of the 2023 Kahramanmaraş earthquake, medical institutions experienced a large influx of patients requiring acute multidisciplinary surgical and medical care. This study aimed to evaluate the patient demographics and treatment management of survivors admitted to our reconstructive plastic surgery department. Materials and Methods: We retrospectively analyzed the age, sex, time under the wreckage, time of admission, types and locations of injuries, treatment modalities, receipt of hyperbaric oxygen therapy, and receipt of vacuum-assisted closure therapy of the earthquake victims referred to our department. Results: The definitive management of all 42 earthquake survivors admitted to our department was reviewed. This included five free flaps, four regional flaps, 18 split-thickness skin grafts, and one maxillofacial fracture repair. Eight patients were treated conservatively including two with non-displaced maxillofacial fractures. Of the 26 patients treated for lower extremity injuries, four were already amputees. Among the remaining 22 patients with such injuries, one underwent Charcot amputation plus free flap reconstruction to preserve extremity length and one underwent below-the-knee amputation. Of the 16 upper extremity injuries, two patients referred with extensive forearm necrosis underwent forearm amputation. To preserve extremity length and ensure the limbs were suitable for biomechanical orthoses, free transverse upper gracilis musculocutaneous flaps and free chimeric Anterolateral- Vastus Lateralis musculocutaneous flaps were performed. Conclusion: This study illustrates the value of multi-modal reconstructive plastic surgery in the treatment of disaster survivors, particularly in the management of multi-trauma.

Modeling frequency shifts in small-scale beams with multiple eccentric masses

Studying the dynamics of small-scale beams with attached particles is crucial for sensing applications in various fields, such as bioscience, material science, energy storage devices, and environmental monitoring. Here, a stress-driven nonlocal model is presented for the free transverse vibration of small-scale beams carrying multiple masses taking into account the eccentricity of the masses relative to the beam axis. The results show excellent agreement with the experimental and numerical data in the literature. New insights into the frequency shifts and mode shapes of the first four vibrational modes of stress-driven nonlocal beams with up to three attached particles are presented. The study investigates the inverse problem of detecting the location and mass of an attached particle based on natural frequency shifts. The knowledge acquired from the present study provides valuable guidance for the design and analysis of ultrasensitive mechanical mass sensors.

Plasmon near-field coupling and universal scaling behavior in shifted-core coaxial nano-cavity pair

We computationally and analytically investigate the plasmon near-field coupling phenomenon and the associated universal scaling behavior in a pair of coupled shifted-core coaxial nano-cavities. Each nano-cavity is composed of an InGaAsP gain medium sandwiched between a silver (Ag) core and an Ag shell. The evanescent coupling between the cavities lifts the degeneracy of the cut-off free transverse electromagnetic (TEM) like mode. The mode splitting of the supermodes is intensified by shifting the metal core position, which induces symmetry breaking. This coupling phenomenon is explained with spring-capacitor analogy and circuit analysis. The numerical simulation results reveal an exponential decay in the fractional plasmon wavelength relative to the ratio of gap distance and core shifting distance, which aligns with the plasmon ruler equation. In addition, by shifting the Ag cores in both cavities toward the center of the coupled structure, the electromagnetic field becomes strongly localized in nanoscale regions (hotspots) in the gain medium between the cavities, thus achieving extreme plasmonic nanofocusing. Utilizing this nanofocusing effect, we propose a refractive index sensor by placing a fluidic channel between the two cavities in close vicinity to the hotspots and reaching the highest sensitivity of ∼700nm/RIU.

Analytical solution for the free transverse vibration of an elastically connected annular plate system with discontinuities

Due to the performance requirements, structural discontinuities are inevitable in engineering structures. Free vibration of an elastically connected annular plate system with discontinuities has not yet been reported in the literature. In this study, an analytical method is developed for the free vibration of an annular plate system with discontinuities along its radius. The annular plates are connected continuously using an elastic layer. The coupled vibration equations of the annular plate system were decoupled into a series of uncoupled general “vibration” equations which are then transferred into a symplectic dual system. The general “vibration” state can then be analytically described in terms of waves utilizing the elastic wave theory. Using the analytical wave modes and satisfying the compatibility and boundary conditions at the discontinuities, a frequency equation can be obtained analytically. In numerical examples, the free vibrations of systems consist of two and three annular plates were investigated. The accuracy of the proposed method is verified by comparison with literature and finite element method (FEM).

Model of influence of a rope defect on the spectrum of its free transverse vibrations

In earlier work the possibility of diagnosing a defect of a steel wire rope by spectral composition of its free transverse vibrations was substantiated. In the present work, an analytical model of transverse vibrations of a steel wire rope with local damage is proposed. The presence of the defect in the model is taken into account only in the form of a loss of bending stiffness of the corresponding section without changing the specific mass along the length. The model represents three homogeneous rope sections “stitched” together, where the middle one represents a defective section with a lower value of bending stiffness. According to the model calculations, it is shown that the character of the dependence of the natural frequencies of oscillations on their number practically does not change in the presence of a defect. However, its presence and location affects the ratio of vibration amplitudes of undamaged sections, which can be used to monitor the condition of the rope.

Higher-order trigonometric series-based analytical solution to free transverse vibration of suspended laminated composite slabs

Suspended floors can be designed as effective pendulum seismic isolators for high-rise buildings. However, research studies on the free vibration of suspended laminated composite slabs are relatively limited. This paper presents a comprehensive analytical solution to the free vibration problem of suspended laminated composite slabs. The equations of elasticity are used to establish the equation of motion. The critical factors influencing free vibration are explicitly considered, including the material anisotropy, number of layers, elastic properties, rotatory inertia, and transverse shear of plates. The higher-order trigonometric series are utilized to solve the dynamic equations. The developed analytical solution is a complete and realistic form of the existing analytical solutions in literature and has the capability of converging fast. The proposed analytical solution does not have a dependency on the shape function as well as separate-of-variable forms unlike the Finite Element Method (FEM). Moreover, the FEM requires an in-depth mesh convergence analysis, particularly for higher-magnitude natural frequencies, which is not the case for the proposed analytical solution for any infinite range of eigenfrequencies. The proposed solution procedure is first verified by the simplified problems available in the literature. For more complex problems, the finite element analysis results obtained from Abaqus are employed to validate the analytical solution. The comparison demonstrates that the proposed analytical solution is accurate and reliable for a wide range of case-study examples. It is found that the natural frequencies of suspended laminated composite slabs are significantly influenced by the crucial factors under investigation.

An exact closed-form explicit solution of free transverse vibration for non-uniform multi-cracked beam

Non-uniformity and damage are the two primary subjects in studying the vibrations of the beam-type elements. An exact closed-form explicit solution for the transverse displacement of a non-uniform multi-cracked beam with any type of boundary conditions is introduced. The generalized functions and the distributional derivative concepts are adopted. Four fundamental functions are introduced. These functions make the boundary conditions' process and compute the frequency equation more convenient. By introducing the non-dimensional parameters, the non-dimensional motion equation of the damaged beam with an arbitrary count of cracks is derived, and its exact closed-form explicit solution is obtained based on the four introduced fundamental functions. The standard method of computing these functions is presented, and the closed-form of these functions is determined for eight cases like uniform and conical beams. The closed-form of the frequency equation and mode shapes of the non-uniform multi-cracked beam are derived for several boundary conditions. The influence of the count of cracks, their location and intensity, and the boundary conditions on the natural frequency and mode shape are assessed by running a numerical study. The first and second frequencies of a conical beam are computed to verify the obtained results by applying this newly presented closed-form solution and the Differential Quadrature Element Method. A good agreement is evident when the obtained results are compared.

Size effect in ultrasensitive micro- and nanomechanical mass sensors

The size dependent free transverse vibration of the micro- and nanocantilever mass sensors is studied. The general case of a sensor with an arbitrary number of attached particles is considered. The domain is divided into different segments at the cross-sections where the particles are located, and the displacement fields are described based on the Bernoulli-Euler beam theory. The size effect is introduced into the formulation by assuming the constitutive equation of the stress-driven nonlocal theory of elasticity. The eigenvalue problem is generated by solving the equation of motion in each segment of the sensor and imposing the variationally consistent and higher-order constitutive boundary and continuity conditions. The natural frequencies and their sensitivity to the attachment of a small mass are analyzed analytically. It is shown that the frequency shifts resulting from attachment of a small mass can be explicitly defined as a function of the frequency and mode shape of the unloaded sensor. The model is used to numerically study the natural frequencies of sensors loaded by one to three particles. Comprehensive results are presented on the effect of the size dependency on the frequency shifts of the first four modes of vibration. It is revealed that neglecting the size effect may result in wrong detections of the masses of the attached particles.

Molecular dynamics simulation of free transverse vibration behavior of single-walled coiled carbon nanotubes

Coiled carbon nanotubes (CCNTs) belong to one of the prominent classes of carbon nanostructures with unique mechanical properties and vibrational behavior due to their helical geometries. In this paper, the free transverse vibration behavior of single-walled CCNTs is investigated by molecular dynamics (MD) simulations and the adaptive intermolecular reactive empirical bond-order (AIREBO) potential under different boundary conditions (B.Cs.). The beating phenomenon is observed in CCNTs due to the presence of longitudinal, transverse, and torsional coupled vibrations and the proximity of their corresponding frequency. Generally, the frequency of the CCNTs decreases by increasing the length () or the number of pitches ( Moreover, the pitch angle plays a more decisive role compared to other geometric parameters. At constant length () of CCNTs, the frequency increases by enhancing the pitch angle Furthermore, the fundamental frequency range of the studied CCNTs is obtained less than 331.9 GHz for lengths greater than 2 nm under different boundary conditions. This indicates that CCNTs have a higher vibration sensitivity than straight CNTs. Therefore, CCNTs can be a proper alternative to straight CNTs in sensors. The results of this study can be used in the design and analysis of nanoelectromechanical systems (NEMs) with CCNTs elements as well as to calibrate continuum mechanics methods.

Semi-Analytical Solution of Transverse Vibration of Cylinders with Non-Circular Cross-Section Partially Submerged in Water

The free transverse vibration of a surface-piercing, vertical cylinder partially submerged in water was studied. The cylinder had an arbitrary non-circular, but symmetric, cross-section in the vibration direction. The water was assumed to be an incompressible and inviscid fluid. The effect of the surface waves of water was neglected in the analysis. The exact solution of velocity potential of water was derived by the method of separation of variables. The unknown coefficients in the solution of the velocity potential were expressed in the form of integral equations, including the dynamic deformation of the beam. Then, the governing differential equation of bending vibration of the cylinder under the hydrodynamic pressure was obtained. The Galerkin method was used to obtain the eigenvalue equation by expanding the wet modes of the cylinder into a series of dry modes. The elliptical cylinders partially submerged in water were taken as the numerical example. The accuracy of the proposed method was evaluated by the convergence studies. As a consequent result, the non-dimensional added virtual mass incremental (NAVMI) factor solutions were compared to the present Galerkin solutions, which can be used as a benchmark test for more sophisticated numerical simulations of computational fluid dynamics.

Vibration of prestressed beams: Experimental and finite-element analysis of post–tensioned thin-walled box-girders

In published works, very different explanations are given for the effect of prestressing on the beam dynamics, especially on the relationship between the vibrational effects caused by an external compressive force and those due to a prestressing force. To solve this conflict, free transverse vibrations of a post–tensioned thin-walled steel box-girder were investigated. Its fundamental frequencies were then measured for different values of prestressing. Subsequently, the experimental data were compared with a formula considering shear effects. The experimental data were also compared with two high-fidelity finite-element models assuming geometric nonlinearities. According to the obtained findings, and comparisons with tests reported in literature, the beam dynamics strongly depends on the contact of the cables with the surrounding section. If the tendons are not in contact with the surrounding cross-section, the beam dynamics due to an external compressive force is practically coincident to that caused by a prestressing force for low values of prestressing. In this case, the dynamics of prestressed beams are initially ruled by the compression-softening effect. For high values of prestressing, the beam would behave as a shallow arc with horizontal elastic supports. In this case, an increase of fundamental frequency is observed, but the yield stress would be exceeded. Conversely, in thin-walled steel girder-bridges with tendons in contact with the cross-section or draped with a deviator, the fundamental frequency is practically unaffected by prestressing. Thus, the fundamental frequency cannot be used as indicator for identifying long-term phenomena of prestressing losses, such as anchorage slips, tendon friction and relaxation.

Dynamics of axially moving beams: A finite difference approach

In this paper, a finite difference approach is being presented as the most reliable technique to investigate the non-linear transverse vibration of an axially moving beam. Firstly, Hamilton’s principle is used to derive the governing hyperbolic partial differential equation (HPDE) of free transverse vibration. Then finite difference along with state space method is used to convert the partial differential equation into a system of coupled first-order ordinary differential equations (ODE’s). Comparison of the proposed finite difference model is made with both the numerical and analytical models. It is noted that the finite difference model is in excellent agreement with the modal analysis approach (analytical solutions) as compared to the generalized integral transform technique GITT (numerical method). A parametric study was also presented to examine the impact of system parameters, such as axial translation speed and flexure rigidities of the beam on the transverse response amplitude, frequencies and instabilities. The transverse vibration of the beam at selected points along its length demonstrates higher-frequency oscillations that corresponds to a lower axial speed. With the increase of beam flexural rigidity, the divergence critical speed increases. Coupled effect of axially moving beam and rotating rolls is also considered.

Observation of Ultrabroadband Striped Space-Time Surface Plasmon Polaritons

Because surface plasmon polaritons (SPPs) are surface waves characterized by one free transverse dimension, the only monochromatic diffraction-free spatial profiles for SPPs are cosine and Airy waves. Pulsed SPP wave packets have been recently formulated that are propagation-invariant and localized in the in-plane dimensions by virtue of a tight spectral association between their spatial and temporal frequencies, which have thus been dubbed “space-time” (ST) SPPs. Because of the spatiotemporal spectral structure unique to ST-SPPs, the optimal launching strategy of such novel plasmonic field configurations remains an open question. We present here a critical step toward realizing ST-SPPs by reporting observations of ultrabroadband striped ST-SPPs. These are SPPs in which each wavelength travels at a prescribed angle with respect to the propagation axis to produce a periodic (striped) transverse spatial profile that is diffraction-free. We start with a free-space ST wave packet that is coupled to a ST-SPP at a gold-dielectric interface, and unambiguously identify the ST-SPP via an axial beating detected in two-photon fluorescence produced by the superposition of incident ST wave packet and the excited surface-bound ST-SPP. These results highlight a viable approach for efficient and reliable coupling to ST-SPPs and, thus, represent the first crucial step toward realization of the full potential of ST-SPPs for plasmonic sensing and imaging.

Arbitrary decay for a nonlinear Euler-Bernoulli beam with neutral delay

In this paper, the free transverse vibration of a nonlinear Euler- Bernoulli beam under a neutral type delay is considered. In order to suppress the beam transverse vibrations, a boundary control based on the Lyapunov method is designed. The novelty of this paper is the ability to get a wide variety of energy decay rates under free vibration conditions.

Analytical and Numerical Analysis of Injection Pump (Stepped) Shaft Vibrations Using Timoshenko Theory

Abstract The free transverse vibrations of shafts with complex geometry are studied using analytical methods and numerical simulations. A methodology is proposed for evaluating the results of a natural transverse vibration analysis as generated by finite element (FE) models of a shaft with compound geometry. The effectiveness of the suggested approach is tested using an arbitrarily chosen model of the injection pump shaft. The required analytical models of the transverse vibrations of stepped shafts are derived based on the Timoshenko thick beam theory. The separation of variables method is used to find the needed solutions to the free vibrations. The eigenvalue problem is formulated and solved by using the FE representation for the shaft and for each shaft-simplified model. The results for these models are discussed and compared. Additionally, the usefulness of the Myklestad–Prohl (MP) method in the field of preliminary analysis of transverse vibration of complex shaft systems is indicated. It is important to note that the solutions proposed in this paper could be useful for engineers dealing with the dynamics of various types of machine shafts with low values of operating speeds.

DETERMINATION OF TENSIONS OF SUSPENDED ROPES OF THE BRIDGE BY FREQUENCY OF NATURAL OSCILLATIONS

The article deals with the issues of development and use of equipment for digital measurements of rope tension based on the frequency of free transverse oscillations. accurate measurement of rope tension is of practical importance. The relevance of this task for the national economy of Ukraine lies in the need to develop a simple and reliable method and equipment for quick and convenient measurement by construction engineers and operating engineers of rope tension in the construction industry. The practical significance of the work lies in the need to timely bring the span structure of the Arch Bridge of the Podilsky bridge crossing over the Dnipro River in Kyiv to the design position after the installation of metal structures with the transfer of the weight of the bridge truss to four main supports and 64 suspension cables with full unloading of four mounting supports for further arrangement of the bridge deck and completion of construction works. The object of the research is the process of measuring the tension of suspension ropes from the own weight of the metal part of the bridge during bringing the truss of the Arch Bridge to the design position of the metal structural elements of the bridge. The subject of the study is the determination of the impact of the combined movement of the upper attachment points (threaded cylindrical couplings) of 64 suspended ropes on the redistribution of the frequencies of natural oscillations and tensions in their contours.

Free transverse vibration analysis of general polygonal plate with elastically restrained inclined edges

In this study, a semi-analytical solution for the free transverse vibration of polygonal isotropic thin plates with arbitrary shapes and elastically restrained edges is obtained. All edges including inclined edges are elastically restrained by setting two groups of boundary springs along each edge of the polygonal plate to simulate the boundary forces and moments. Specifically, the complex surface integrals over the irregular plate area are simplified into a summation of plate boundary points by introducing the divergence theorem. The Chebyshev polynomial series are adopted to expand the displacement of the polygonal plate. Then, the Ritz method is performed to obtain the natural frequencies and mode shapes of several polygonal plates, such as triangular plates, quadrilateral plates, hexagonal plates, and irregular polygonal plates. An experiment study is performed and the validated comparisons between the current results and the reference results demonstrate that the proposed method can obtain accurate eigenpairs for general polygonal plates. The present method offers a unified procedure to address the vibration of polygonal plates, in which the change in the geometrical shape of plates can be readily converted with the increase or decrease in the corresponding boundary points. The results show that when the geometry and boundary restraints of a general polygonal plate are axisymmetric, the vibration modes will also present the feature of axial symmetry. Furthermore, cutting off a small part of the plate shows little influence on the modal shape whereas the influence on natural frequencies depends on the boundary conditions.

Application of free transverse gracilis myocutaneous flap for soft tissue defects of foot and ankle

To investigate the effectiveness of free transverse gracilis myocutaneous flap for soft tissue defects of foot and ankle. Between January 2017 and December 2020, 16 cases (17 feet) of soft tissue defects of foot and ankle were repaired with free transverse gracilis myocutaneous flaps. There were 10 males and 6 females, with an average age of 38 years (range, 23-60 years). There were 9 cases of left foot, 6 cases of right foot, and 1 case of bilateral feet. The causes of soft tissue defect were traffic accident injury in 3 cases, heavy object smash injury in 4 cases, machine injury in 3 cases, infection in 4 cases, electrical burn in 1 case, and synovial sarcoma after operation in 1 case. The wounds located at the distal plantar in 2 cases (2 feet), the heel and ankle in 6 cases (6 feet), the dorsum of the foot in 7 cases (8 feet), and the first metatarsophalangeal joint to the medial malleolus in 1 case (1 foot). The size of wounds ranged from 6 cm×5 cm to 18 cm×7 cm. The size of flap ranged from 11 cm×6 cm to 21 cm×9 cm. The donor site was sutured directly. After operation, 1 case (1 foot) of flap vascular crisis, 1 case (1 foot) of partial necrosis of the flap, and 1 case of partial dehiscence of the incision at donor site occurred, all of which healed after symptomatic treatment. The other flaps survived, and the incisions at donor and recipient sites healed by first intention. All patients were followed up 12-36 months (mean, 24 months). Except for 1 case (1 foot) of swollen flap, which underwent two-stage trimming, the other flaps had good shape and texture. All the flaps had a protective feeling. At last follow-up, Kofoed scores of foot and ankle function ranged from 73 to 98 (mean, 89.7); 13 cases were excellent, 2 cases were good, and 1 case was poor, with an excellent and good rate of 93.8%. Linear scar was formed at the donor site without adverse effect on lower limb function. The free transverse gracilis myocutaneous flap is an effective flap for repairing large soft tissue defects of foot and ankle due to its advantages of large excisable area, less variation of vascular anatomy, and concealment of donor site.