Flexural Frequencies Research Articles

Flexural resonant frequencies of an AFM cantilever in viscoelastic surface contact mode using modified nonlocal elasticity theory

Flexural resonant frequencies of an AFM cantilever in viscoelastic surface contact mode using modified nonlocal elasticity theory

Machine learning-enabled characterization of concrete mechanical strength through correlation of flexural and torsional resonance frequencies

In this study, an assessment of concrete compressive strength was conducted using an impulse excitation data-driven machine learning (ML) framework. The model was constructed upon a deep neural network and aided by the backpropagation method, ensuring a precise training process. In contrast to prior research, which mainly focused on mixture components, a meaningful relationship between physical parameters—resonant frequencies and elastic moduli—and compressive strength was established by our ML model. Remarkable performance was demonstrated, with a root mean square error value of 2.8MPa and a determination factor of 0.97. Through Pearson analysis, correlations between input features and output targets, ranging from −0.29 to 0.90, were revealed. Notably, the strongest correlations with compressive strength were found in Young's and shear moduli, derived from flexural and torsional frequencies, highlighting the pivotal role of dynamic elastic response in concrete's mechanical behavior. Furthermore, the findings indicated slight prediction deviations in cases involving samples with a high Poisson's ratio. This work illuminates the potential for accurate compressive strength prediction by leveraging concrete's dynamic response, particularly flexural and torsional modes, thereby opening avenues for research into concrete compressive strength without direct consideration of sample ingredients.

TSDT vs CPT and FSDT for Free Vibration Analysis of Functionally Graded Incompressible Plates

This article studies vibrational behavior of incompressible functionally graded plates through utilizing classical, first-order shear, and third-order shear deformation plate theories. Plate material properties are presumed to differ continuously in the thickness direction concurringto a power law function. The motion and continuity equations are produced using three different plate theories, and then they are analytically solved for rectangular plates with simple supports utilizingNavier's method. The results are verified by obtaining the plate natural frequency for the power law index value equals zero and comparing them to those reported in previous works. It is shown that transverse vibrational analysis of the classical and first-order shear deformationplate theories for incompressible plates are not as precise as thecompressible ones. It is shown that this issue is due to the fact that according to those theories, unlike the higher order theories, the hydrostatic pressure cannot participate in carrying the bending loads. Consequently, the equivalent flexural stiffness and as a result flexural frequencies decrease. So, to analyze the vibrational behavior of functionally graded incompressibleplates, whether the plate is either thin or thick, higher order theories should be adopted. Also, it is demonstrated that TSDT is the simplest shear deformation plate theory for which the hydrostatic pressure can contribute to withstandig the bending moments. So, it can be a practical theory for free vibration analysis of functionally graded incompressible plates. Finally, this theory has been taken into consideration to analyze the vibrational behavior of rectangular plates made of functionally graded incompressible materials Also detailed parametric studies have been carried out.

Optomechanical Frequency Comb Based on Multiple Nonlinear Dynamics.

Phonon-based frequency combs that can be generated in the optical and microwave frequency domains have attracted much attention due to the small repetition rates and the simple setup. Here, we experimentally demonstrate a new type of phonon-based frequency comb in a silicon optomechanical crystal cavity including both a breathing mechanical mode (∼GHz) and flexural mechanical modes (tens of MHz). We observe strong mode competition between two approximate flexural mechanical modes, i.e., 77.19 and 90.17MHz, resulting in only one preponderant lasing, while maintaining the lasing of the breathing mechanical mode. These simultaneous observations of two-mode phonon lasing state and significant mode competition are counterintuitive. We have formulated comprehensive theories to elucidate this phenomenon in response to this intriguing outcome. In particular, the self-pulse induced by the free carrier dispersion and thermo-optic effects interacts with two approximate flexural mechanical modes, resulting in the repetition rate of the comb frequency-locked to exact fractions of one of the flexural mechanical modes and the mode hopping between them. This phonon-based frequency comb has at least 260 comblines and a repetition rate as low as a simple fraction of the flexural mechanical frequency. Our demonstration offers an alternative optomechanical frequency comb for sensing, timing, and metrology applications.

Dynamic property evaluation of pipeline clamp based on analyzing the propagation characteristics of flexural wave in pipeline

The external clamp of hydraulic pipeline plays an important role in strengthening pipeline stiffness and improving vibration attenuation ability. In this study, wave propagation method is proposed to evaluate the translational and rotational stiffness and their loss factors of the clamp by analyzing the flexural wave propagation characteristics of pipeline. In order to validate the measured dynamic properties, experimental modal analysis was performed on the two-end elastically-supported pipeline. By modelling the pipeline with translational and rotational edge restraints, the analytical modal frequency parameters, wave numbers, and waveform coefficients were obtained. By comparing of the first-order flexural mode frequencies between experiment and analysis, the dynamic stiffness predicted by the wave propagation method was validated. The effects of the magnitude of torque, direction, clamping torque cycle, and clamp size on the complex dynamic properties of pipeline clamp were investigated. The proposed wave propagation method allows non-destructive continuous monitoring of a clamp stiffness, provides additional information about the vibration attenuation feature. It has advantages in clamp applications and is an effective methodology for measuring the dynamic properties of viscoelastic materials.

Static elastic modulus prediction at early ages using a modified resonant test for concrete cylinders using mems microphones

Concrete Young’s modulus is seldom verified on-site due to the time-consuming and costly nature of current testing standards. This article proposes a new, quick and affordable testing methodology to estimate the ultimate static elastic modulus of normal strength concrete cylinders on-site at early ages using a smartphone. Impact-resonance tests were performed on several concrete cylinders from different mixtures at different ages, using an accelerometer and a smartphone microphone to measure the cylinders' flexural and longitudinal resonant frequencies. Measurements from both sensors were compared to show the validity of estimating the dynamic elastic modulus using acoustic signals from the cylinders recorded with a smartphone's built-in microphone. The cylinders' static and dynamic elastic moduli were determined, and the change in elastic modulus over time as the cylinders aged was also examined. This study shows the advantages of microphones over accelerometers, being less susceptible to measurement errors and proposes a filter algorithm to extract the resonant frequencies from environmental noise. A forecasting methodology to estimate static elastic modulus based on early dynamic impact-resonant tests can help engineers make early decisions on their supplied concrete on-site.

Effect of intramodal and intermodal nonlinearities on the flexural resonant frequencies of cantilevered beams

Effect of intramodal and intermodal nonlinearities on the flexural resonant frequencies of cantilevered beams

Vibration-based prediction of residual fatigue life for composite laminates through frequency measurements

Fiber reinforced polymer (FRP) structures may experience cumulative fatigue damage during their service life which can lead to structural failure. This paper focuses on predicting the residual fatigue life of FRP structures using vibration parameters. The relationship between residual fatigue life and natural frequencies is examined through modal testing and fatigue measurements on FRP beam specimens. Two prediction methods; semi-empirical models and machine learning (ML) algorithms, are utilized. The semi-empirical models are derived from existing “residual stiffness” models based on the relationship between bending stiffness and flexural frequencies. ML algorithms Support Vector Machine (SVM) and Artificial Neural Network (ANN), are developed for fatigue life prediction. Experimental validation is performed using measured frequencies during fatigue testing of FRP beams. The ML algorithms can use multimode frequencies unlike single mode of semi-empirical models. The verification results show that the ML algorithms can be used to predict the residual fatigue life with the selection of the appropriate mode of frequency. The results show that ML algorithms outperform single-mode frequency inputs, and the use of higher modes of measured frequencies improves the precision of fatigue life prediction. An inverse algorithm based on SVM exhibits higher prediction accuracy and stability, even with limited training samples.

Tuning the flexural frequency of overhang-/T-shaped microcantilevers for high harmonics

High-harmonic (HH) frequencies in microcantilevers impose several applications in precision detection thanks to the higher sensitivity of the higher modes in comparison to the fundamental modes. In this study, we showed that by tuning the cantilever length by changing the clamped position, the dimensional ratio of the overhang to the main cantilever part is altered and the HHs could be effectively obtained. Multiple HH frequencies have been achieved, from the 4th to 8th order of the second and from the 11th to 26th order of the third-mechanical mode versus the first mode, and these orders are much higher if higher modes are used. The analytical calculation is in agreement with available results of other groups. HH behavior when the cantilever interacts with the sample is also examined and is strongly dependent on the overhang parameters. These results could guide the experimentalist in the tuning and controlling of the HHs in detecting objects.

Quantifying Shallow-Depth Concrete Delamination using Impact-Echo

Corrosion-induced concrete deck delamination is quite common in bridges. Locating these embedded delaminations is important to assess the extent of the damage, the remaining member capacity and any necessary rehabilitation. The impact-echo (IE) is a simple and straightforward non-destructive testing (NDT) technique by which the depth and extent of concrete delamination may be estimated. It is effective in detecting the location and determining the depth of relatively deep delaminations in concrete. Delaminations that occur near the concrete surface can also be detected by the IE method. However, the exact depth cannot be quantified due to difficulties in analysing the flexural mode that dominates the vibration response over the corresponding delaminated region. This study developed an IE-based procedure to quantitatively estimate the depth of shallow depth delaminations in concrete slab members. Four slab specimens were prepared, each with three artificial delaminations with varying shapes and sizes at shallow depths. The frequency contour maps showed good agreement with the actual location of the delaminations. The perimeter-to-depth ratio of the delaminated region can be used to analyze the flexural mode vibration frequency. Two equations are proposed that relate the depth of arbitrarily shaped delaminations to the flexural mode vibration frequency measured over the shallow-depth delaminations. Keywords: impact echo, concrete delamination, concrete slabs, flexural mode vibration, non-destructive evaluation (NDE)

Study on dynamic impact factor of girder bridges due to vehicle load model

The dynamic effects of moving vehicle on bridge are generally treated as withstand static loads that are recommended an increment by dynamic impact factors (IMs) (or dynamic amplification factors) in many design codes, that are a function of either the span or the first flexural natural frequency of the bridge. The value of the IM will relate to safe and economical in new bridge designs, evaluate recommendation and operation of bridges. Due to the bridge-vehicle interaction model, previous studies have shown that the calculated IM from field measurements could be higher than the values specified in design codes. Currently, studies on IM often focus on using interaction models with multi mass vehicles move on bridge that are increasingly similar to real models. This study develops a 2D three-axle vehicle–bridge model to analysis the dynamic response of the girder bridge subjected to moving loads consider to some vehicle parameters with the each axle is modelled in two masses, each mass is connected to a spring and a damping corresponding to the suspension and tire. In addition, depending on the stiffness parameters of the suspension and tires of the analyzed vehicle model, the IM results of this study are different from those of some authors and the bridge design rules. Based on the dynamic analysis of the bridge under the vehicle loading consider the stiffness of tire and suspensions, the calculation of the IM needs to be considered more carefully in the process of designing new bridges or existing bridges.

Excitation response analysis of hollow cylinders under helical surface tractions for dominant flexural guided wave generation

Dominant flexural mode excitation of helical waves in hollow cylinders by applying helical surface tractions, equivalent to exciting obliquely propagating plate waves in the unwrapped plate, is reported. However, this approach cannot be generalized with theoretical underpinnings. The response of hollow cylinders under helical surface tractions is investigated using normal mode expansion method. Purity of the target flexural mode depends on the mode wave structures at excitation frequencies and the helix angle of the helical excitation. With helical surface tractions, only flexural modes with large circumferential and longitudinal displacements, usually torsional flexural modes, can be effectively generated. The target flexural mode and excitation frequency should be selected carefully for better purity. The helix angle for the target mode should diverge considerably from other modes, especially those with large circumferential and longitudinal displacements. The apparently oblique propagation of the flexural mode can also be explained theoretically. The helically excited flexural mode comprises two orthogonal wave structures with identical flexural modes that are out of phase in the propagation direction, causing periodically changing circumferential orientation of the combined wave structure and oblique wave front. Finite element simulations and experiments agree well with theoretical predictions.

Combined influence of rotary inertia and shear coefficient on flexural frequencies of Timoshenko beam: numerical experiments

Combined influence of rotary inertia and shear coefficient on flexural frequencies of Timoshenko beam: numerical experiments

Anisotropy of Young's Modulus of DD6 from 25 to 1200 °C Based on Nondestructive Dynamic Method

The Young's modulus is an essential factor for improving turbine blade design. The present study aims to obtain the flexural frequencies (f1) and corresponding dynamic Young's modulus (Ed) of Ni‐based single‐crystal DD6 across a temperature range of 25–1200 °C using a nondestructive dynamic testing method. The relationship between the elastic constants and various crystal orientations is derived by employing the transformation of the elastic matrix. In addition, finite element (FE) simulation is conducted to calculate the flexural frequency (f1) of the [001] crystal orientation. The findings indicate that the dynamic Young's modulus (Ed) decreases as the temperature increases within the range of 25–1200 °C. Furthermore, the Ed values for different crystal orientations follow the trend: Ed[1] < Ed[11] < Ed[111]. This suggests significant anisotropy in the material. The normalized model, matrix transformation calculation method, and finite element method demonstrate high accuracy in predicting the elastic modulus of DD6, as evidenced by the good correspondence between the fitting curves obtained using the normalization method and the test results. These results have practical applications in engineering, particularly in turbine blade design and other applications, and serve as valuable references for mechanical property testing and finite element simulations.

INFLUENCE OF BOLTED SPLICE CONNECTIONS ON THE GLOBAL BEHAVIOUR OF STEEL LATTICE TELECOMMUNICATION TOWERS

The bolted joints in the leg and the bracing members of the lattice transmission towers are always subjected to predominant axial forces, which will cause joint slip that greatly affects the global be-haviour of the whole structure. The paper shows the results of the numerical modelling of the re-sponse of the steel lattice communication tower, with height h = 40.5 m located in Rzeszów. A comparison was made of five tower models, differing in the characteristics of the joint force-elongation relationship, including stiffness of the components and also joint slippage, coming from Category A joints. The paper presents the difference in displacements and rotations of chosen tower panels, internal forces in leg members, as well as in the fundamental flexural frequency obtained without considering the force-displacement characteristic and with four different ways of modelling of joints behaviour

Coupled Thin Film Hydrogenated Amorphous Silicon Microresonator Arrays

Mechanically coupled resonators can potentially improve the sensing capabilities of MEMS resonators. This work presents novel weakly and moderately coupled MEMS bridge resonators with up to four degrees-of-freedom (DOF), with thin-film hydrogenated amorphous silicon thin films as structural layers fabricated on glass substrates by surface micromachining at temperatures no greater than 175 °C. The electrostatically actuated coupled resonators exhibited flexural fundamental resonance frequencies near 1 MHz. Coupled resonance modes were simulated by Finite Element Method and characterized using optical and electrical sensing. Laser Doppler vibrometry was used to scan the coupled mode shapes and confirm resonance mode attribution. Coupled resonators with 4-DOF exhibited motional resistances ~25 times lower than single resonators (1-DOF) actuated with identical voltages. Common (in-phase) and independent (out-of-phase) actuation of the coupled resonators was implemented, resulting in distinct dynamic behaviors of the coupled array. The fabrication process presented in this work is easily scalable to higher degrees-of-freedom and to large-area substrates, which makes it a good fit for large-scale sensing applications. [2022-0161]

Real-Time Monitoring of Temperature-Dependent Structural Transitions in DNA Nanomechanical Resonators: Unveiling the DNA–Ligand Interactions for Biomedical Applications

Despite being widely recognized as of paramount importance in molecular biology, real-time monitoring of structural transitions in DNA complexes is currently limited to complex techniques and chemically modified oligonucleotides. Here, we show that nanomechanical resonators made of different DNA complexes, such as pristine dsDNA, ssDNA, and DNA intercalated with dye molecules or chemotherapeutic agents, are characterized by unique fingerprint curves when their flexural resonance frequency is tracked as a function of temperature. Such frequency shifts can be successfully used to monitor structural variations in DNA complexes, such as B-to-A form and helix-to-coil transitions, thus opening implications in both environmental studies─for example, trucking the effects of heavy metal exposure on human or vegetable DNA molecules─and in vitro experiments for the evaluation of the effects of drugs on patient DNA.

Auxetic meta-disk for independent control of flexural and torsional waves

Locally resonant elastic metamaterials have a unique characteristic of forming a low-frequency bandgap where wave propagation is inhibited. In this study, we present an auxetic meta-disk, a novel design of a local resonator capable of independent control of the flexural and torsional wave propagation in a pipe. The auxetic meta-disks are perforated with rationally designed auxetic patterns, whose mode-dependent deformation is the key mechanism enabling to manipulate the flexural and torsional natural frequencies of the meta-disks simultaneously. The capabilities of auxetic meta-disks in controlling wave propagation are thoroughly investigated using finite element analysis, and its applicability to elastic wave mode filtering is presented. Because of the simplicity in design and installation, the proposed concept is expected to be practical and applicable to various fields of vibration isolation or non-destructive inspection that require considering more than one vibration mode.

Scanning and separating vertical and torsional–flexural frequencies of thin-walled girder bridges by a single-axle test vehicle

An effective procedure is proposed for scanning and separating the vertical (flexural) and torsional–flexural frequencies of thin-walled girder bridges by a moving single-axle test vehicle, modeled as a two degree-of-freedom (DOF) system to account for the vertical and rocking motions. The response of the vehicle is not directly used, since it may mask the bridge frequencies by self frequencies. Instead, the wheel-bridge contact responses are used for being free of vehicle’s frequencies. To start, closed-form solutions are derived for the vertical, lateral, and torsional vibrations of the mono-symmetric beam. Then, the contact responses are calculated from the vehicle responses, considering the discrete nature of field data. The vertical and torsional–flexural frequencies of the bridge are separated by using the vertical and rocking motions derived from the contact responses without prior knowledge of the mode shapes. The proposed technique is numerically validated with the following conclusions: (1) the wheels’ contact responses outperform the vehicle response in that more high frequencies of the bridge can be detected; (2) the torsional–flexural​ frequencies can better be detected from the wheel closer to the bridge edge; and (3) the vertical and torsional–flexural frequencies of bridges can be successfully separated by the proposed procedure even in the presence of pavement roughness, which is helpful for field applications.

Viscoelastic free vibration analysis of in-plane functionally graded orthotropic plates integrated with piezoelectric sensors: Time-dependent 3D analytical solutions

This paper proposes an accurate three-dimensional framework for elastic and viscoelastic free vibration investigation of in-plane functionally graded (IPFG) orthotropic rectangular plates integrated with piezoelectric sensory layers. The developed analytical framework is capable of considering layer-wise unidirectional linear functional gradation in both stiffness and density of the orthotropic composite layers. 3D piezoelasticity-based governing equations of motion are formulated in mixed form by employing Hamilton’s principle, and further solved analytically for Levy-type support conditions using the power-series-based extended Kantorovich method (EKM) jointly with Fourier series. The displacements, stresses, and electrical variables (electric field and electric potential) are solved as the primary variables that ensure the point-wise interlayer continuity and electro-mechanical support conditions. The viscoelastic property of the orthotropic interlayer is defined by employing Biot model, which is similar to the standard linear viscoelastic model. The correctness and efficacy of the present mathematical model are established by comparing the present numerical results with published literature and 3D finite element results, obtained by utilizing user material subroutine in the commercial FE software ABAQUS. An extensive numerical study is performed for various configurations and thickness ratios to investigate the influences of in-plane gradation, viscoelasticity and their coupled effects on the free-vibration response of hybrid laminated plates. It is found that in-plane gradation of stiffness and density remarkably alters the flexural frequencies and corresponding mode shapes of the hybrid intelligent rectangular plates. The flexural frequencies and stresses in the plate can be modified by selecting suitable grading indexes. Another interesting observation is that the in-plane gradation shows a considerably less effect on the electrical response of piezoelectric layers, which can play a vital role in the design of sensors and actuators for dynamic applications. Further, the numerical study demonstrates a potential time-dependent structural behaviour based on the present viscoelastic modelling. The consideration of viscoelasticity could be crucial for analysing the mechanical behaviour of a wide range of polymer composites more realistically and for prospective temporal programming in smart structural systems by exploiting the viscoelastic effect. Although the present analytical solution has been proposed for the free-vibration investigation of smart in-plane functionally graded (IPFG) viscoelastic plates, it can also be utilized directly to analyze the symmetric and asymmetric laminated piezoelectric smart plates with constant properties.