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The present study introduces a one-dimensional finite element (FE) model that utilizes third-order deformation kinematics to analyze the flexural vibration of two-layered composite beams with partial shear slip. The proposed model incorporates a three-node straight beam element, utilizing the field-consistent approach and full numerical integration of the stiffness matrix. This approach is adopted to effectively address stress oscillation and shear locking issues, ensuring accurate and reliable results. The analysis focuses on the third-order deformation kinematics of longitudinal displacement within the beam depth, examining each of the two layers individually. The interface between the two material layers is joined using deformable shear connectors, which are represented as dispersed shear springs over the length of the beam. This study focuses on conducting a flexural vibration analysis of two-layered composite beams. The analysis includes the examination of both free vibration and forced vibration responses while considering or omitting the influence of damping under various loading conditions. The validity of the proposed FE model is assessed by the utilization of a two-dimensional model developed within the ABAQUS software. Additionally, the suggested model is evaluated through the process of verification by comparing it with previously published results. [ABSTRACT FROM AUTHOR]

The Acoustic Black Hole (ABH) is an effective structure for harvesting and dissipating energy from flexural waves. It works by reducing the thickness of the ABH wedge in a power law relationship with m ≥ 2, which rapidly decreases the local phase velocity of flexural waves and leads to an energy convergence effect. However, the vibration performance may differ if the tapered wedge does not meet the requirements of a typical ABH. This article introduces and discusses two types of "pseudo-ABH" wedges: linear-degenerate ABH and step-degenerate ABH. These wedges do not follow the power-law and continuity conditions of typical ABH, respectively. To establish the dynamic models of pseudo-ABH wedges, the lumped-mass transfer matrix method (LTMM) and traveling wave analysis are introduced and validated using analytic solutions of the non-uniform one-dimensional Euler-Bernoulli beam and finite element method. Meanwhile, a good match between the results of the Timoshenko and Euler-Bernoulli beam theory also indicates the correctness of our model. The energy ratio and reflection coefficient are defined to characterize the energy accumulation effect and vibration absorption performance of the pseudo-ABH wedges. The vibration performance of the linear-degenerate ABH is closer to the typical ABH than the step-degenerate ABH. The step-degenerate ABH has more effective energy accumulation and reduction performance for individual frequencies. However, as the number of segments in the step-degenerate ABH increases, its dynamic performance becomes closer to that of the typical ABH. The novelty of this article is to study vibration energy accumulation and absorption characteristics of pseudo acoustic black hole wedges using LTMM model, disclose the differences of linear and step degenerate ABH for their performance, and recommend the step degenerate ABH in place of the typical ABH of a power law thickness relationship. [ABSTRACT FROM AUTHOR]

Metallic dissipators have gained considerable attention in the seismic structural design industry in recent years because of their ability to provide stable hysteresis behavior and excellent energy dissipation capacity. Among these dissipators, the U-shaped flexural plate (UFP) has gained wide acceptance. This research primarily focuses on the numerical modeling of UFP and its innovative application, known as the multiple UFP dissipater (MUD). The research methodology involves conducting finite-element analysis of both the single UFP model and the MUD model under monotonic and cyclic loading conditions using Abaqus. The numerical models were validated against the experimental results. The findings of this study provide valuable insights into the local deformation behavior of UFP during rolling motion, including the variations in the yield area and stress distribution at critical cross sections. Additionally, a parametric study was performed to investigate the influence of various geometric parameters, such as the section modulus and the slenderness ratio of the flange of UFP. The numerical model of MUD enables a comprehensive understanding of how different components within MUD function as an integrated unit. Furthermore, the relationship between the overall stiffness of MUD and the stiffness of each individual component within the system was discussed. [ABSTRACT FROM AUTHOR]

This study presents analytical solutions using the finite sine transformation methodology (FSTM) for the natural dynamic solutions of thick beams. The Euler-Bernoulli beam theory (EBBT) disregards the contributions of transverse shear strains due to the Euler-Bernoulli-Navier orthogonality hypothesis used in its formulation and is unsuitable for thick beams. It derived a variational formulation of flexural vibration equations of sinusoidal shear deformable beams using first principles approach. The governing equation is formulated for transverse dynamic loading and in-plane compressive force as a non-homogeneous partial differential equation (PDE). The PDE did not need shear correction factors. The formulation yielded a cosine function shaped transverse shear strain and stress distribution which was maximum at the neutral axis and vanished at the beam surfaces. The PDE was solved for free flexural vibration where it became homogeneous due to the absence of forcing excitation forces. The FSTM was used for solving simply supported beams since sinusoidal kernel complies with end conditions. The problem simplifies for harmonic excitation to an algebraic eigenvalue problem solvable using algebraic methods. The roots are utilized to compute modal vibrations and the resonant vibration frequency at the first mode, (n = 1). The resonant frequencies obtained are identical with past results that used theory of elasticity technique. The results for the first five vibration modes are also close to previous results obtained thick beam models for all modes and aspect ratios considered. The effectiveness of the FSTM and its accuracy has been demonstrated for simply supported thick beam vibration problems. [ABSTRACT FROM AUTHOR]

Manipulating elastic waves propagating in the desired manner has attracted substantial attention, and the metasurfaces offer the important ideas to achieve this goal. In particular, it will be more advantageous if wave function switching can be achieved without changing the microstructure of the metasurface. In the paper, a knob elastic metasurface is designed to realize the regulation of flexural wave covering the 0–2π range of phase shift by rotating the angle of the knob. When the metasurface is in the turn-on state, the angles of the knob at different positions can be adjusted reasonably though the generalized Snell's law to achieve several phenomena of anomalous refraction, beam focus, and non-paraxial self-acceleration of flexural wave in a wide frequency. And when the metasurface is placed in the turn-off state, the total reflection of the flexural wave can be realized, and then bidirectional vibration isolation can be achieved. [ABSTRACT FROM AUTHOR]

In the study, a tunable metagrating of flexural waves by using knob elastic metasurface is presented. By precisely designing the angles of the rotary knobs, the gradient of the upper and lower half regions of the metasurface can be made symmetric to realize the beam splitting of the flexural wave and the phenomenon of the acoustic bottle beam. The numerical results confirm the broadband and robustness of the metasurface in terms of the flexural wave manipulation capability, which provides a basis for the design of the beam splitter device. More importantly, the switching of these functions can be done by a simple rotation of the knob angle without the need to redesign the new metarsurface. [ABSTRACT FROM AUTHOR]

The vibrations of a floating ice cover under the action of moving disturbances of variable intensity are studied. The model of vibrations of a floating ice cover is based on the linearized fluid mechanics equations and the linear classical theory of vibrations of plates. The ice cover is considered as a thin elastic isotropic plate. The critical velocities at which the nature of the wave disturbances changes both in front of the disturbance source and behind it are determined. The critical velocities as functions of the source oscillation frequency are studied, six critical velocities being obtained. It is shown that from one to seven wave systems are formed depending on the velocity of the source and the frequency of its oscillations. The corner zones in which these waves are formed are determined. The effect of compression and tension forces on the critical velocities and the corner zones in which the waves propagate has been studied. [ABSTRACT FROM AUTHOR]

The objective of this study was to determine the reasonable flexural functions of ultra-wide box girders, reveal the mechanism of the shear lag effect, and improve the analysis theory of ultra-wide box girders. Considering a single-box three-chamber thin-walled box girder as an example, starting from an uneven transfer of shear flow, the flexural displacement function of the curved box girder under the influence of shear deformation of each plate was derived according to the flexural theory of a thin-walled box girder, balance equation of a thin-walled microelement plate, and theory of plane stress. The energy variational method was used to analyze the flexural displacement function, providing a theoretical solution for the shear lag effect of the curved box girder. A displacement correction of the cantilever plate displacement function was performed by comparing the calculation results for the shear lag coefficients. The results indicated that under the shear deformation of each plate, the flexural displacement functions of the wing and web plates of the box girder no longer satisfy the assumption of plane section. The flexural displacement function is a quadratic function of the transverse wing plate, and the web height is the sum of the first- and third-order functions. The theoretical calculation results agree sufficiently well with the experimental results, proving that the flexural displacement function of the box girder under the influence of the shear deformation of each plate is reliable. [ABSTRACT FROM AUTHOR]

Arteriosclerosis is a major risk factor for cardiovascular disease and results in arterial vessel stiffening. Velocity estimation of the pulse wave sent by the heart and propagating into the arteries is a widely accepted biomarker. This symmetrical pulse wave propagates at a speed which is related to the Young's modulus through the Moens Korteweg (MK) equation. Recently, an antisymmetric flexural wave has been observed in vivo. Unlike the symmetrical wave, it is highly dispersive. This property offers promising applications for monitoring arterial stiffness and early detection of atheromatous plaque. However, as far as it is known, no equivalent of the MK equation exists for flexural pulse waves. To bridge this gap, a beam based theory was developed, and approximate analytical solutions were reached. An experiment in soft polymer artery phantoms was built to observe the dispersion of flexural waves. A good agreement was found between the analytical expression derived from beam theory and experiments. Moreover, numerical simulations validated wave speed dependence on the elastic and geometric parameters at low frequencies. Clinical applications, such as arterial age estimation and arterial pressure measurement, are foreseen. [ABSTRACT FROM AUTHOR]

The near surface mounted (NSM) carbon fiber-reinforced polymer (CFRP) strengthening technique, combined with gradually anchored prestressed technique, is utilized to delay the occurrence of concrete cover separation (CCS) and enhance the ductility of reinforced concrete beams. The load-carrying capacity of fully prestressed beams and gradually prestressed beams are investigated under both static and fatigue loading conditions. The study focused on the effect of gradient prestress on flexural behavior of strengthened beams, analyzed the failure mode, characteristic load, ductility, and stress distribution at CFRP-concrete interface under both prestress and load conditions. Results indicate that gradually prestressed beams outperform fully prestressed ones in restraining crack development, delaying yield of tensile reinforcement, improving bearing capacity and avoiding CCS failure. Bearing capacity was significantly increased by up to 35.48%, while ductility was greatly improved by 100.33% with ultimate deflection for gradually prestressed beams compared to fully prestressed ones. The fatigue life of gradually prestressed beams, which experienced a transition from CCS failure mode to fatigue fracture of tensile reinforcement, was significantly extended. Additionally, their ductility at failure was also greatly enhanced, thus confirming the effectiveness of gradually prestressed NSM CFRP strengthening technique. [ABSTRACT FROM AUTHOR]

An active elastic metasurface has more flexibility than a passively modulated elastic metasurface, owing to the manipulation of the phase gradient that can be realized without changing the geometrical configuration. In this study, a negative proportional feedback control system was employed to provide positive active control stiffness for adaptive unit cells, with the aim of achieving the active modulation of the phase gradient. The relationship between the control gain and the phase velocity of the flexural wave was derived, and the transfer coefficients and phase shifts of the flexural wave through the adaptive unit cells were resolved using the transfer matrix method. Finite element simulations for wave propagations in the adaptive unit cells were conducted, and they verified the analytic solutions. Based on this theoretical and numerical work, we designed active elastic metasurfaces with adaptive unit cells with sub-wavelength thicknesses according to the generalized Snell's law. These metasurfaces show flexibility in achieving abnormal functions for transmitted waves, including negative refraction and wave focusing, and transforming guided waves at different operating frequencies by manipulating the control gain. Therefore, the proposed active metasurface has great potential in the fields of the tunable manipulation of elastic waves and the design of smart devices. [ABSTRACT FROM AUTHOR]

Purpose: Functionally graded material (FGM) is usually used in high temperature environment. Thick FGM spherical shells usually rarely consider the shear deformation effect of thickness. So the purpose of this study was to investigate the natural frequency directly from the homogeneous matrix under free vibration, in which elements contain the third-order shear deformation theory (TSDT) effect. Methods: This study was based on the formulations containing temperature-dependent FGM properties, nonlinear displacements, dynamic equations of motion and fully homogeneous equation. Thus the determinant of fully homogeneous coefficient matrix in sinusoidal oscillations can be used to calculate the numerical data of natural frequencies. Results: The numerical results of natural frequencies for SUS304/Si3N4 constituent materials were obtained. These results include the effects of stiffness integrals, c1 term, density integrals, temperature-dependent properties and power law index of FGMs on the vibrations of flexural, shear and twist modes. Some non-dimensional frequency parameters were also compared with published literature. Conclusions: Usually the values of dimensional first natural frequency are greater in value with c1=0 than that with c1=0.925925/mm2, including the TSDT effect, for a given meridional angle in thick FGM spherical shells. [ABSTRACT FROM AUTHOR]

This work reports an ultrasonic long waveguide sensor for measuring the fluid level utilizing longitudinal L(0, 1), torsional T(0, 1), and flexural F(1, 1) wave modes. These wave modes were transmitted and received simultaneously using stainless-steel wire. A long waveguide (>12 m) covers a broader region of interest and is suitable in the process industry's hostile environment applications, "fluid levels and temperature measurements." In this work, we used fluids "diesel, water, and glycerin" for measuring fluid levels based on the sensor's reflection factors from time domain and frequency domain signals. We examined the impact of wave mode attenuation effects for long waveguide sensor design while changing the waveguide lengths. Initially, we obtained the L(0, 1) and T(0, 1) modes reflections from the 12.6 m waveguide length when one end of the long waveguide was fixed with a shear transducer at 45° orientation. Subsequently, we want to study and identify all wave modes (especially F mode) travel distances. Hence, we would like to investigate the guided wave propagation characteristics (attenuation, ultrasonic velocity, and frequency of all wave modes) in the long waveguide while cutting systematically at intervals of 1 m, starting from its original length of the waveguide 12.6 m by analyzing the A-scan signals of various lengths of a single waveguide. This simple and cost-effective technique can monitor the high fluid depths and temperature in power plants, oil, and petrochemical industries while designing a long waveguide sensor with appropriate ultrasonic parameters. [ABSTRACT FROM AUTHOR]

Flexural-gravity wave blocking occurs in the presence of lateral compressive force. The existing expansion formulae for the velocity potential were limited in the case of distinct real roots of the dispersion relation with the multiplicity one. This limitation is overcome, and we obtain the complete solution for the flexuralgravity wave-maker problem at blocking and saddle points by deriving the expansion formula for velocity potential using the Fourier transform corresponding to the roots of the dispersion relation with multiplicity two and three, respectively. Further, we check the convergence of the newly derived expansion formulae by using the spectral representation of the associated eigenfunction. It has been proved that the eigenfunctions related to the expansion formulae are linearly dependent and satisfy the orthogonal modecoupling relation. Next, we solve a model problem of flexural-gravity wave scattering by a crack using the derived expansion formulae and establish the energy balance relation by applying Green's integral theorem at blocking points for infinite water depth. In addition, we have presented the validation of energy balance relation involving the generalized scattering coefficients. [ABSTRACT FROM AUTHOR]

The subject of the paper is a simply supported standard wide-flange H-beam. Cross sections of this beam is analytically described as a three-layer structure. The shear effect in its successive layers is taking into account with consideration of the classical shear stress formula called Zhuravsky shear stress. Based on Hamilton’s principle, two differential equations of motion are obtained. These equations are analytically solved and the fundamental natural frequency of flexural vibration for this beam is derived. Exemplary calculations are carried out for selected five I-beams. [ABSTRACT FROM AUTHOR]

This study examines the formation of triads of flexural gravity wave in a homogeneous fluid within the context of blocking dynamics due to the presence of shear current. This study will enable us to understand the distribution of wave energy on an ice-covered sea surface. New classes of triads for flexural gravity waves are introduced depending on the direction of wave propagation with following and opposing currents. The study reveals that triad formation occurs due to the interaction of flexural gravity waves irrespective of the presence of compression and current, which has not been found in the case of free surface gravity waves. In addition, at most, three triads are formed in the case of flexural gravity waves in the presence of following and opposing currents prior to the threshold of blocking. In contrast, at least three triads are formed for any frequency within the primary and secondary blocking limits for certain values of compressive force and current speed. On the other hand, 11 triads are formed in the presence of uniform current speed as well as in the case of linear shear current with constant vorticity for a certain frequency within the blocking limit for higher values of compressive force and current speed. [ABSTRACT FROM AUTHOR]

The 2D electrons trapped in vacuum near the atomically thin dielectric (ATD, mono- or N -layer film of h -BN or transition metal dichalcogenide) are considered. ATD is suspended above the back gate and forms the capacitor, which is controlled by the biased voltage determining 2D concentration, n 2 D . It is found that the leakage current through ATD is negligible, and the effect of the polarizability of ATD is weak if N ≤ 5. At temperatures T = 0.1 – 15 K and n 2 D = 5 × 10 8 – 10 10 cm − 2 , one deals with the Boltzmann liquid having a macroscopic thickness of ∼ 100 A. Due to the bending of ATD, the quadratic dispersion law of the flexural vibrations is transformed into the linear one at small wave vectors. The scattering processes of the electrons caused by these phonons or the monolayer islands on ATD are examined and the momentum and energy relaxation rates are analyzed based on the corresponding balance equations. The momentum relaxation times vary over orders of magnitude in the above region (T , n 2 D ) and N. The response may change from the polaron transport, for a perfect single-layer ATD at low T and high n 2 D , to the high-mobility (≥ 10 7 cm 2 / V s) regime at high T and low n 2 D . The quasi-elastic energy relaxation due to phonon-induced scattering is considered, and the conditions for the heating of electrons by a weak in-plane electric field are found. [ABSTRACT FROM AUTHOR]

Vibrations induced by crack propagation in a strip of bonded silicon wafers are studied. A new optical setup enables the fast recording of crack-originated acoustic waves, emitted both ahead and behind the crack front, in bonded and separated wafers, respectively. Three types of crack-induced vibrations are identified, corresponding to different excitations and responses of the system: (1) "pneumatic" vibrations involving inertia and gas expansion/compression, (2) standard flexural waves involving inertia and bending rigidity, and (3) post-crack vibrations involving inertia, bending rigidity, and coupling to gas pressure. We show that a standard "beam on elastic foundation" model can explain these latter vibrations that occur along crack edges and is consistent with the observed frequencies. [ABSTRACT FROM AUTHOR]

The topological interface state for an elastic wave in a one-dimensional system, as reported in the literature, mainly occurs through Bragg scattering, making it difficult to achieve subwavelength wave control and flexible tunability. Here, inspired by the band-folding mechanism, this paper confirms that an interface state can likewise be excited by local resonance. The topological phase transition is accomplished by purposely arranging the locations of local resonators. The system is composed of a uniform thin beam with periodically attached local resonators made from an electrorheological elastomer subjected to adjustable electric fields. By simply doubling the primitive unit cell, the passing bands in the dispersion relation are folded and a folding point falls below the locally resonant bandgap, which can be lifted up by simply tuning the distance between two local resonators to realize a topological phase transition. Furthermore, we demonstrate the dynamic tunability of the working frequency of the topological interface state by using an external electric field to adjust the starting frequency of the local resonance. Since the excited frequency of the interface mode is lower than the resonance frequency, this work overcomes the ineffectiveness of the Bragg topological phononic crystal at low frequencies. Moreover, the use of an electroactive resonator whose parameters are readily tuned also enables the flexible design of a frequency-variable topological system without requiring a geometrical modification of the base structure. This technique may have potential applications, such as vibration isolation or in fabricating a robust waveguide. [ABSTRACT FROM AUTHOR]

This paper presents an experimental investigation into the effect of Z-pin on the low-velocity impact response and flexural properties after impact of the curved CFRP laminates. The Z-pinned specimens are produced using a low-damage pre-hole Z-pinning (PHZ) technique. Unpinned and Z-pinned [0/45/–45/90]4S specimens are both subjected to low-velocity impacts. Nondestructive inspection technique is used to evaluate the internal damage after impact. Subsequently, three-point bending tests are performed to characterize the flexural properties of the impacted specimens. Experimental results indicate that Z-pinned laminate, due to the bridging traction across the delamination cracks provided by pins, can provide an efficient crack arrest mechanism both in impact and bending after impact tests. Compared with the unpinned specimens, the delamination damage projection area (DDPA) is reduced by 28.5–63.5%, depending on the diameter and volume fraction of Z-pin. In addition, Z-pin could improve the residual flexural strength significantly. The specimens with a high Z-pin volume fraction have excellent damage tolerance, leading to an 18.1–76.1% improvement in the residual flexural strength compared with unpinned specimens. [ABSTRACT FROM AUTHOR]

An analytical technique for the solution of plate-type structural members due to the influence of torsional rigidity and other vital parameters is developed in this present study. The governing equation is addressed by the versatile method of Shadnam et al. The method specifically reduces the model equation with variable coefficients to a second-order ordinary differential equation. A parametric study that examined the dynamic influence of torsional rigidity, rotatory inertia and variable elastic foundation on the plate flexure is carried out. It is found that these parameters greatly influenced the dynamic deflection of the plate-type. Thus, an increase in the values of these structural parameters produces a noticeable effect on the critical velocity of the plate-type system. Hence, the risk of a resonating effect is amply reduced. [ABSTRACT FROM AUTHOR]

Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in such structures. Here we report the existence of branched flows of flexural waves in such waveguides. The location of high amplitude motion, away from the launch location, scales as a power law with respect to the variance, and linearly with respect to the correlation length of the spatial variation in the bending stiffness. These scaling laws are then theoretically derived from the ray equations. Numerical integration of the ray equations also exhibit this behaviour—consistent with finite element numerical simulations as well as the theoretically derived scaling. There appears to be a universality for the exponents in the scaling with respect to similar observations in the past for waves in other physical contexts, as well as dispersive flexural waves in elastic plates. [ABSTRACT FROM AUTHOR]

The linear two-dimensional problem of interaction between an hydroelastic wave propagating along an elastic floating ice plate with built-in vertical rigid plate is studied. The fluid under the ice is inviscid and incompressible. The fluid depth is finite. The deflection of the ice plate is described by the linear theory of thin elastic plates. The flow under the ice is potential. The total velocity potential is decomposed into the potential of the incident wave, even potential caused by the vertical motion of the rigid plate, and an odd potential caused by the rotation of the rigid plate. The vertical mode method is used. The third potential is obtained by solving a mixed boundary-value problem numerically using Chebyshev polynomials. The solution is validated by analysis of its convergence. The first and second potentials, and the corresponding deflections and strains of the ice plate, are obtained analytically. The motions of the rigid plate, as well as deflection and strains in the floating plate, are numerically analyzed. It is shown that the rotation of the rigid plate due to the incident wave is the main factor of increasing strains in the ice plate. [ABSTRACT FROM AUTHOR]

In engineering acoustics, the propagation of elastic flexural waves in plate and shell structures is a common transmission path of vibrations and structure-borne noises. Phononic metamaterials with a frequency band gap can effectively block elastic waves in certain frequency ranges, but often require a tedious trial-and-error design process. In recent years, deep neural networks (DNNs) have shown competence in solving various inverse problems. This study proposes a deep-learning-based workflow for phononic plate metamaterial design. The Mindlin plate formulation was used to expedite the forward calculations, and the neural network was trained for inverse design. We showed that, with only 360 sets of data for training and testing, the neural network attained a 2% error in achieving the target band gap, by optimizing five design parameters. The designed metamaterial plate showed a −1 dB/mm omnidirectional attenuation for flexural waves around 3 kHz. [ABSTRACT FROM AUTHOR]

We theoretically, numerically, and experimentally study a lightweight metastructure that can simultaneously reduce vibration and noise in a broad low-frequency range. We introduce spiral slits and micro-perforations in the panel and core plate of a face-centered cubic sandwich structure, respectively. A bottom-up acoustic impedance theory is developed to describe the impedance of a single unit cell. Broadband low-frequency sound absorption is achieved for a 3 × 3 supercell via reinforcement learning optimization. The resonant coupling of the upper spiral panel and the lower panel of the unit can form a wide hybridized bandgap for flexural waves, which is further validated for vibration isolation with a one-dimensional supercell. The proposed multifunctional metastructure provides a new route to design lightweight load-bearing structures with noise and vibration reduction performance for potential applications such as aerospace engineering and transportation vehicles, among others. [ABSTRACT FROM AUTHOR]

The paper is devoted to the analytical modelling of a simply supported expanded-tapered sandwich beam. The simplified analytical model of this beam with omitting the shear effect is elaborated. Based on Hamilton's principle, the differential equation of motion of this beam is obtained. This equation is analytically solved with consideration of the deflection line of this beam subjected to its own weight. The fundamental natural frequencies for exemplary beams are derived. Moreover, the FEM model of the beam in the ABAQUS is developed. The calculation results of the fundamental natural frequency of exemplary beams of these two methods are presented in tables and figures. [ABSTRACT FROM AUTHOR]

Automobile suspension systems use leaf springs, which are responsible for driving comfort and performance. The failure of leaf springs can lead to an accident. In an arctic environment, leaf springs must meet the durability requirements under service loading. From this point of view, quasi-static and fatigue experiments and numerical studies have been done on leaf springs in sub-zero temperature conditions and at room temperatures. In experimental studies, the leaf spring has been used as a beam specimen. Experimental study demonstrates flexural tests on C45 steel beam specimens at room temperature (25 °C) and sub-zero temperature of − 40 °C. The flexural strength of C45 steel is increased at sub-zero temperature in 35.56%. The next step is to perform flexural fatigue testing in displacement control mode under constant amplitude loading conditions. The fatigue life of leaf springs is improved in sub-zero temperature conditioning, after the ductile-to-brittle transition temperatures of selected material. Static and fatigue finite element simulation was carried out with test results to find out the flexural strength and fatigue life of leaf springs. SEM fractography of failed specimens provides insight into the fracture phenomena in C45 beam under quasi-static and fatigue loads. [ABSTRACT FROM AUTHOR]

We present an active exterior cloak for flexural waves propagating in a Kirchhoff plate of infinite extent. The evanescent multipole devices are characterized by Macdonald functions Kn of the required order, which, assuming time-harmonic vibrations, are solutions of the fourth-order biharmonic equation. It is shown that in the region of interfering waves, which emanate from the devices, a field is recreated which cancels the incident wave to yield a region of 'stillness'. An inclusion is then positioned in this region for further investigation, with additional attention given to the boundary condition. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'. [ABSTRACT FROM AUTHOR]

We consider the propagation of flexural and torsional waves in a square lattice of Euler–Bernoulli beams. The refraction and reflection of waves across interfaces between two dissimilar lattices is investigated. By carefully controlling the inertial and elastic properties of the lattice elements, we demonstrate that it is possible to induce negative refraction and other associated phenomena. These effects are shown to be broadband and are facilitated by the unprecedented control over wave propagation afforded by the interaction between torsional and flexural waves and the additional freedom associated with the applied forcing. Closed-form analytical findings are accompanied by numerical simulations, which demonstrate negative refraction, unidirectional reflection and mode trapping. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 2)'. [ABSTRACT FROM AUTHOR]

This study focuses on damped propagation characteristics of bulk-type waves in a sandwich nanoplates. The nanoplates is made up of homogenous core and functionally graded material (FGM) face sheets while resting on a viscoelastic type substrate, called viscoelastic-Winkler foundation. Using a refined shear deformable theory (RSDT) of plate in conjunction with general nonlocal strain gradient theory (NSGT), this research contribution tries to find small-scale triple coupled (axial-shear-bending) governing equations by developing the assumptions of Hamiltonian principle. The derived equations are solved analytically to find the damped flexural wave responses of the introduced structure. The results demonstrated the effectiveness of the proposed size-dependent continuum theory to study damped flexural wave propagation nano-scale plate without boundaries. Results show that the visco-Winkler foundation, small-scale parameters, sandwich arrangements, and wave number affect the dispersion of waves. The obtained conclusions can be utilized for the designing process of small-scale composites. [ABSTRACT FROM AUTHOR]

The motion of a vibrating object is determined by the way it is held. This simple observation has long inspired string instrument makers to create new sounds by devising elegant string clamping mechanisms, whereby the distance between the clamping points is modulated as the string vibrates. At the nanoscale, the simplest way to emulate this principle would be to controllably make nanoresonators slide across their clamping points, which would effectively modulate their vibrating length. Here, we report measurements of flexural vibrations in nanomechanical resonators that reveal such a sliding motion. Surprisingly, the resonant frequency of vibrations draws a loop as a tuning gate voltage is cycled. This behavior indicates that sliding is accompanied by a delayed frequency response of the resonators, making their dynamics richer than that of resonators with fixed clamping points. Our work elucidates the dynamics of nanomechanical resonators with unconventional boundary conditions, and offers opportunities for studying friction at the nanoscale from resonant frequency measurements. The motion of a vibrating object is set by the way it is held. Here, the authors show a nanomechanical resonator reversibly slides on its supporting substrate as it vibrates and exploit this unconventional dynamics to quantify friction at the nanoscale. [ABSTRACT FROM AUTHOR]

The flexural wave propagation in a micro-beam mounted on viscoelastic foundation is considered in the present work. The mechanical behavior of the micro-beam is modeled by nonlocal strain gradient elasticity with the size-effects taken into account. The constraint is modeled by the Pasternak foundation with the rheology behavior modeled by fractional-order viscoelasticity. The main concerns are the dispersion and attenuation feature of five kinds of possible flexural waves derived from the governing equations of the presented micro-beam model. The influences of the nonlocal effects, strain gradient effects and the fractional-order viscoelastic effects are investigated by a parameter study in the numerical examples. This research is helpful for the design of micro-sensor, micro-actuator and energy-harvest devices in micro electric-mechanic system (MEMS). [ABSTRACT FROM AUTHOR]

The aim of this research is to use a simple acoustic method of a very near field recording, which enables measurement and display of oscillation modes, to estimate the velocity of flexural waves, based on the wavelengths of standing waves measured on the sample. The paper analyses cases of 1D geometry, flexural waves that occur on a beam excited by an impulse. Measurements were conducted on two different samples: steel and a wooden beam of the same length. Due to the appearance of evanescent waves at the boundary regions, the distance between the nodes of standing waves that occur deviates from half the wavelength, which can be compensated using a correction factor. Cases of fixed and free boundary conditions were analysed. By quantifying how much the boundary conditions change the mode shape function, it can be predicted how the mode of oscillation changes if the boundary conditions change, which can also find application in musical acoustics and sound radiation analysis. [ABSTRACT FROM AUTHOR]

Plane-strain motion of a flexural seismic metasurface in the form of a regular array of thin Kirchhoff plates attached to the surface of an elastic half-space is analysed. Two types of contact conditions, including simply supported plates and plates moving along horizontal rails are studied. Dispersion of time harmonic waves is investigated both asymptotically and numerically. A major effect of the contact conditions on metasurface behaviour is discovered. In particular, it is shown that frequency band gaps are not the feature of the array composed of simply supported plates. It is also demonstrated that the scaling laws, expressed through geometric and material problem parameters, drastically differ from each other for two considered setups. [ABSTRACT FROM AUTHOR]

This paper uses numerical and asymptotic methods to investigate the fluid dynamics underlying the anomalously large attractive forces that were recently observed in squeeze-film levitation systems driven by resonant vibrations of a flexible oscillator. Namely, in a recent experimental study, a thin plastic disk driven near one of its natural frequencies attractively levitated, for the first time, an object weighing several hundred grams. This behavior is in stark contrast with that of rigid-body systems, which produce attractive forces thousands of times weaker and only within a limited range of operating conditions. Flexural systems driven by standing-wave deformations of the oscillator are addressed in this paper in a unifying matched-asymptotic analysis that accounts for effects of fluid viscosity, inertia, and compressibility, as well as pressure variations beyond the outer boundary of the squeeze film. While the weak attractive forces produced by rigid-body systems are known to depend critically on the existence of a net pressure drop across this peripheral region, the present analysis reveals that the augmented attractive load capacity of resonant flexural systems is associated instead with spikes of underpressure near the nodes of the standing wave. Furthermore, the wavenumber, which represents the number of nodes in the waveform, is found to correlate strongly with the attractive load capacity as well as the range of frequencies and oscillator surface areas for which attractive forces can be produced. [ABSTRACT FROM AUTHOR]

Textile-reinforced mortar (TRM) is used to strengthen reinforced concrete (RC) structures using a textile and inorganic matrix. TRM is a part of textile-based composites; the basic structural behaviors, application methods, and methodologies for the extension of actual structures in TRM were studied. However, structural behavior and performance verification which depict the long-term service situation and fatigue is limited. Therefore, this study, verified the flexural behavior of TRM-strengthened beams and their fatigue performances using carbon- and alkali-resistant (AR) glass textiles through 200,000 load cycles. TRM-strengthened beams were applied to an optimization strengthening method which consisted of whether the textile was straightened. According to the test results, the strengthening efficiency of TRM-strengthened beams when subjected to cyclic loading was lower than that of the monotonic loading, except for the straightened carbon textile specimen. The average efficiency of the AR-glass textile (straightened and non-straightened) and carbon (non-straightened) was 0.86 compared to the TRM-strengthened beam subjected to monotonic loading in terms of flexural strength. In the case of deflection, the average efficiency of the AR-glass textile type was similar to the monotonic loading test results, while that of the non-straightened carbon textile was improved. The Ca-S specimen that was used to straighten the carbon textile showed a reliable structural performance with a strength efficiency of 0.99 and a deflection efficiency of 0.97 compared to the monotonic load test. Therefore, TRM strengthening using a straightened carbon textile is expected to be sufficient for the fatigue design of TRM-strengthened beams. [ABSTRACT FROM AUTHOR]

In the present study, the interface debonding area between face sheets and the foam cores of the sandwich panels were inspected using the thermography method for the five groups of the samples. These samples were manufactured with different processes divided into two main groups; one‐step manufacturing process and two‐step manufacturing process. All of the specimens were subjected to the three‐point bending test after thermography detection technology. The one‐step manufactured samples presented the highest flexural strength and minimum discontinuity. Integrated infusion process in comparison with other processes shows about 40% superiority in mechanical properties at least. The results showed that Indentation beneath the loading roller is the initial failure mode of the one‐step manufactured samples. In addition, the main failure mode of the two‐step manufactured samples is the core shear mode. [ABSTRACT FROM AUTHOR]

An applied theory describing the transverse vibrations of a cantilever bimorph in an alternating magnetic field is presented. The bimorph is made of piezoactive materials, which is a multilayer composite with alternating piezoelectric and piezomagnetic layers. The mechanical and physical properties of such a composite are specified by their effective constants. This theory can serve as a model for energy harvesting devices under the action of an external alternating magnetic field. Within the framework of the theory, quadratic distributions of electric and magnetic potentials over the cantilever thickness are assumed inhomogeneous in its longitudinal direction. The stress-strain state of the bimorph, the distribution of electric and magnetic fields, and its natural frequencies are calculated. In addition, the case where the potential at one of electrodes is unknown is examined. The results of calculations in the low-frequency region are compared with those found by a finite-element model based on a system of partial differential equations built in the COMSOL Multiphysics package. A comparison showed a good agreement between the calculated field characteristics and the data of finite-element modeling in the entire area of the bimorph, except in the vicinity of the beam fixation and its free end. [ABSTRACT FROM AUTHOR]

Conformal transformation method (CTM) has been extensively applied to control propagation of electromagnetic waves and acoustics waves due to the form-invariant property of Maxwell equations and acoustic equations. However, CTM’s application in elastic waves is rarely reported due to the governing equation of elastic waves do not have form invariant property. In this paper, through igniting evanescent waves at the interface of conformally mapped Mikaelian lens with hyperbolic secant refractive index profile, CTM is successfully used to achieve highly efficient (above 75%) broadband (30âˆ'80 kHz) achromatic high-resolution flexural wave focusing in thin plate with full width at half maximum (FWHM) around 0.2 λ. The proposed Mikaelian lens is designed by linking refractive index with the thickness in plates. Simulated results agree well with theoretical prediction. This high performance for flexural wave focusing could be used for energy harvesting and medical imaging. [ABSTRACT FROM AUTHOR]

We propose an efficient semi-analytical method capable of modeling the propagation of flexural waves on cracked plate structures with any forms of excitations, based on the same group of vibration characteristics and validated by a non-contact scanning Laser Doppler Vibrometer (LDV) system. The proposed modeling method is based on the superposition of the vibrational normal modes of the detected structure, which can be applied to analyze long-time and full-field transient wave propagations. By connecting the vibration-based transient model to a power flow analysis technique, we further analyze the transient waves on a cracked plate subjected to different excitation sources and show the influence of the damage event on the path of the propagating waves. The experimental results indicate that the proposed semi-analytical method can model the flexural waves, and through that, the crack information can be revealed. [ABSTRACT FROM AUTHOR]

Using fluid--structure interaction computationalmodelling, the hydrodynamic performance of bio-inspired elastic propulsors with tapered thickness that oscillate in an incompressible Newtonian fluid at Reynolds number Re = 2000 is investigated. The thickness tapering leads to an acoustic black hole effect at the trailing edge of the propulsor that slows down and attenuates flexural waves, thereby minimizing the flexural wave reflection and enhancing travelling wave propulsion. The simulations reveal that, by tuning the propulsor thickness profile modulating the acoustic black hole effect, the tapered propulsors can be designed to vastly outperform the uniformly thick propulsors in terms of the hydrodynamic efficiency and thrust, especially for the post-resonance frequencies. The enhanced hydrodynamic performance is directly linked to the ability of the tapered propulsors to generate travelling waves with a large amplitude displacement at the trailing edge. The results have implications for the development of highly efficient bio-mimetic robotic swimmers and, more generally, the better understanding of the undulatory aquatic locomotion. [ABSTRACT FROM AUTHOR]

Lightweight concrete (LWC) is one of the most important building materials nowadays. Many research studies were focused on LWC produced using lightweight aggregates. However, limited work was cited for LWC produced using polystyrene beads. In this study, LWC beams strengthened with carbon fibre reinforced polymer (CFRP) and glass fibre reinforced polymer (GFRP) were experimentally tested to investigate the improvement in their flexural and shear behaviours. LWC in this investigation was achieved by partial replacement of normal aggregate by polystyrene beads and resulted in approximately 30% less weight compared to Normal weight concrete. Fourteen Reinforced Concrete (RC) LWC beams of 100 mm by 300 mm cross section having an overall length of 3250 mm were tested under four-point bending. These beams were designed, detailed, and tested to obtain flexural and shear mode of failure. These beams were divided into two groups based on the intended failure mode. In each group, six beams were strengthened using CFRP and GFRP laminates, while the remaining one beam was used as control. The tested parameters were the type of FRP, the width of the laminates used in shear strengthening, and the number of layers used in flexural strengthening. It was found that strengthening of LWC beams using CFRP and GFRP layers resulted in increasing the loading capacity and decreasing deflection as compared to control. The strengthening with CFRP and GFRP is also suitable in reducing the crack width and crack propagation which is more significant in LWC beams. The experimental results were also compared with the expressions in codes for forecasting the strength of LWC beams and it was that these expressions are compatible with the experimental results. [ABSTRACT FROM AUTHOR]

The nonlinear vibration characteristics of rotating axially moving conical shells are investigated in the current paper. The nonlinear equations of motion and strain compatibility equation based on Donnell's nonlinear shell theory are obtained. Three nonlinear equations of motion are reduced to a radial equation by applying the appropriate Airy stress function, forming a set of equations with the compatibility equation. The compatibility equation is solved by employing the seven degrees of freedom with respect to the system's flexural mode shape. By substituting the flexural mode shape into the equation of motion and applying the Galerkin method, seven nonlinear coupled nonhomogeneous ODEs are achieved, then the set of equations is transformed into the normal form where it has been solved by the numerical method. The effects of the axial and rotational velocity on bifurcation diagrams, frequency response curves, time history, and the phase portraits of the system are discussed. The results of the present paper are validated against available data, and good agreements are achieved. [ABSTRACT FROM AUTHOR]

For the nonlinear equations of thickness-shear vibration and flexural vibration of quartz crystal plate considering geometric and material nonlinearity, the equations are transformed and solved by the newly proposed extended Galerkin method. The strongly coupled frequency-response relationships of thickness-shear and flexural vibrations of quartz crystal plate are obtained respectively, and the frequency-response curves under the influence of different amplitude ratios and different driving voltages are drawn. The numerical results show that the optimal aspect ratio size of quartz wafer should be selected to avoid the strong coupling of the two modes. The change of driving voltage will cause the obvious change of thickness-shear vibration frequency of quartz crystal resonator. The frequency shift value must be controlled within the allowable value of common piezoelectric acoustic devices. The solution of high frequency nonlinear vibration equations of quartz crystal plate by extended Galerkin method lays a foundation for nonlinear finite element analysis and partial field effect analysis. [ABSTRACT FROM AUTHOR]

Subglacial hydrology modulates basal motion but remains poorly constrained, particularly for soft-bedded Greenlandic outlet glaciers. Here, we report detailed measurements of the response of subglacial water pressure to the connection and drainage of adjacent water-filled boreholes drilled through kilometre-thick ice on Sermeq Kujalleq (Store Glacier). These measurements provide evidence for gap opening at the ice-sediment interface, Darcian flow through the sediment layer, and the forcing of water pressure in hydraulically-isolated cavities by stress transfer. We observed a small pressure drop followed by a large pressure rise in response to the connection of an adjacent borehole, consistent with the propagation of a flexural wave within the ice and underlying deformable sediment. We interpret the delayed pressure rise as evidence of no pre-existing conduit and the progressive decrease in hydraulic transmissivity as the closure of a narrow (< 1.5 mm) gap opened at the ice-sediment interface, and a reversion to Darcian flow through the sediment layer with a hydraulic conductivity of ≤ 10−6 m s−1. We suggest that gap opening at the ice-sediment interface deserves further attention as it will occur naturally in response to the rapid pressurisation of water at the bed. [ABSTRACT FROM AUTHOR]

In this paper, inspired by origami structures, we offer a very simple tuning method to overcome the limitations of general elastic metasurfaces, where only a certain functionality at a certain frequency range can be achieved, by designing a reflective metasurface based on foldable/deployable zig-zag structures. By utilizing peg/screw connections, the folding angles of the zig-zag structures can be easily tuned while also being fixable. By tuning the folding angle, the subunit of the zig-zag metasurface can cover a 2π phase shift span and the phase shift can be tuned continuously, and almost linearly, with respect to the folding angle. With a simple folding motion, the tunable reflective metasurface can steer reflected flexural waves in different directions and focus-reflected flexural waves with different focal distances. In addition to demonstrating tunable performance, the mechanism that associates the changing speed of the phase shift is explained. The proposed tunable zig-zag elastic metasurface provides a new way to design reconfigurable metamaterials/metasurfaces. [ABSTRACT FROM AUTHOR]

The present study deals with analyzing the dynamic behavior of a smart beam coupled with piezoelectric materials in the unimorph and bimorph configurations connected to resonant shunt circuits. The resonant shunt circuit connection is applied to promote and passively modulate the vibration and flexural wave propagation attenuation. A Spectral Element Method (SEM)-based approach for the periodic smart structure is developed that is capable of efficiently analyzing various configurations of periodicity and piezoelectric attachments in a generic framework. The wave attenuation is obtained based on the Transfer Matrix Method (TMM). Numerical analyses reveal that the effective wavenumber presents local attenuation behavior at the same frequencies of the vibration as per the shunt design, indicating the shunt circuit's impedance associated with tuned frequency. The internal resonance characteristics of the resonant shunt circuits and their effects on the beam response are investigated in detail. The proposed periodic smart beam system along with the spectral element approach for analyzing the dynamics and wave propagation behavior of such systems, lays out further potential avenues for designing more complex configurations of smart structures and multifunctional metamaterials. [ABSTRACT FROM AUTHOR]