Search Results (49)

This paper provides an overview of various size-dependent theories based on modified/consistent couple stress and strain gradient theories (CSTs and SGTs), highlighting the development of two-dimensional (2D) refined and advanced shear deformation theories (SDTs) and three-dimensional (3D) pure analytical and semi-analytical numerical methods, including their applications, for analyzing the static and dynamic behaviors of microscale plates and shells made from advanced materials such as fiber-reinforced composites, functionally graded (FG) materials, and carbon nanotube/graphene platelet-reinforced composite materials. The strong and weak formulations of the 3D consistent CST, along with their corresponding boundary conditions for FG microplates, are derived and presented for illustration. A comparison study is provided to show the differences in the results of a simply supported FG microplate’s central deflection, stress, and lowest natural frequency obtained using various 2D size-dependent SDTs and 3D analytical and numerical methods based on the consistent CST. A parametric study is conducted to examine how primary factors, such as the effects of dilatational and deviatoric strain gradients and couple stress, impact the static bending and free vibration behaviors of a simply supported FG microplate using a size-dependent local Petrov–Galerkin meshless method based on the consistent SGT. Influences such as the inhomogeneity index and length-to-thickness ratio are considered. It is shown that the significance of the impact of various material length-scale parameters on the central deflection and its lowest natural frequency (in the flexural mode) of the FG microplate is ranked, from greatest to least, as follows: the couple stress effect, the deviatoric strain gradient effect, and finally the dilatational strain gradient effect. Additionally, when the microplate’s thickness is less than 10⁻⁷ m, the couple stress effect on its static and dynamic behaviors becomes saturated. Conversely, the impact of the dilatational and deviatoric strain gradients consistently influences the microplate’s static and dynamic behaviors. Full article

Low-spatial-resolution measurements from contact sensors and excessive measurement noise have impeded the implementation of vibration-based damage detection. To tackle these challenges, we propose a novel vision-based damage detection method combining multi-scale signal analysis theory and data fusion algorithm. For high-spatial-resolution vibration measurements, phase-based optical flow estimation algorithm is adopted to deploy virtual sensors on the structure, yielding reliable mode shapes. We then introduce the concept of entropy into damage detection. A novel damage index, defined in Gaussian multi-scale space and named multi-scale local information entropy (MS-LIE), is proposed. The MS-LIE integrates the multi-scale analysis component and the entropy analysis component, addressing both the issue of detection sensitivity and noise immunity, thereby showcasing enhanced performance. Moreover, a data fusion technique for multi-scale damage information is developed to further mitigate the noise-induced uncertainty and pinpoint damage locations. A series of numerical and experimental scenarios are designed to validate the method, and the results indicate that the proposed method accurately detects single and multiple damages in noisy environments, obviating the need for baseline data as a reference. Full article

Mine transboundary mining has been occurring frequently in recent years, and this illegal behavior has brought great potential danger to mine safety while also causing greater losses of state-owned assets. However, the current method of monitoring transboundary mining is still mainly based on underground verification by supervisors, which is far from meeting the demand for supervision. Microseismic monitoring technology is effective for monitoring transboundary mining due to its ability to locate vibration signals. For mine transboundary mining monitoring, this paper proposes a microseismic electronic fence method focusing on mine boundary locating, which differs from the routine microseismic monitoring used in mining operations. This method focuses its key monitoring area on the mine boundary. The deployment mode, number of sensors, and localization theory are analyzed, and numerical simulation and field measurement data analysis results show that the microseismic electronic fence method can achieve a localization accuracy of 15–20 m for underground microseismic events in the vicinity of mine boundaries, which can be effectively applied to the monitoring of transboundary mining activities. Full article

Cracks, common indicators of deterioration in bridge frameworks, frequently stem from wear and rust, leading to increased local flexibility and changes in the structure’s dynamic behavior. This study examines how these cracks affect the dynamics of footbridges when subjected to loads generated by walking individuals. The pedestrian is modeled as a linear oscillator, while the cracked bridge is represented by a simply supported beam following Euler–Bernoulli’s theory. The use of the Dirac delta function allows for the precise representation of the localized stiffness reduction at the crack location, facilitating the calculation of analytical expressions for the beam’s vibration modes. The research suggests that the presence of cracks minimally affects the bridge’s mid-span displacement. However, with a limited depth of cracks, the appearance of cracks notably amplifies the mid-span acceleration amplitude of the bridge, leading to a pronounced concentration of energy at the third natural frequency of the bridge in the acceleration spectrum. As the depth and number of cracks increase, the acceleration amplitude continues to decrease, but the corresponding spectrum remains almost unchanged. The study’s outcomes enhance the comprehension of how cracks affect the performance of bridge structures when subjected to loads from pedestrians, offering insights for the monitoring and evaluation of the condition of cracked footbridges. Full article

This paper presents an analytical study on the in-plane vibrations of a rectangular elastic lattice plate. The plane lattice is modelled considering central and angular interactions. The lattice difference equations are shown to coincide with a spatial finite difference scheme of the corresponding continuous plate. The considered lattice converges to a 2D linear isotropic elastic continuum at the asymptotic limit for a sufficiently small lattice spacing. This continuum has a free Poisson’s ratio, which must be lower than that foreseen by the rare-constant theory, to preserve the definite positiveness of the associated discrete energy. Exact solutions for the in-plane eigenfrequencies and modes are analytically derived for the discrete plate. The stiffness characterising the lattice interactions at the boundary is corrected to preserve the symmetry properties of the discrete displacement field. Two classes of constraints are considered, i.e., sliding supports at the nodes, one normal and the other parallel to the boundary. For both boundary conditions, a single equation for the eigenfrequency spectrum is derived, with two families of eigenmodes. Such behaviour of the lattice plate is like that of the continuous plate, the eigenfrequency spectrum of which has been given by Rayleigh. The convergence of the spectrum of the lattice plate towards the spectrum of the continuous plate from below is confirmed. Two continuous size-dependent plate models, considering the strain gradient elasticity and non-local elasticity, respectively, are built from the lattice difference equations and are shown to approximate the plane lattice accurately. Full article

The vibrations of plate structures placed in a supersonic flow was considered. The undisturbed fluid flow was parallel to the plate. This type of problem is especially important in the aerospace industry, where it is named panel flutter. It has been noticed for a long time that panel flutter may be problematic at high speeds. In this article, two specific problems were treated: in the first one, the plate was in the form of an infinite strip and the flow was in the direction of its finite length. Rigid walls indefinitely extended from the sides of the plate. In the second problem, the plate was a finite rectangle and the flow was parallel to one of its sides. The rest of the plane of the rectangle was again rigid. The first problem was a limiting case of the second problem. The flow was modeled by piston theory, which assumes that the fluid pressure on the plate is proportional to its local slope. This approximation is widely used at high speeds (supersonic speeds in the range of M > 1), and reduces the interaction between the fluid flow and the vibrations of the plate to an additional term in the vibration equation. The resulting problem can be solved by assumed mode methods. In this study, the solution was also found by using the collocation method. The contribution of this study is the correlation between the flutter velocity and the other parameters of the plate. The main result is the flutter velocity of the free fluid flow under which the plate vibrations become unstable. Finally, simple expressions are proposed between the various non-dimensional parameters that allows for the quick estimation of the flutter velocity. These simple expressions were deduced by least squares fits to the computed flutter velocities. Full article

One of the effective methods of non-destructive testing of structures is active vibration diagnostics. This approach consists of the local dynamic impact of the actuator on the structure and the registration of the vibration response. Testing of massive reinforced concrete structures is carried out with the use of actuators, which are able to create sufficiently high-impact loads. The actuators, which are based on piezoelectric elements, cannot provide a sufficient level of force and the areas where it is possible to register the vibrations excited by such actuators are quite small. In this paper, we propose a variant of a piezoactuator with attached mass, which ensures an increase in the level of dynamic impact on the structure. The effectiveness of this version is verified by numerical modeling of the dynamic interaction of the actuator with a concrete slab. The simulation was carried out within the framework of the theory of elasticity and coupled electroelasticity. An algorithm for selecting the value of the attached mass is described. It is shown that when vibrations are excited in a massive concrete slab, an actuator with an attached mass of 1.3 kg provides a 10,000-fold increase in the force compared to an actuator without attached mass. In the pulse mode, a 100-fold increase in force is achieved. Full article

The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with a view to reformulating and studying de Broglie’s double-solution program in the modern language of classical field theory. Notably, the entire family is local and Lorentz-invariant, follows from a variational principle, and exhibits time-invariant, two-way coupling between particle and pilot-wave field. We first introduce a variational framework for generic pilot-wave systems, including a derivation of particle-wave exchange of Noether currents. We then focus on a particular limit of our system, in which the particle is propelled by the local gradient of its pilot wave. In this case, we see that the Compton-scale oscillations proposed by de Broglie emerge naturally in the form of particle vibrations, and that the vibration modes dynamically adjust to match the Compton frequency in the rest frame of the particle. The underlying field dynamically changes its radiation patterns in order to satisfy the de Broglie relation $p=\hslash k$ at the particle’s position, even as the particle momentum p changes. The wave form and frequency thus evolve so as to conform to de Broglie’s harmony of phases, even for unsteady particle motion. We show that the particle is always dressed with a Compton-scale Yukawa wavepacket, independent of its trajectory, and that the associated energy imparts a constant increase to the particle’s inertial mass. Finally, we see that the particle’s wave-induced Compton-scale oscillation gives rise to a classical version of the Heisenberg uncertainty principle. Full article

The lattice dynamical properties of dilute InAs_1−xN_x/InP (001) epilayers (0 ≤ x ≤ 0.03) grown by gas-source molecular beam epitaxy were carefully studied experimentally and theoretically. A high-resolution Brüker IFS 120 v/S spectrometer was employed to measure the room-temperature infrared reflectivity (IRR) spectra at near-normal incidence (θ_i = 0). The results in the frequency range of 180–500 cm⁻¹ revealed accurate values of the characteristic In-As-like and In-N-like vibrational modes. For InAs_1−xN_x alloys, a classical “Drude–Lorentz” model was constructed to obtain the dielectric functions $\tilde{\mathsf{\epsilon }}\left(\mathsf{\omega }\right)$ in the far IR regions by incorporating InAs-like and InN-like transverse optical ${\mathsf{\omega }}_{\mathrm{T}\mathrm{O}}$ modes. Longitudinal optical ${\mathsf{\omega }}_{\mathrm{L}\mathrm{O}}$ phonons were achieved from the imaginary parts of the simulated dielectric loss functions. The theoretical results of IRR spectra for InAs_1−xN_x/InP (001) epilayers using a multi-layer optics methodology provided a very good agreement with the experimental data. At oblique incidence (θ_i ≠ 0), our study of s- and p-polarized reflectance (R_s,p(ω)) and transmission (T_s,p(ω)) spectra allowed the simultaneous perception of the ${\mathsf{\omega }}_{\mathrm{T}\mathrm{O}}$ and ${\mathsf{\omega }}_{\mathrm{L}\mathrm{O}}$ phonons of the InAs, InN and InAs_0.97N_0.03 layers. Based on the average t-matrix Green’s function theory, the results of local vibrational modes for light ${\mathrm{S}\mathrm{i}}_{\mathrm{I}\mathrm{n}}^{+}$ donors and ${\mathrm{S}\mathrm{i}}_{\mathrm{A}\mathrm{s}}^{-}, {\mathrm{C}}_{\mathrm{A}\mathrm{s}}^{-}$ acceptors in InAs were found in good agreement with the existing Raman scattering and infrared spectroscopy data. $\mathrm{I}\mathrm{n}\mathrm{I}\mathrm{n}\mathrm{N}$, however, the method predicted an in-band mode for the ${\mathrm{M}\mathrm{g}}_{\mathrm{I}\mathrm{n}}^{-}$ acceptor while projecting an impurity mode of the ${\mathrm{S}\mathrm{i}}_{\mathrm{I}\mathrm{n}}^{+}$ donor to appear just above the maximum ${\mathsf{\omega }}_{\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{I}\mathrm{n}\mathrm{N}}[\equiv 595 {\mathrm{c}\mathrm{m}}^{-1}$] phonon frequency region. In InAs_1−xN_x/InP (001) epifilms, the comparison of reflectivity/transmission spectra with experiments and the predictions of impurity modes for isoelectronic donor and acceptor impurities in InAs and InN can be valuable for appraising the role of defects in other technologically important semiconductors. Full article

The crystal family of potassium titanyl phosphate (KTiOPO${}_4$) is a promising material group for applications in quantum and nonlinear optics. The fabrication of low-loss optical waveguides, as well as high-grade periodically poled ferroelectric domain structures, requires a profound understanding of the material properties and crystal structure. In this regard, Raman spectroscopy offers the possibility to study and visualize domain structures, strain, defects, and the local stoichiometry, which are all factors impacting device performance. However, the accurate interpretation of Raman spectra and their changes with respect to extrinsic and intrinsic defects requires a thorough assignment of the Raman modes to their respective crystal features, which to date is only partly conducted based on phenomenological modelling. To address this issue, we calculated the phonon spectra of potassium titanyl phosphate and the related compounds rubidium titanyl phosphate (RbTiOPO${}_4$) and potassium titanyl arsenate (KTiOAsO${}_4$) based on density functional theory and compared them with experimental data. Overall, this allows us to assign various spectral features to eigenmodes of lattice substructures with improved detail compared to previous assignments. Nevertheless, the analysis also shows that not all features of the spectra can unambigiously be explained yet. A possible explanation might be that defects or long range fields not included in the modeling play a crucial rule for the resulting Raman spectrum. In conclusion, this work provides an improved foundation into the vibrational properties in the KTiOPO${}_4$ material family. Full article

The vibrational properties of molecular crystals in the terahertz range are controlled by the interplay of intermolecular and intramolecular interactions. The resulting delocalized normal modes span a substantial number of atoms within the unit cell of the molecular crystals and cannot be easily attributed to a specific stretching or bending mode. Several compounds were studied to understand the nature of normal modes. However, a systematic analysis of saccharides is still missing. This study investigates the terahertz vibrational properties of various saccharides, including glucose, galactose, lactose, cellobiose, and cellulose. The terahertz spectra were measured using terahertz time-domain spectroscopy. The samples were carefully characterized, and the residual Fabry–Perot oscillations were removed to obtain the absorption coefficient and refractive index of the saccharides. Density functional theory simulations were used to obtain theoretical terahertz spectra, considering hydrogen bonding interactions with an enhanced version of the van der Waals non-local density functional. The results revealed differences in low-energy vibrational modes frequencies, influenced by molecular structure properties, hydrogen bonding networks, and water content. Librations and internal vibrations were identified as dominant dynamics in the saccharides, with significant mixing between intermolecular and intramolecular vibrations. This comprehensive analysis sheds light on the vibrational behavior of saccharides in the terahertz range. Full article

In order to alleviate the structural vibrations induced by traffic loads, in this paper, a phonon crystal plate with functionally graded materials is designed based on local resonance theory. The vibration damping performance of the phonon crystal plate is studied via finite element numerical simulation and the band gap is verified via vibration transmission response analysis. Finally, the engineering application mode is simulated to make it have practical engineering application value. The results show that the phonon crystal plate has two complete bandgaps within 0~150 Hz, the initial bandgap frequency is 0.00 Hz, the cut-off frequency is 128.32 Hz, and the internal ratio of 0~100 Hz is 94.13%, which can effectively reduce the structural vibration caused by traffic loads. Finally, stress analysis of the phonon crystal plate is carried out. The results show that phonon crystals of functionally graded materials can reduce stress concentration through adjusting the band gap. The phonon crystal plate designed in this paper can effectively suppress the structural vibration caused by traffic loads, provides a new method for the vibration reduction of traffic infrastructure, and can be applied to the vibration reduction of bridges and their auxiliary facilities. Full article

For the application of low-frequency vibration damping in industry, a cylindrical cavity double-layer plate-type local resonance phononic crystal structure is proposed to solve low-frequency vibration in mechanical equipment. Initially, using COMSOL 5.4 software, the bending wave band gap is calculated in conjunction with elastic dynamics theory and the BOLOCH theorem to be 127–384 Hz. Then the mechanism of bending wave gap is analyzed by combining element mode shape and an equivalent model. Subsequently, the bending vibration transmission characteristics of the crystal plate are explained, and the vibration-damping characteristics are illustrated in combination with the time–frequency domain. An experimental system is constructed to verify the vibration-damping properties of crystal plates; the experimental results and simulation results are verified with each other. Finally, the element structural parameters are optimized using the RSM. Fifty-four sets of experiments are designed based on six structural factors and three levels, and the expressions between the bending wave band gap and six structural factors are obtained. Combining the particle swarm algorithm, the optimization is performed with the band gap width as the target. This method is shown to be more accurate than the commonly used interior point method. The structure of cylindrical-cavity-type phononic crystal and the parameter optimization method proposed in this paper provide a certain reference for the design of local-resonance-type phononic crystal. Full article

Hydrogen bonds (HB)s are the most abundant motifs in biological systems. They play a key role in determining protein–ligand binding affinity and selectivity. We designed two pharmaceutically beneficial HB databases, database A including ca. 12,000 protein–ligand complexes with ca. 22,000 HBs and their geometries, and database B including ca. 400 protein–ligand complexes with ca. 2200 HBs, their geometries, and bond strengths determined via our local vibrational mode analysis. We identified seven major HB patterns, which can be utilized as a de novo QSAR model to predict the binding affinity for a specific protein–ligand complex. Glycine was reported as the most abundant amino acid residue in both donor and acceptor profiles, and N–H⋯O was the most frequent HB type found in database A. HBs were preferred to be in the linear range, and linear HBs were identified as the strongest. HBs with HB angles in the range of 100–110°, typically forming intramolecular five-membered ring structures, showed good hydrophobic properties and membrane permeability. Utilizing database B, we found a generalized Badger’s relationship for more than 2200 protein–ligand HBs. In addition, the strength and occurrence maps between each amino acid residue and ligand functional groups open an attractive possibility for a novel drug-design approach and for determining drug selectivity and affinity, and they can also serve as an important tool for the hit-to-lead process. Full article

This research investigates the stabilization and control of an uncertain Euler–Bernoulli nano-beam with fixed ends. The governing partial differential equations of motion for the nano-beam are derived using Hamilton’s principle and the non-local strain gradient theory. The Galerkin method is then applied to transform the resulting dimensionless partial differential equation into a nonlinear ordinary differential equation. A novel fault-tolerant terminal sliding mode control technique is proposed to address the uncertainties inherent in micro/nano-systems and the potential for faults and failures in control actuators. The proposed controller includes a finite time estimator, the stability of which and the convergence of the error dynamics are established using the Lyapunov theorem. The significance of this study lies in its application to the field of micro/nano-mechanics, where the precise control and stabilization of small-scale systems is crucial for the development of advanced technologies such as nano-robotics and micro-electromechanical systems (MEMS). The proposed control technique addresses the inherent uncertainties and potential for faults in these systems, making it a valuable choice for practical applications. The simulation results are presented to demonstrate the effectiveness of the proposed control scheme and the high accuracy of the estimation algorithm. Full article