Displacement Components Research Articles

Mechanically evoked spike responses of pentascolopidial chordotonal organs of Drosophila melanogaster larvae.

Mechanosensitive ensembles of neurons in insects, known as chordotonal organs (COs), function in proprioception, the detection of sound and substrate vibrations. Here, we characterized the mechanical sensitivity of the lateral pentascolopidial CO (lch5) of Drosophila melanogaster larvae to establish its postulated role in proprioception. We developed a physiologically realistic method to replicate proprioceptive input to lch5 by pulling the apodeme (tendon) to which the tips of the neurons attach. We found that lch5 sensory neurons respond transiently with a short latency to the velocity component of stretch displacements and the release of stretch (relaxation). In the mechanosensory mutant inactive, lch5 has a decreased response to mechanical stimuli and a lower overall spontaneous spike rate. Finally, we simulated the input that lch5 receives during crawling and observed spike rate changes of peristaltic body contraction. We provide a characterization of proprioceptive feedback in D. melanogaster larvae and firmly establish the proprioceptive function of lch5 in larval locomotion.

Acoustic properties and attenuation of coupled shaft-submarine hull system under various excitation transfer paths

Pump-jet propulsor excitation transfers to submarine hull along rotor-shaft and duct-stator paths simultaneously. The investigations on the effects of excitation transfer paths on structural vibration and acoustic radiation of submarine are limited. The present work aims to investigate vibro-acoustic characteristics of coupled shaft-submarine hull system utilizing a theoretical wavenumber analysis method and conduct acoustic design. The energy functional of the coupled structure-fluid system of the research object is first developed, and the displacement components of the jointed shell and the acoustic pressure are expanded by the Fourier series along circumferential direction. This allows for obtaining vibro-acoustic responses in the circumferential wavenumber-frequency domain, by which the predominant wavenumbers contributing to acoustic radiation are identified. The discussions reveal that the modes n = 0 and n = 1 respectively dominate the acoustic radiation under axial and vertical rotor loads. The acoustic radiations under duct-stator load are mainly contributed by mode n = 0, and the higher order modes n = 1 and n = 2 determine several acoustic peaks. Furthermore, two acoustic design schemes are proposed to suppress the wavenumbers with high radiation efficiency. It is proven that the design of the symmetric inner foundation and the application of new material are two efficient ways to improve acoustic performance of the submarine.

Magneto-thermoelastic surface waves phenomenon with voids, gravity, initial stress, and rotation under four theories

This paper addresses a significant research gap in the study of surface waves propagation in a nonhomogeneous, within a magneto-thermoviscoelastic material of higher order, initial stress, rotation, gravity effects and voids. This study provides analytical solutions for surface waves propagating through a medium consisting of a magneto-thermoelastic material with voids under the rotation, electro-magnetic field, gravity field and initial stress. The analytical solutions are derived for the displacement components, volume fraction, temperature to Stoneley and Rayleigh waves are computed numerically and presented graphically considering the external parameters impact. Furthermore, this investigates how magnetic field, voids, gravity, initial stress and fiber-reinforced parameters influence these wave phenomena. This investigation provides valuable insights into the synergistic dynamics among electric constituents, voids, Stoneley and Rayleigh waves propagation, enabling advancements in sensor technology, augmented energy harvesting methodologies, and pioneering seismic monitoring approaches. For certain materials, numerical simulations are provided and graphically displayed. The results of this study reveal several unique cases that significantly contribute to the understanding of Rayleigh and Stoneley waves propagation within this intricate material system, particularly in the presence of voids.

Dual-mode Shear Horizontal / Rayleigh-like surface-acoustic-wave configuration on lithium niobate 64° Y-cut

Technologies based on surface acoustic waves (SAWs) find widespread use in wireless communications, signal processing, and sensing applications. In this study, we present an innovative dual-mode SAW configuration using a 64° Y-cut lithium niobate (LN) substrate. The conventional setup, employing interdigital transducers (IDTs) oriented along the crystal X-axis, is known for generating the shear horizontal mode (SH-SAW) with in-plane polarization. Conversely, by utilizing IDTs oriented perpendicular to the X-axis, we introduce effective excitation of a Rayleigh-like SAW (R-SAW), a novel achievement in our research. Through finite element simulations and electro-mechanical analyses, we comprehensively characterize these modes in terms of frequencies, polarizations, propagation losses, and temperature coefficients. Furthermore, we investigate their interaction with liquids by analyzing damping characteristics and acoustic streaming effects using particle image velocimetry (PIV). SH-SAWs exhibit a leaky displacement during propagation with minimal damping in liquids, resulting in weak acoustic streaming—ideal for real-time sensing applications in wet environments. In contrast, non-leaky R-SAWs, characterized by a strong displacement component normal to the surface, exhibit enhanced acoustic streaming, facilitating microfluidic operations. Additionally, R-SAWs demonstrate high sensitivity to mass loading, making them optimal for real-time sensing in dry environments. The ability to generate both SAW modes on the same substrate offers the potential to develop fully electrical-driven, multifunctional integrated sensing platforms with SAW-driven microfluidic capabilities. This unique capability promises novel solutions in bio-sensing, leveraging the complementary strengths of the two acoustic modes in detection and sample handling.

Semi-analytical solutions for land subsidence due to groundwater withdrawal

This paper introduces novel semi-analytical models tailored for estimating land subsidence resulting from groundwater extraction in confined aquifers. These models offer high scalability, allowing them to be applied to various well configurations and pumping schedules. Their development involves the numerical integration of two key analytical solutions: the “nucleus of strain” (NoS) (Mindlin and Chen, 1950), which represents a localised zone within the aquifer where a unit change in pore pressure leads to deformation and subsequent surface displacement, and the classic Theis equation (Theis, 1935) for the pore pressure changes induced by a constant-rate well pumping from a laterally unbounded aquifer. These integrations yield surface displacement components, both horizontal and vertical, expressed as functions of two dimensionless spatial–temporal variables, which encompass aquifer depth, thickness, well placement, pumping schedules, and critical hydro-geomechanical parameters like hydraulic conductivity, porosity, vertical compressibility, and water compressibility. Proposed are two distinct modelling approaches: one employing a lookup table (LT) derived from numerical integration results, and the other providing direct closed-form surface displacement solutions by fitting LT data with “hinge models”, which use piecewise-linear functions linked by sigmoidal curves for computational efficiency. In both cases, surface displacement components are estimated by plugging in the dimensionless variables. Conditions of variable pumping from multiple wells can be addressed by applying superposition of solutions. In essence, these semi-analytical models offer swift computational capabilities for understanding and forecasting land subsidence dynamics. Their scalability makes them adaptable to a wide array of well configurations and scheduling scenarios, rendering them valuable for numerous applications. They are particularly significant for providing preliminary estimates of the impacts of groundwater development, conducting “what-if” tests, and performing sensitivity analyses to identify key factors affecting land subsidence risk. This underscores the importance of these models in sustainable groundwater resource management and in mitigating land subsidence and its associated consequences.

Modelling transient unloading-triggered dynamic responses in rock mass under a non-hydrostatic geo-stress

Transient excavation unloading of in situ stress affects the stability of surrounding rock in the deep tunnel engineering. This paper focuses on the dynamic responses triggered by the transient unloading of a non-hydrostatic geo-stress field in deep-buried engineering. With resort to the integral transformation, the frequency-domain responses of stress, displacement and velocity components induced by the transient unloading are obtained under a non-hydrostatic in situ stress. Based on the numerical inversion of the Laplace transformation, the corresponding time-domain theoretical results are determined. Agreement of the current solutions with the existing results and the numerical simulations verifies the proposed scheme in this paper. The elastic analytical results indicate that the influence of unloading path on the stress redistribution is characterized by the unloading rate. The higher the unloading rate is, the larger the stress magnitude is. The smaller the unloading time is, the more remarkable vibration is. The elasto-plastic dynamic numerical responses are investigated on the basis of a self-developed code, elasto-plastic cellular automaton (EPCA), which is a module of CASRock. The numerical results demonstrate that the transient excavation unloading results in the stress redistribution and concentration of surrounding rock mass, inducing damage for the case of exceeding the capacity of rock mass. For the small lateral pressure coefficient (less than 0.25), the tensile-shear failure is the major damage mechanism of surrounding rock, while the shear failure is the major damage mechanism for the large lateral pressure coefficient. The analytical and numerical results can provide theoretical basis for the support and reinforcement of underground tunnel.

Rayleigh-type wave in non-planar pre-stressed nearly incompressible elastic structure

The primary objective of the current work is to establish the impacts of planar boundary and non-planar boundary on the displacement components (DCs) of Rayleigh-type wave propagation in an elastic structure. The elastic structure, precisely, incorporates a pre-stressed nearly incompressible elastic material in the half-space along with the non-planar boundary at the free surface. The methodology applied features variable separable technique and Taylor’s series expansion along with substitution method to establish the expressions for DCs and frequency relation. The frequency relation of Rayleigh-type wave is obtained for the situation considering planar free surface, which is further reduced as a special case of the study and validated with the classical result present in the literature. The DCs of Rayleigh-type wave have been numerically computed, and their reliance on wave number have been exhibited graphically. In addition to this, the influences of affecting parameters viz., hydrostatic stress, principal Cauchy stress and curvature parameter on DCs have been traced out. The computational result also manifests the domain of existence of Rayleigh-type wave propagating in the considered model in the presence of planar free surface.

Seismic performance of carbonated recycled aggregate concrete shear walls

The carbonated modification method is recognized as an effective method to enhance recycled aggregates (RA), but there is currently a lack of research on carbonated recycled aggregate concrete (CRAC) used for structural engineering. This paper investigated the impact of CRAC on the seismic performance of shear walls, quasi-static tests of one natural aggregate concrete (NAC) shear wall and four concrete shear walls with different replacement ratios (30 %, 50 %, 70 %, and 100 %) of carbonated recycled aggregate (CRA) were conducted. The ductility, energy dissipation, stiffness, strength degradation, and lateral displacement components of CRAC shear walls were evaluated. The results indicate that the seismic behavior of the shear walls degraded as the replacement rate of CRA increased. Based on the comprehensive evaluation of failure patterns and seismic performance, the replacement rate of CRA is suggested to be taken as 70 % in the concrete shear walls. Finally, the strut-and-tie model was validated as an effective method for predicting the shear capacity of CRAC shear walls, and the accurate softening coefficient constant C of the strut-and-tie model for CRAC and RAC shear walls was proposed.

3D electro-elastic static analysis of advanced plates and shells

The proposed three-dimensional (3D) coupled electro-elastic shell model allows the static analysis of smart structures embedding classical piezoelectric and functionally graded piezoelectric layers. Plates, cylindrical and spherical panels are investigated in both sensor and actuator configurations. The primary variables of the coupled model are displacement components and the electric potential. Therefore, displacements, stresses, strains, electric potential and electric displacements are calculated for smart structures used as sensors (applied mechanical load) and smart structures used as actuators (applied electric potential). In the case of spherical shells, 3D equilibrium equations are coupled with the 3D divergence electric displacement equation. The obtained coupled system is also valid for cylindrical shells and plates thanks to the use of a mixed curvilinear orthogonal reference system. The partial differential governing equations are solved using the Navier harmonic form and the exponential matrix method for simply supported structures. Preliminary assessments are proposed to validate the model and further benchmarks are analyzed to discuss the effects connected with the thickness ratio, the lamination scheme, the load conditions, the geometry of the structures and the employed materials. The main innovation point of the proposed model is the possibility to analyze several geometries including different materials and applied loads by means of a unique and general formulation where partial differential equations are solved in closed form. The use of functionally graded piezoelectric materials allows to eliminate all stress component discontinuities at each layer interface.

The Impact of Rotation and Inclined Load on a Nonlocal Fiber-Reinforced Thermoelastic Half-space via Simple-phase-lag Model

Abstract Purpose The purpose of the present study is to discuss the impacts of rotation, inclined load, nonlocal parameter, and an empirical material constant on various physical variables of a fiber-reinforced thermoelastic medium. Methods The present problem was studied using the simple phase-lags (DPL) model. Using normal mode analysis, the precise expressions for the temperature, stress, and displacement components are found. Results Matlab software is used to do numerical computations. Comparisons are done between the outcomes obtained and those expected for various nonlocal parameter values, rotation, an empirical material constant, and inclined load. Conclusion The nonlocal parameter and rotation play a big part in how the physical fields are distributed. The distributions of the physical fields are significantly influenced by the inclined load and an empirical material constant.

Investigation of the Zero-Frequency Component of Nonlinear Lamb Waves in a Symmetrical Undulated Plate.

When an ultrasonic pulse propagates in a thin plate, nonlinear Lamb waves with higher harmonics and a zero-frequency component (ZFC) will be generated because of the nonlinearity of materials. The ZFC, also known as the static displacement or static component, has its unique application on the evaluation of early-stage damages in the elastic symmetrical undulated plate. In this study, analysis of the excitation mechanism of the ZFC and the second harmonic component (SHC) was theoretically and numerically investigated, and the material early-stage damage of a symmetrical undulated was characterized by studying the propagation of nonlinear Lamb waves. Both the ZFC and SHC can be effectively employed in monitoring the material damages of the undulated plate in its early stage. However, several factors must be considered for the propagation of the SHC in an undulated plate because of the geometric curvature and interference between the second harmonics during propagation, preventing efficient application of this technique. If the fundamental wave can propagate in the plate regardless of the plate boundary conditions, an accumulative effect always exists for the ZFC in a thin plate, indicating that the ZFC is independent of the structural geometry. This study reveals that the ZFC-based inspection technique is more efficient and powerful in characterizing the damages of a symmetrical undulated plate in the early stage of service compared to the second harmonic method.

Three-dimensional vibration analysis of multilayered composite and functionally graded piezoelectric plates and shells

In the present paper, a coupled 3D exact electro-elastic shell model for Functionally Graded (FG) and composite piezoelectric structures is proposed. Primary variables of the electro-elastic model are the electric potential and the three displacement components. The model allows to evaluate the piezoelectric effect in terms of frequencies and vibration modes. Both closed and open circuit configurations are analyzed and compared. The 3D equilibrium equations and the 3D divergence electric displacement equation for spherical shells give the set of partial differential equations for the electro-elastic problem. The proposed model for spherical shells automatically degenerates into simpler models for plates and cylindrical shells via properly considerations on radii of curvature along in-plane directions. The orthogonal mixed curvilinear coordinates α, β and z are employed. The partial differential governing equations have constant coefficients considering fictitious layers and they are solved using the Navier harmonic form and the exponential matrix method. These features lead to an exact solution for simply-supported boundary conditions. Free vibration analyses are conducted and circular frequencies for the first three thickness vibration modes are computed. After a global assessment phase to verify the correctness of the developed model, new benchmarks are proposed: different thickness ratios and material configurations are investigated. The present work can be intended as a reference general solution for those scientists interested in the study of piezoelectric structures via 2D analytical and numerical formulations.

Kinematic changes in dairy cows with induced hindlimb lameness: transferring methodology from the field of equine biomechanics

Lameness is a common issue on dairy farms, with serious implications for economy and animal welfare. Affected animals may be overlooked until their condition becomes severe. Thus, improved lameness detection methods are needed. In this study, we describe kinematic changes in dairy cows with induced, mild to moderate hindlimb lameness in detail using a “whole-body approach”. Thereby, we aimed to identify explicable features to discriminate between lame and non-lame animals for use in future automated surveillance systems. For this purpose, we induced a mild to moderate and fully reversible hindlimb lameness in 16 dairy cows. We obtained 41 straight-line walk measurements (containing > 3 000 stride cycles) using 11 inertial measurement units attached to predefined locations on the cows’ upper body and limbs. One baseline and ≥ 1 induction measurement(s) were obtained from each cow. Thirty-one spatial and temporal parameters related to limb movement and inter-limb coordination, upper body vertical displacement symmetry and range of motion (ROMz), as well as pelvic pitch and roll, were calculated on a stride-by-stride basis. For upper body locations, vertical within-stride movement asymmetry was investigated both by calculating within-stride differences between local extrema, and by a signal decomposition approach. For each parameter, the baseline condition was compared with induction condition in linear mixed−effect models, while accounting for stride duration. Significant difference between baseline and induction condition was seen for 23 out of 31 kinematic parameters. Lameness induction was associated with decreased maximum protraction (−5.8%) and retraction (−3.7%) angles of the distal portion of the induced/non-induced limb respectively. Diagonal and lateral dissociation of foot placement (ratio of stride duration) involving the non-induced limb decreased by 8.8 and 4.4%, while diagonal dissociation involving the induced limb increased by 7.7%. Increased within-stride vertical displacement asymmetry of the poll, neck, withers, thoracolumbar junction (back) and tubera sacrale (TS) were seen. This was most notable for the back and poll, where a 40 and 24% increase of the first harmonic amplitude (asymmetric component) and 27 and 14% decrease of the second harmonic amplitude (symmetric component) of vertical displacement were seen. ROMz increased in all these landmarks except for TS. Changes in pelvic roll main components, but not in the range of motion of either pitch or roll angle per stride, were seen. Thus, we identified several kinematic features which may be used in future surveillance systems. Further studies are needed to determine their usefulness in realistic conditions, and to implement methods on farms.

Dynamic response mechanism of the hole subjected to the 3D point source disturbance in an isotropic formation

Accurate estimation of the effects of dynamic disturbances on stress concentration is crucial for the stability of rock engineering and the corresponding analytical approaches are needed. This study presents an analytical approach to calculate the relative stress distribution with a point source inside and outside a hole using the linear theory of elasticity. The Helmholtz potentials and Sommerfeld integral are employed to describe the displacement and stress components, and then formulate the equilibrium equations to solve the equivalent stress distribution around the hole. Numerical examples demonstrate the impact of model parameters on the equivalent stress, such as frequency, hole radius, source location, etc. It is found that sometimes high frequencies can make the equivalent stress greater far from the source than that close to the source. Additionally, when the ratio of the distance between the source and the hole axis to the hole radius exceeds ten, the equivalent stress distribution around the hole remains nearly constant. This approach can be used for the design and assessment of underground engineering structures' stability under dynamic disturbances.

Dynamic Analysis of 2D FG Porous Thick Cylindrical Shells Under Thermal Shock

In this research, a thick hollow cylindrical shell made of bidirectional functionally graded open cell porous materials under internal thermal shock according to the classical theory of linear thermo-elasticity is examined for the first time. The cylinder is made of a porous cellular material and its porosity varies along both radial and axial directions continuously. The governing motion equations are obtained by using 2D-axisymmetric theory of linear thermo-elasticity rather than shell theories. This theory represents thickness stretching and gives more precise results. Graded finite element method is employed to model the problem. Applying this method rather than conventional FEM leads to more accurate results, especially for dynamic analyses. The cubic higher order element is used for dividing the solution domain. To obtain transient temperatures, Crank–Nicolson algorithm is used and then the Newmark procedure is used to derive time responses of displacement and stress components. The time history of displacements and stress components for different radial and axial power law exponents, porosity coefficient, boundary conditions, length-to-thickness ratio and two different porosity patterns are investigated in detail. The obtained results show that thermal-induced vibration is generally caused by hoop stress, and frequency and amplitude of vibrations and velocity of stress waves are considerably influenced by the porosity distribution, porosity coefficient and power law exponents in both directions.

Magnetic field and initial stress on a rotating photothermal semiconductor medium with ramp type heating and internal heat source

This manuscript addresses a significant research gap in the study by employing a mathematical model of photo thermoelastic wave propagation in a rotator semiconductor medium under the effect of a magnetic field and initial stress, as well as ramp-type heating. The considered model is formulated during the photothermal theory and in two-dimensional (2D) electronic-elastic deformation. The governing equations represent the interaction between the primary physical parameters throughout the process of photothermal transfer. Computational simulations are performed to determine the temperature, carrier density, displacement components, normal stress, and shear stress using the application of Lame’s potential and normal mode analysis. Numerical calculations are carried out and graphically displayed for an isotropic semiconductor like silicon (Si) material. Furthermore, comparisons are made with the previous results obtained by the others, as well as in the presence and absence of magnetic field, rotation, and initial stress. The obtained results illustrate that the rotation, initial stress, magnetic field, and ramp-type heating parameter all have significant effects. This investigation provides valuable insights into the synergistic dynamics among a magnetization constituent, semiconducture structures, and wave propagation, enabling advancements in nuclear reactors' construction, operation, electrical circuits, and solar cells.

Analysis of an initially stressed functionally graded thermoelastic medium (type III) without energy dissipation

The current investigation deals with the deformation of a non-homogeneous thermoelastic half space under hydrostatic initial stress for the Green–Naghdi model III. The medium is supposed to be rotating with a constant angular velocity. The non-homogeneous properties of the material are along the x-direction. At the first instance, the problem has been solved analytically to obtain stress and displacement components. Further, the numerical values of these expressions are evaluated using a computer program for a particular medium. The numerical values obtained are then presented graphically to show the effect of initial stress parameter and non-homogeneity parameter on the quantities.

The Thermodynamic Responses of FG Conical/Cylindrical/Annular Panels with Circumferentially Variable Dimensions

This paper is the first to develop a meshless thermodynamic model with circumferentially variable dimensions to analyze the thermal-vibration mechanisms of typical functionally graded (FG) panel-type structures, mainly including conical, cylindrical, and annular panels. The longitudinal variation of the panel-type structure’s circumferential dimensions is taken into account according to specific rules. The Thin Plate Inverse Mapping (TPIM) meshless shape functions are introduced to characterize the displacement components associated with each substructure. Thermodynamic equations are formulated based on FSDT thermo-elastic theory as well as Hamilton’s principle. Rectangular and exponential pulse loads are taken into consideration for forced vibration analysis in this formulation. Numerical convergence and comparative cases are provided. Solutions from the literature and finite element simulation results are utilized for comparison, revealing that the percentage differences observed are all less than 0.025%. This confirms the reliability and accuracy of the developed analysis model. In conclusion, a detailed investigation is conducted on the influences of geometrical dimensions, boundary conditions, as well as thermal and external loads on the thermodynamic behaviors of FG panel-type structures with circumferentially variable dimensions.

Ritz Solutions of Stationary Random Vibrations for GPL-Reinforced FG Rectangular Plate

This paper aims to establish a comprehensive model for evaluating the response characteristics of functionally graded graphene platelet-reinforced composite (FG-GPLRC) rectangular plates under stationary random acceleration excitation. Utilizing the first-order shear deformation theory (FSDT) and Halpin–Tsai assumptions, a dynamic model for the rectangular plate is derived, followed by obtaining the variational solution using the Rayleigh–Ritz method. To describe displacement components associated with dynamic equations and boundary conditions, a spectral geometry method (SGM) is employed. Additionally, a pseudo-excitation method (PEM) is utilized for the analysis of stationary random vibration. The proposed calculation method is validated through convergence analysis and comparative evaluation with existing literature and finite element models. Furthermore, the study investigates the influence of various factors, such as boundary conditions, the number and size of functionally graded rectangular plate layers, GPL distribution types, and material parameters, on the stationary random response attributes of FG rectangular plates. This research contributes to a deeper understanding of the dynamic response of functionally graded materials in structural configurations and offers a valuable analytical approach for researchers in this field.

Legendre–Ritz solutions for vibration characteristics of three-dimensional double-layer lattice truss sandwich plates

In this paper, Legendre–Ritz solutions for vibration characteristics of double-layer lattice truss sandwich plates are proposed based on three-dimensional (3-D) elasticity theory. Double-layer lattice truss sandwich plates consist of three face sheets and two cores. The face sheets are composed of fiber-reinforced composites and the cores are composed of pyramidal lattice trusses made of isotropic materials. The pyramidal lattice core is equated to a homogeneous plate according to equivalence principle. Based on 3-D elasticity theory and pseudo excitation method (PEM), each layer's energy expressions of double-layer lattice truss sandwich plates are constructed. After that, Legendre polynomials are adopted to describe displacement components in length, width and thickness directions. On this basis, the Rayleigh-Ritz method is used to solve energy functions to obtain motion equations of double-layer lattice truss sandwich plates. The accuracy and validity of the present method are corroborated by comparisons with references and finite element method (FEM). Additionally, in order to find out effects of relevant parameters on dynamical characteristics of double-layer lattice truss sandwich plates, parametric studies are carried out by means of some numerical examples.