In order to reveal the influence of vertical and radial deformation and improve the accuracy of the calculation model of pile-soil dynamic interaction, an analytical solution of vertical dynamic impedance considering the three-dimensional wave influence of pile-soil is proposed. First, the Biot three-dimensional porous elastic medium governing equation is used to describe the dynamic behavior of saturated soil, and the pile is regarded as a three-dimensional rod with radial and vertical deformation, and its dynamic behavior is described by Navier motion equation. Then the motion equations of pile-soil are solved by the method of separation variables, and the dynamic impedance expression of pile is given. The accuracy of the proposed solution is verified by comparing with the FEM results and existing solutions. Finally, the three-dimensional solution is compared with the plane strain solution, the radial simplified solution and the one-dimensional solution. The results show that the radial deformation of the pile under the three-dimensional fluctuation effect has a significant effect on the dynamic impedance. Ignoring the radial deformation of pile will lead to overestimate the static stiffness of pile-soil system and underestimate the peak dynamic impedance of pile-soil system. When the excitation frequency �� ≤ 5 Hz, the utilization of the three-dimensional strict solution is more advantageous to obtain the dynamic impedance of the pile. In the range of excitation frequency, the radial deformation of single-phase soil can be ignored.

This article discusses the application of the method of integral equations for the numerical evaluation of sound scattering characteristics by a finite elastic cylindrical shell placed in a liquid medium and separated by one or more elastic partitions. The shell has hemispherical ends and is also filled with a liquid medium. The scattered sound field is determined based on the combined use of Kirchhoff-type integral equations and an integral equation for the displacement vector of an elastic medium obeying the Lame equation. Boundary conditions for stresses and displacements are formulated for each of the shell's contact surfaces with the external and internal media. The approach under consideration is based on the numerical transformation of continuous integral equations into a system of linear algebraic equations using curved isoparametric boundary elements. Based on the numerical results, a comparative assessment of the effect of the partition on the scattered sound field for various wave sizes of the shell and location angles was obtained.

This study presents a comprehensive vibration analysis of fluid-loaded sandwich microshells, featuring fluid-permeated high-performance porous cores and piezoelectric face sheet coatings supported on spatially varying Winkler-Pasternak elastic substrates. A fluid-saturated porous core with adjustable fluid permeation qualities is positioned between two piezoelectric face sheets in the sandwich microshell arrangement. The porous core demonstrates outstanding performance features. The impact of fluid saturation in the porous core is examined by the Skempton coefficient, which measures the correlation between pore pressure and applied stress in the fluid-saturated medium. The velocity potential function technique is used to explain the irrotational flow characteristics, and the fluid motion is controlled by the assumption of perfect fluid behavior. To account for size-dependent effects present in microstructures, the analytical framework combines modified strain gradient theory (MSGT) with first-order shear deformation theory (FSDT). Analytical solutions are obtained by applying Fourier series expansions to the governing equations of motion, which are derived from Hamilton's principle. Extensive parametric studies show that the factors that significantly affect frequency fluctuations include the liquid level, applied electric voltage, MSGT length scale parameters, elastic medium characteristics, imperfection type and Skempton coefficient.

Summary We simulate an instantaneous time mirror (ITM), i.e., a rapid short duration change in elastic material properties, using numerical experiments in time-varying isotropic elastic media. Our implementation in the seismic wave propagation software SeisSol is based on high-order discontinuous Galerkin discretization with ADER time stepping. We develop an eigenvector-based analytical solution for time interfaces for general linear hyperbolic wave systems and apply it to analyze the energy balance at time boundaries and ITMs. The energy increases for all intermittent medium changes for all impedance scaling factors. Our numerical implementation is validated against these analytical solutions and achieves high-order convergence. Its accuracy is further corroborated by estimates of reflection and transmission coefficients and observed frequency shifts across time boundaries, and by acoustic wave speed estimates obtained from focal spots associated with ITM-generated converging P waves that are consistent with theoretical predictions and ground truth values, respectively. We use the ITM implementation to simulate the partitioning of seismic body waves excited by a point source in a spatially homogeneous elastic full space. The response to an intermittent short change in the elastic parameters yields a diverging and converging P and S wavefield. A systematic scaling of the elastic parameters is then used to steer independent ITM reflections of either P or S waves. Numerical ITM solutions as developed here can be used to synthesize converging wavefields in seismic imaging applications, and more generally to analyze the behavior and manipulation of seismic wavefields in space-time varying media.

The paper discusses dislocations in an elastic medium within the geometric theory of defects. All locally flat separable metrics in three dimensions are found. They describe dislocations that occur by cutting (inserting) a wedge, ellipsoid, hyperboloid or paraboloid of rotation and elliptical, hyperbolic or parabolic cylinders with subsequent gluing of the formed edges. The obtained dislocations have an important property: variables in the corresponding Hamilton–Jacobi equation for geodesics are completely separable resulting in the Liouville integrability of geodesic equations. In addition, variables in the Laplace equation also admit complete separation of variables. To our knowledge, elliptic, hyperbolic and parabolic dislocations are described for the first time.

Summary Full-waveform inversion has been broadly adopted for acoustic and elastic media, but it lacks widely accepted methods for robust uncertainty quantification. This lack is in part due to an absence of assessment of proposed uncertainty quantification strategies. Here, we investigate four relatively inexpensive uncertainty estimation approaches based on truncated singular value decomposition of the inverse problem Hessian and its inverse. We numerically test these approaches across a range of parameter scales and application problems. We find that uncertainty estimates based on truncated singular value decomposition of the Hessian outperform those based on singular values of the inverse Hessian, due to both favorable singular value spectra of the former, and the greater ease of sampling the Hessian.

This paper investigates the thermal vibration characteristics of double-walled carbon nanotubes (DWCNTs) embedded in an elastic medium. Unlike most existing studies, we employ both strain-driven (eD) and stress-driven (sD) two-phase local/nonlocal integral models (TPNIMs) to account for nonlocal effects in the beam deformation, elastic foundation response, and thermally induced stresses simultaneously. The governing equations and associated boundary conditions are rigorously derived through Hamilton’s principle, establishing a complete thermomechanical formulation. The constitutive framework transforms integral relations between generalized strain and nonlocal stress fields into equivalent differential forms through systematic incorporation of constitutive boundary constraints. Notably, we provide closed-form solutions for nonlocal thermal stress components, capturing temperature-dependent effects. Numerical solutions for the vibration frequencies are obtained using the generalized differential quadrature method (GDQM). Our results demonstrate the significant influence of the nonlocal parameters, elastic foundation stiffness and thermal stress magnitude on the vibrational response. These effects are quantified for different boundary conditions, providing new insights into the thermo-mechanical behavior of DWCNTs.

This study investigates the propagation and reflection of harmonic plane waves in a homogeneous, isotropic, heat-conducting elastic medium governed by the Moore–Gibson–Thompson (MGT) thermoelasticity model. Using a perturbation technique for frequency-dependent analysis, we examine two coupled longitudinal waves—CP-type (elastic-dominant) and CT-type (thermal-dominant)—which exhibit dispersion and attenuation, while the uncoupled SV-type shear wave remains non-dispersive and undamped. At low frequencies, the CP-wave phase speed decreases by ∼4.6% and its attenuation rises by 15% as the thermoelastic coupling constant increases from 0.01 to 0.1. At high frequencies, the CT-wave attenuation is ∼40% lower than the CP-wave, indicating enhanced long-range energy transport. Reflection of CP-waves at rigid boundaries under insulated and isothermal conditions is analyzed, with copper showing a CT-wave reflection peak of 0.68 at ∼65° incidence, highlighting significant mode conversion. This work, focusing solely on the MGT model without non-local effects, provides quantitative insights into wave behavior, relevant for ultrasonic testing, seismic modeling, and thermal stress management.

Compared to the conventional high-order staggered-grid finite-difference method (C-SFD), the time–space domain dispersion-relation-based high-order staggered-grid finite-difference method (TS-SFD) can suppress the numerical dispersion more efficiently to achieve higher modeling accuracy when applied to numerically solving the velocity–stress acoustic equation. The enhanced modeling accuracy of TS-SFD is attributed to the difference-coefficient calculation approach based on the time–space domain dispersion relation, which makes the difference coefficients change adaptively with the propagation velocity of seismic waves in the medium. However, when numerical simulation of the velocity–stress elastic wave equation is conducted with TS-SFD, if the difference coefficients are calculated based on the time–space domain P-wave dispersion relation, the modeling accuracy of P-wave is high, while that of S-wave is low and vice versa . To address the limitation of TS-SFD in ensuring high modeling accuracy for both P- and S-wave, in this article, we propose a novel strategy to conduct elastic wave numerical simulation with TS-SFD, in which the decoupled P- and S-wave elastic wave equations are numerically solved with TS-SFD, and the difference coefficients are calculated based on the time–space domain P- and S-wave dispersion relations, respectively. Numerical dispersion analysis and numerical simulation examples show that the simulation strategy proposed in this article can ensure high simulation accuracy for both P- and S-wave. Stability analysis shows that this simulation strategy can effectively improve the stability of elastic wave numerical simulation with TS-SFD. In addition, the simulation strategy has the additional advantage of automatically separating the P- and S-wave, which provides a solid foundation for the subsequent analysis of P- and S-wave propagation characteristics in elastic media and elastic wave reverse time migration.

Buckling stability analysis of corrugated pipes buried in an elastic medium

Momentum bias within one-dimensional elastic media introduces non-reciprocal phenomena in the propagation of elastic waves, manifesting as Willis coupling in the governing wave equation. To the best of our knowledge, the implications of Willis coupling being the sole coupling mechanism within elastic media and the understanding of non-reciprocity through finite structure analysis remain unexplored. In this paper, a non-reciprocal wave phenomenon with pure Willis coupling is synthesized using feedback control in mechanical lattices consisting of masses, grounded springs, and linear actuators. The proposed system presents a unique lack of physical connections between masses, allowing for pure Willis coupling through feedback forces exerted by the linear actuators. The dynamical behavior of a unit cell segment from an infinite lattice chain is considered, and the emergent non-reciprocal dispersion relation is detailed, including an analytical quantification of the Brillouin-zone translation resulting from pure Willis non-reciprocity. Analytical derivations of the eigenpairs of a finite lattice configuration are established, and the theoretical analyses reveal the mechanism of non-reciprocity through the lens of the lattice's natural frequencies and corresponding mode shapes.

Rapid computation of sound transmission in fluid-filled pipes coupled with an outer elastic medium

Homogenization model for a dense elastic medium of cylindrical scatterers and based on a realistic pair correlation function

Exceptional points and chiral mode conversion in non-Hermitian elastic media

Numerous studies have examined soil-structure interaction (SSI) effects on the seismic response of high-rise buildings, comparing them to fixed-base models. These investigations have integrated SSI into dynamic analyses and highlighted key provisions in major seismic codes. However, most research focuses on regular structures with uniform mass, stiffness, and strength distribution, while only a few addresses geometric irregularities. (Stewart, 2012 & J-Priyadarshini, 2013). This study employs ROBOT Structural Analysis 2019 to numerically model an irregular 8-storey reinforced concrete structure (with horizontal and vertical irregularities) under seismic loading, considering SSI and comparing its response to that of a regular structure. The soil is modeled as a homogeneous, linearly elastic medium using spring elements. Four dynamic analyses are performed: one with a fixed base and three incorporating SSI for different soil types per the Algerian Seismic Code (RPA 2024) . These analysis results are compared with those of the fixed-base structure. The findings indicate that the effect of the ISS on the dynamic modal response (particularly the fundamental period) grows with soil flexibility and becomes even more pronounced in irregularly shaped structures. Thus, both structural irregularity and the flexibility of soil amplify the ISS’s impact on dynamic behavior. Regarding seismic response, fixed-base assumptions lead to overestimated internal forces in walls and columns for all building types, while relative displacements are underestimated in regular buildings and show a more significant increase in irregular ones. The results demonstrate that soil-structure interaction significantly affects the seismic performance of buildings, particularly those with irregular geometry

We propose an ultrasonic metamaterial characterized by triple-negative effective material properties of mass density, bulk modulus, and shear modulus for wave penetration through elastic barriers. A theoretical framework based on a transformation method with folding and compression mapping reveals that triple negativity is pivotal for metamaterials to serve as elastic complementary media. Our metamaterial features a rotationally symmetric and crosswise arrangement of coated mass inclusions embedded within a base matrix. This design is tailored to attain triple negativity originating from the dipolar, monopolar, and quadrupolar resonances induced by collective motion between the inclusions and the base matrix. Due to its triple negativity, ultrasonic waves undergo near-zero reflections and near-zero phase changes as they traverse the metamaterial and barrier, acoustically canceling out the physical space of the blocking medium. Numerical simulations under an ultrasonic beam demonstrate that the metamaterial, when partially attached to the incident side of an elastic barrier, remarkably enhances the acoustic intensity from 2% to 72% in the transmitted region. The proposed metamaterial holds broad potential for diverse applications, including antireflection coating, non-destructive testing, underwater communication, and ultrasonic neuroimaging.

Abstract Using a classical irreversible thermodynamics of internal variables (CIT-IV) with Ciancio’s procedure, viscous-inelastic flow relations have been derived by generalizing the Duhamel-Neumann law for ordinary thermoelastic phenomena in isotropic media and the relations for elastic media and for Maxwell, Jeffreys and Poynting-Thomson bodies. Furthermore, a heat equation with two relaxation times has been derived that generalizes the Fourier and Maxell-Catteno-Vernotte (MCV) equations without having to introduce assumptions that are non found sense in physics. In this paper the authors not only apper to be effective from a mathematical point of view but is direct in physical applications. In this context, through the simple description of the ultra-fast process of energy transmission from a laser source to metal film, using the principles of thermodynamics, the heat equation is derived in the case of isotropic viscoanelastic media subject to constant strain. The solution, obtained numerically with the finite element method, not only highlights the physical significance of the phenomenological coefficients, but also specifies the limits of the previous theories of the MCV.

Summary Realistic models of earthquake sequences can be simulated by assuming faults governed by rate-and-state friction embedded in an elastic medium. Exploring the possibility of using such models for earthquake forecasting is challenging due to the difficulty of integrating Partial Differential Equation (PDE) models with sparse, low-resolution observational data. This paper presents a machine-learning-based reduced-order model (ROM) for earthquake sequences that addresses this limitation. The proposed ROM captures the slow/fast chaotic dynamics of earthquake sequences using a low-dimensional representation, enabling computational efficiency and robustness to high-frequency noise in observational data. The ROM’s efficiency facilitates effective data assimilation using the Ensemble Kalman Filter (EnKF), even with low-resolution, noisy observations. Results demonstrate the ROM’s ability to replicate key scaling properties of the sequence -namely the magnitude-frequency, moment-duration, and moment-area relationships- and to estimate the distributions of fault slip rate and state variable, enabling predictions of large events in time and space with uncertainty quantification. These findings underscore the ROM’s potential for forecasting and for addressing challenges in inverse problems for nonlinear geophysical systems.

A crack-like defect in the form of a physical section with a characteristic thickness in a linearly elastic medium is studied. The thickness of the physical section is considered as a linear parameter. For an external load, the stress-strain state of the neighborhood of the physical section is determined by the finite element method, allowing stress vectors on the free surface to be different from zero. On the basis of the thermomechanical relation, the energy characteristic of the J-integral type, including stress vectors on the free surface in the vicinity of the crack-like defect, is determined in the form of three additive integral summands. The part of the energy characteristic on the end surface of the physical section and the summands on the shores contiguous to the end are isolated. We solved the loading problems of applying normal rupture and transverse shear to the physical section based on the solution in the finite element complex ANSYS for the physical section and the model of representation of the medium on the continuation of the physical section as a layer, which is homogeneous in the thickness distribution of the stress-strain state. We compared the energy response, when the linear parameter tends to zero value, and the values of the J-integral for the crack representation in the form of a mathematical section. The correspondence of the J-integral value for the mathematical section to the considered energy characteristic at a relatively small value of the linear parameter is obtained. At the same time, its part on the end surface, depending on the model under consideration, is more than sixty per cent. For the physical section using the layer model, the closeness of the investigated characteristic to the value of the J-integral for the mathematical section is shown at a significantly lower value of the elastic modulus of the layer material with respect to the basic medium. At the same time, the influence of non-face summands of the energy characteristic is found to decrease.

The article presents the analysis of asymptotic series expansions generalized to the case of anisotropic linearly elastic media representing fields of displacements, strains and stresses around the tip of an acute crack in anisotropic media. We study anisotropic materials with the simplest cubic symmetry and fields in the proximate neighbourhood of the crack tip. The asymptotic series are constructed on the essential principles of the classical theory of elasticity of an anisotropic body. By analyzing the series associated with the fields at the crack tip, it is shown that higher approximations with coefficients called generalized stress intensity factors have an essential impact on the accurate and relevant representation of the stress field to expand the zone of the asymptotic solution. Using the example of a plane problem for an infinite anisotropic plane with the cubic symmetry of properties (with different tensors of elastic modules having three independent elements) with different crack orientations relative to the axes of the symmetry of elastic properties, it is shown that in the generalized series, in addition to the first two terms (containing stress concentration factors and T-stresses), terms of higher orders of smallness should be preserved. The circumferential -apportionments of the stress components at various spans from the crack tip are assembled with the retention of a different quantity of series terms to obtain sufficiently accurate approximations. A comparison of the dependencies of the tensor components on the polar angle obtained taking into account the different quantity of series terms clearly indicates the need to retain the higher approximations of the series. In order to expand the area in which the solution in the series is valid, it is necessary to preserve a larger number of terms. All computations were performed for real materials which elastic constants were determined using the molecular dynamics method for single-crystal substances with a face-centered cubic (FCC) lattice.