In this paper, the governing differential equation of a beam with axial force is studied using the Lie symmetry method. Considering the inhomogeneous beam and non-uniform axial load, the governing equation is a fourth-order linear partial differential equation with variable coefficients with no closed-form solution. We search for a favourable coordinate system where the governing equation has a simpler-form

A nonlocal Kirchhoff plate model with fourth-order strain gradient theory is firstly proposed to study variations with band gap frequencies and vibration energy distribution. The temperature rise is supposed to vary linearly through the thickness of the periodic nanoplate structures. The dynamic equations of finite periodic nanoplate structures under thermal load with the small-scale effect and the

It is a key to reveal the failure mechanism and constitutive relation of the anchor segment of the anchor cable. By using the self-developed pull-twist coupling device, the pull-out tests for anchor cables with non-rotation and free rotation conditions were carried out, respectively, and the pull-out load–torque–displacement curves were obtained to study the failure mechanism and constitutive relation

Structures made of functionally graded materials (FGM) are successful attempts to enhance the mechanical properties of homogeneous materials. On the other hand, periodically architected structures provide phenomenal opportunities to design structures much lighter than their bulk counterparts showing exceptional mechanical characteristics. In the present study, to utilize the advantages of both technologies

A novel thermodynamic framework for the continuum mechanical response of nonlinear solids is described. Large deformations, nonlinear hyperelasticity, viscoelasticity, and property changes due to evolution of damage in the material are all encompassed by the general theory. The deformation gradient is decomposed in Gram–Schmidt fashion into the product of an orthogonal matrix and an upper triangular

The linear crack between two dissimilar elastic isotropic half-spaces under normal pulse loading is considered. The system of boundary integral equations for displacements and tractions in the frequency domain is derived from the dynamic Somigliana identity and adapted to solve the problem in the time domain. The numerical convergence of the method with respect to the number of the Fourier coefficients

Defects including topological and vacancy defects have been observed in graphene during fabrication. Defects are also introduced to break the lattice symmetry of graphene and thereby obtain enhanced optoelectronic and other properties. It is important that gains in certain properties due to the presence defects are not at the expense of mechanical strength which is important in handling graphene and

Nanoporous materials exhibit remarkable mechanical properties, which are influenced by their surface effects and microstructures. Here, we theoretically analyze Young’s modulus of various regular polygonal prism structures, which represent the first-level (conventional) nanoporous material and higher-level hierarchical nanoporous material. The effects of surface elastic modulus, porosity, residual

This paper aims to study the buckling and bending analysis of curvilinearly stiffened plates by using an isogeometric approach. First-order shear deformation theory is adopted to model the behaviors of stiffened plates. Based on the employed approach, it is easy to model stiffeners with different sizes and layouts, since the degrees of freedom for the whole structure are integrated into those of the

In the current paper, the vibrational behavior of viscoelastic cylindrical shells under moving internal pressure is studied, analytically. The viscoelastic behavior is considered as viscoelastic in shear and elastic in the bulk. The equations of motion are extracted based on the classical shell theory by applying Hamilton’s principle. These equations which are a system of coupled partial differential

In this paper, we analyze a linear problem describing the vibrations of a coupled suspension bridge. The single-span roadbed is modeled as an extensible thermoelastic beam of Timoshenko type. The main cable is modeled as an elastic string and is connected to the roadbed by a distributed system of elastic springs. For this linear model, we obtain the existence and uniqueness of solutions by using the

A novel active elastic metamaterial plate is proposed, with tunable vibration band-gap characteristics is by using the periodically placed piezoelectric actuator and sensor pairs along one direction of the plate. Active control strategies are employed to actively adjust the band-gap properties of the metamaterial plate. Displacement and acceleration feedback control methods are applied to design the

We first characterize strain solitary waves propagating in a fluid-filled membrane tube when the fluid is stationary prior to wave propagation and the tube is also subjected to a finite stretch. We consider the parameter regime where all traveling waves admitted by the linearized governing equations have nonzero speed. Solitary waves are viewed as waves of finite amplitude that bifurcate from the quiescent

We consider the axisymmetric contact problem of a multi-elastic layer with various elastic constants bonded to an elastic semi-infinite substrate indented by rigid flat-ended cylindrical and spherical indenters. The transfer matrix method is applied to each elastic layer, and dual integral equations are reduced to an infinite system of simultaneous equations by expressing the normal contact stress

In this paper, we deal with the numerical analysis of the Lord–Shulman thermoelastic problem with porosity and microtemperatures. The thermomechanical problem leads to a coupled system composed of linear hyperbolic partial differential equations written in terms of transformations of the displacement field and the volume fraction, the temperature and the microtemperatures. An existence and uniqueness

The transversely isotropic response of pristine as well as defective boron nitride nanotubes (BNNTs) containing Stone–Wales (SW) defects was comprehensively studied via molecular dynamic simulations with a three-body Tersoff force field. The elastic properties and the failure behavior of BNNTs were studied under the transversely isotropic loading conditions, namely uniaxial tension, twisting moment

This paper introduces the interval perturbation method into the sensitivity analysis of statistical energy analysis (SEA) models. The damping loss factors and coupling loss factors are treated as the design parameters, while the modal energy of each subsystem is considered as the decision-making target. The variation of the design parameter is characterized by an interval form, and the ratio between

Eringen’s nonlocal elasticity theory is one of the most attractive approaches to investigate the intrinsic scale effect of nanoscopic structures. Eringen proposed both integral and differential nonlocal models which are equivalent to each other over unbounded continuous domains. Although the Eringen nonlocal models can be used as very useful tools for modeling the mechanical characteristics of nanoscopic

In this paper, the dynamic stiffness method (DSM) is developed for the vibration analysis of laminated cylindrical and conical shells, which are partially filled or surrounded by quiescent fluid. The Reissner and Naghdi’s thin shell theory and incompressible fluid equations are employed on the structures and fluid, respectively, so as to characterize the fluid–structure coupling model. Shell elements

The current work describes the optimum design of a tuned mass damper inerter (TMDI) to control a benchmark 10-story base-excited linear shear building under seismic excitations. Mass and inertance ratios are preselected, and optimum free vibration parameters of the TMDI (i.e., natural frequency and damping ratios) are calculated for single degree-of-freedom (SDOF) and multi degree-of-freedom (MDOF)

Problems of inflation, extension and torsion of hyperelastic rods and tubes are of great interest for modelling and characterizing rubber-like materials and soft biological tissues. For incompressible and compressible hyperelastic tubes, analytical solutions for the problem of inflation, extension and torsion have not been proposed. In this research, the problem of inflation, extension and torsion

The purpose of this paper is to understand the capability and consistency of large eddy simulation (LES) in Eulerian–Lagrangian studies aimed at predicting inertial particle dispersion in turbulent wall-bounded flows, in the absence of ad hoc closure models in the Lagrangian equations of particle motion. The degree of improvement granted by LES models is object of debate, in terms of both accurate

We derive the equations of motion for the dynamics of porous medium, filled with incompressible fluid. We use a variational approach with a Lagrangian written as the sum of terms representing the kinetic and potential energy of the elastic matrix, and the kinetic energy of the fluid, coupled through the constraint of incompressibility. As an illustration of the method, the equations of motion for both

Based on Hamilton’s principle, a general three-dimensional mechanical model with consideration of the consistent couple stress theory is established in this paper, and the dynamic governing equations and boundary conditions are derived strictly. After that, inspired by the high-frequency theory established by Mindlin, a novel two-dimensional theory of micro-plates is proposed. Governing equations and

This paper examines the effect of traversing vehicles on the vibration of the supporting bridge. It shows that the effect of vehicle–bridge interaction (VBI) on the mechanical system of the bridge breaks down into three constituent mechanisms: (a) an additional damping, (b) an additional stiffness, and (c) a modified loading term. The study characterizes these three mechanisms with explicit analytical

This paper examines a condition for the existence and uniqueness of a finite deformation field whenever a Gram–Schmidt (QR) factorization of the deformation gradient \({\mathbf {F}}\) is used. First, a compatibility condition is derived, provided that a right Cauchy–Green tensor \({\mathbf {C}} = {\mathbf {F}}^T {\mathbf {F}}\) is prescribed. It is well-known that under this condition a vanishing of

This paper focuses on the boundary control of a Timoshenko beam with a tip mass in space. Compared with an Euler–Bernoulli beam model, the coupling of the Timoshenko beam’s transverse vibration and its cross-sectional rotation makes it difficult to develop the controller. The Timoshenko beam is essentially a distributed parameter system, the motion of which can be described using partial differential

When a single-degree-of-freedom underdamped system is subjected to a step function force in order that it eventually acquires a constant displacement, its response shows undershoots and overshoots. Since a step function force is difficult, if not impossible, to apply to many aerospace, civil, and mechanical engineering systems because of their inertias, this paper looks at simple forces that can be

In this study, an aeroelastic model that accounts for the fluid–structure interaction is developed to investigate vibration and stability of rectangular plates in contact with sloshing fluid on one side and under supersonic aeroelastic load on the other side. The fifth-order shear deformation theory, which is capable of considering rotary inertia and transverse shear stress, is employed to model the

Nanoindentation is employed to characterize the mechanical properties at the nanoscale. This paper considers the mechanical response of a nanoscale elastic layer on an elastic substrate that is indented by an adhesively bonded flat-ended rigid cylindrical punch. The complete Gurtin–Murdoch continuum model is employed to capture the size effects. The contact problem is analyzed by relating displacements

This paper aims to investigate the free and forced vibration behavior of a sandwich beam with functionally graded porous core and composite face layers embedded with shape memory alloy (SMA). Three different porosity patterns are assumed through the thickness direction of the core, and composite face layers are reinforced with carbon nanotubes (CNT). The sandwich beam is resting on an elastic foundation

Pore pressure variations owing to fluid injection-extraction from deep sedimentary basins can potentially trigger shear slipping along pre-existing faults. We use a coupled two-phase flow and geomechanical model to better understand the physical processes associated with simultaneous injection of \(\hbox {CO}_{2}\) and production of \(\hbox {CH}_{4}\). The model considers permeability changes induced

The present paper studies the fundamental solution and plane wave propagation in swelling porous thermoelastic material. It is observed that there exist three longitudinal waves and two transversal waves propagating with different velocities. Numerical computations are performed to obtain the phase velocity and attenuation coefficients of plane waves in the medium and the values so obtained are presented

Using conformal mapping and the image method, we derive an analytic solution to the problem of an isotropic elastic bimaterial involving a screw dislocation interacting with a semi-infinite interface crack, a semi-infinite crack in the upper half-plane perpendicular to the interface, and another semi-infinite crack in the lower half-plane also perpendicular to the interface. Closed-form expressions

Under compression, a cyclically precompressed nanopillar supports greater load than its as-fabricated counterpart. Such an improvement on mechanical properties takes place only when the preloading process is tuned carefully with regard to a particular pillar being tested. This experimental evidence raises a question: does a cyclic preloading applied simultaneously to an ensemble of nanopillars enhance

The dynamic crushing behaviors of FCC lattice structures with various rotation angles are explored by numerical simulations. According to the localization band formed by the cell collapse, several deformation modes are distinguished. The effects of the orientation angle and the crushing velocity on the mechanical properties of the lattice are investigated. It is shown that the deformation mode depends

This paper provides an exact solution for a cusp-type crack problem in plane elasticity. The solution of the studied problem depends on the conformal mapping technique and complex potentials. The stress intensity factors at the cusp-type crack tip can be evaluated accordingly. Some particular characters for the SIF (stress intensity factor) solution have been found. Particularly, if a compression loading

Sea ice is floating ice which is formed by the freezing of ocean water in the polar regions of the Earth, i.e., the Arctic and the Antarctic. Thus, a closed smooth ice surface can be formed consisting of these ice configurations. In recent years, the simulation of sea ice evolution, especially for the use in climate models, became more important, see, for instance, Danilov et al. (Geosci Model Dev

A mode-III crack embedded in a homogeneous isotropic elastic layer of nanoscale finite thickness is studied in this article. The classical elasticity incorporating surface elasticity is employed to reduce a nonclassical mixed boundary value problem, where the layer interior obeys the traditional constitutive relation and the surfaces of the layer and the crack are dominated by the surface constitutive

This paper compares simple interatomic potentials for carbon nanostructures with hexagonal lattice, by investigating the in-plane and the out-of-plane tensile behaviour of single-layer graphene sheets. Attention is given both to potentials already considered in the literature and to a new one, which we call the damped DREIDING potential, in which damping functions are added to the DREIDING potential

This paper investigates the bandgap properties of a piezoelectric periodic nano-beam considering size and surface effects using a modified couple stress theory. The nano-beam is made of some finite periodic arrays of piezoelectric (PZT-5H) and epoxy segments. The Bloch theorem for periodic materials together with the transfer matrix method are employed for analyzing the problem. The band structure

Microbeam resonators are widely used due to their scientific and engineering applications. The accurate prediction of thermoelastic damping (TED) is necessary to evaluate the performance of resonators at micro- and nanoscales with less energy dissipation. This article aims to present an analytical method for analyzing TED and dynamic behavior of microbeam resonators based on the Moore–Gibson–Thompson

In this paper, we research Noether’s theorems of fractional generalized Birkhoffian systems in terms of classical and combined Caputo derivatives. First, the generalized Pfaff–Birkhoff principle and Birkhoff’s equations with classical and combined Caputo derivatives are given. Then, in the case of without and with transforming time, respectively, we obtain two kinds of Noether symmetry and their conserved

An effective technique is proposed for identifying the track modulus, i.e., the foundation stiffness of the rails, using the contact-point response of the moving test vehicle. First, for a simple beam resting on an elastic foundation under a moving sprung mass, closed-form solutions are derived for the responses of the vehicle and its contact point with the rail. It is shown that the track modulus

Resonance phenomena in impacting systems can be defined as an amplitude increasing during periodically applied impacts. The wave cancellation phenomenon is defined as application of certain conditions to cancel the wave fully. The double impact system is defined as the application of the first impact with a certain duration \(\tau \) and then the application of a counter impact in a certain time \(\tau

An analytical solution is given to the problem of non-uniform torsion of an elliptical cylinder made of functionally graded anisotropic linear elastic material. The material moduli of the considered anisotropic non-homogeneous elastic bar are smooth functions of the axial coordinate. The contour of the elliptical cross section depends on the elastic constants. This dependence provides the zero warping

The stationary probability density function (PDF) solution of a variable-mass system is calculated under Gaussian white noises and Poisson white noises, respectively. For small mass disturbance, the corresponding Fokker–Planck–Kolmogorov equation and Kolmogorov–Feller equation of the system are derived. The solution procedure based on the exponential–polynomial closure (EPC) method is formulated to

This paper considers solutions that can determine the nature of the stress singularity in the vicinity of a singular point for two-dimensional and three-dimensional closed composite wedges. A comparative analysis of stress singularity exponents is carried out for closed composite wedges with perfectly bonded interfaces and homogeneous wedges with stress-free edges. Using analysis results, it is possible

The present article deals with the propagation of Rayleigh surface waves in a homogeneous orthotropic medium based on Eringen’s nonlocal thermoelasticity. This thermoelastic problem is studied under the purview of Green–Naghdi model type III of hyperbolic thermoelasticity in the presence of voids. The normal mode analysis is employed to obtain a vector matrix differential equation which is then solved

The temperature variation within two elastic bodies in perfect thermoelastic contact may cause the contact area to become convex and hence lead to a reduction in the size of the contacting surface. In receding thermoelastic contact problems, the final size of the contact zone is independent of the applied loads, being only affected by the thermomechanical properties of the solids. However, the final

In this article, a novel mathematical model is theoretically developed by incorporating a memory-dependent derivative (MDD) into the temperature-rate-dependent thermoelasticity theory (Green–Lindsay) on three mathematical aspects in order to study the spatial behavior of the thermal signals in an isotropic, homogeneous, thermoelastic continuum. Firstly, to ensure the thermodynamic consistency of the

The present work analyzes numerical simulations of long flexible fibers in two-dimensional flows. The focus is on the frequency at which caustics occur and the characterization of the collisions among fibers. The continuous flexible fibers are modeled as a set of connected rigid cylinders, where forces are applied to the center of mass of each cylinder determining their motion and fiber deformation

The present investigation is concerned with the reflection of plane waves at the free surface of a homogeneous, isotropic, nonlocal, micropolar rotating thermoelastic medium. The entire thermoelastic medium is rotating with a uniform angular velocity. It is observed that there exist four coupled plane waves, which travel through the medium with distinct speeds. Using appropriate boundary conditions

An interesting recent finding is that, in a medium of nearly linear elastic materials, the stem cell differentiation responds to the Young’s modulus of elasticity. It is discussed here that the more general mechanical identifier of differentiation is indeed the stiffness (rather than the Young’s modulus). Specifically, for nonlinear (and thus more realistic/physiologically mimetic) materials the stiffness

This work documents the first account of advanced mechanical properties of six commercial lipsticks, some of which serve as market leads. We systematically studied their nonlinear viscoelastic properties under large amplitude oscillatory shear deformations. At large strains, all lipsticks showed intercycle strain softening, the extent of which initially depended on the prototype in the nonlinear regime

The present work is devoted to the investigation of the free vibrations of a homogeneous isotropic nonlocal thermoelastic cylinder with void. Time-harmonic variations are used to reduce the governing partial differential equations to a system of ordinary differential equations. The frequency equation for the continuation of vibrations for the mode numbers in the considered cylinder is deduced in closed

A review is presented of measurement techniques to characterise dispersed multiphase flows, which are not accessible by means of conventional optical techniques. The main issues that limit the accuracy and effectiveness of optical techniques are briefly discussed: cross-talk, a reduced signal-to-noise ratio, and (biased) data drop-out. Extensions to the standard optical techniques include the use of

The paper focuses on the evaluation of the effective properties of linear viscoelastic composites with a periodic structure, containing long cylindrical fibers of circular cross-section and for two different cell arrangements: square and hexagonal unit cells. For this purpose, we use the two-scale asymptotic homogenization method (AHM) and a numerical homogenization method (NHM). Based on the correspondence

This paper presents a new total Lagrangian Timoshenko beam formulation with the isogeometric analysis approach for a geometrically nonlinear analysis of planar curved beams. The proposed formulation is derived from the two-dimensional continuum theory, and a beam configuration is characterized by the beam axis and the director vectors of cross sections. Non-uniform rational B-spline (NURBS) curves

In this work, the behavior of a temperature-sensitive hydrogel micro-channel is investigated by considering fluid–structure interaction (FSI). The micro-channel behavior is simulated numerically via both FSI and non-FSI frameworks. The results show the importance of FSI effects in these devices. FSI consideration affects the performance of the under-study micro-channel such as its closing temperature