Hyperbolic neutral points of plane magnetic fields are the main feature in simple models of magnetic reconnection. There is some discussion on the stability of the magnetic geometry as depending on the boundary conditions. We consider a classical family of self-similar solutions to the magnetohydrodynamic equations in a bounded neighborhood of the neutral point and connect them with well behaved solutions

This study considers finite elastic deformation and rupture in rubber-like materials under quasi-static loading conditions by employing the bond-associated weak form of peridynamics with nonuniform horizon. The weak form of peridynamic equilibrium equation is derived based on the Neo-Hookean material model with slight compressibility. The nonlocal deformation gradient tensor is computed in a bond-associated

The problem of finding the equilibrium conditions for the stand of a physical pendulum to which, in particular, the forces of dry (Coulomb) friction are applied, is treated. Two statements of the problem are considered: the symmetric case of the system plane-parallel motion and the case of supporting of the stand on a horizontal plane by three points. The certain problems on equilibrium of a rigid

For systems of partial differential equations in three spatial dimensions, dynamical conservation laws holding on volumes, surfaces, and curves, as well as topological conservation laws holding on surfaces and curves, are studied in a unified framework. Both global and local formulations of these different conservation laws are discussed, including the forms of global constants of motion. The main

The stability and bifurcation behaviors of fractional-order vibro-impact system are investigated, where a two-degrees-of-freedom vibro-impact oscillator excited by external harmonic excitation is considered. The approximate analytical solution of the fractional-order vibro-impact system is acquired based on the approximate equivalent integer-order system of fractional-order system obtained by the averaging

In this paper, we consider a system of balance laws sufficiently general to contain the equations describing the thermomechanics of a one-dimensional continuum; this system involves some constitutive functions depending on the elements of the so called state space assumed to contain the spatial gradients of some of the unknown fields. The compatibility of the constitutive equations with an entropy-like

A stochastic averaging method for single degree of freedom(SDOF)strongly nonlinear system under combined harmonic and Poisson white noise excitations is proposed by using generalized harmonic functions. The averaged stochastic differential equations (SDEs) and the Generalized Fokker-Plank-Kolmogorov (GFPK) equation for the stationary joint probability density of amplitude and phase difference are derived

A path integration method is used to discuss the stochastic response of a marine riser excited parametrically and externally by correlated Gaussian white noises. On the basis of the nonlinear vibration equation of a marine riser, the first-order vibration mode is studied and its governing equation is formulated. The response probability density function (PDF) is further developed by a path integration

In this study, a new approach is developed to determine the starting pressure head gradient and flowrate of a Bingham plastic through a fractal fracture network. The trace length of fracture is assumed to follow a power-law fractal distribution. The aperture of the fracture is related to the trace length by a scaling relationship. Flow in each fracture is treated as rectangular channel-type flow. A

This paper presents a kinematic assumption free and thermodynamically consistent non-linear formulation incorporating finite strain and finite deformation for thermoviscoelastic plates/shells based on the conservation and balance laws of the classical continuum mechanics (CCM) in R3 (see Surana and Mathi, (2020) for linear theory). The conservation and balance laws in Lagrangian description with finite

Ridge-cracked blisters form when ridge cracking occurs in a biaxially compressed film on a relatively rigid substrate during buckle-delamination. The observation of telephone-cord (TC) blister with wavy ridge crack indicates that the ridge-cracked blister is not straight-sided as it used to be. How ridge cracking influences the profile of buckle-delamination remains unclear. Based on Föppl–von Kármán

Varying time delay feedback has found wide applications in stabilization and controlling of nonlinear dynamic systems. It has been a challenging topic to analyze nonlinear systems with time delay feedback, especially when the delay is varying. Here in this paper an analytical criterion is deduced, according to which alternate stability switches can be determined for nonlinear oscillators equipped with

A constitutive relation was developed in Part I for describing the response of a class of visco-elastic bodies, wherein the left Cauchy–Green tensor, the symmetric part of the velocity gradient, and the Cauchy stress tensor are related through an implicit constitutive relation. Here, we study a boundary value problem within the context of the model namely the inhomogeneous deformation of the body,

Robotic Automated Fiber Placement (RAFP) has revolutionized manufacturing of large aerostructures in recent years. From producing lower costing parts to reducing scrap, RAFP has also helped in manufacturing large parts with contours precisely, with repeatable production once the RAFP machine is programmed. RAFP manufacturing allows a designer to utilize curvilinear fiber paths specifically designed

Precision motion stages are used in advanced manufacturing, metrological applications, and semiconductor industries for high precision positioning with high speed. However, friction-induced vibration undermines the performance of a servo-controlled motion stage. Recently, it was found that passive isolation in the form of friction isolator is very effective to mitigate the undesirable effects of friction

A nonlinear stochastic delay differential system with symmetry SD oscillator is investigated to detect weak signal. Firstly, the stochastic Melnikov function and the chaos threshold are obtained by using the stochastic mean square criterion. Secondly, the stochastic center manifold and the stochastic averaging method are used to obtain the one-dimensional Itoˆ equation and the corresponding FPK equation

Cavitation in soft solids has been intensively studied in the past. In previous works, soft solids are often assumed to be incompressible in the modeling. However, in practice, many soft solids are compressible. In this article, we try to find analytical solutions of cavity expansion in a slightly compressible hyperelastic solid. In the formulation, we adopt one commonly used compressible neo-Hookean

The free vibration displacement of an undamped hardening Duffing oscillator is described in exact form by a Jacobi elliptic function. Unlike an undamped linear oscillator, whose displacement is described by a trigonometric function, a Jacobi elliptic function is difficult to interpret by a simple inspection of the function arguments. The displacement of a linear oscillator is often visualised as a

In order to improve vibration isolation, soft components can be used in engineering applications, but this can lead to excessive static deflection. An ideal vibration isolator should have a high static stiffness to ensure that it has sufficient load carrying capacity; at the same time, it should have a low dynamic stiffness to maximize the vibration isolation frequency range. Recently, high static

A finitely deformed elastic half-space subject to compressive stresses will experience a geometric instability at a critical level and exhibit bifurcation. While the bifurcation of an incompressible elastic half-space is commonly studied, the bifurcation behavior of a compressible elastic half-space remains elusive and poorly understood to date. The main objective of this manuscript is to study the

The Acoustic Black Hole (ABH) effect refers to a special vibration damping technique adapted to thin-walled structures such as beams or plates. It usually consists of a local decrease of the structure thickness profile, associated to a thin viscoelastic coating placed in the area of minimum thickness. It has been shown that such structural design acts as an efficient vibration damper in the high frequency

In this paper, an efficient numerical strategy is used to study the geometrically nonlinear static bending of functionally graded graphene platelet-reinforced composite (FG-GPLRC) porous plates with arbitrary shape. Porous nanocomposite plates including cutout with various shapes can be modeled by the present approach. Four types of porous distribution scheme and four GPL dispersion patterns are selected

In this paper, we develop a 2-dimensional membrane model for the inelastic response of nominally leathery materials applicable to many tissues, particularly skin. These materials, while nominally elastic, show substantial and complex hysteretic response under cyclic loading (usually referred to as the Mullins-type softening). Furthermore, they exhibit both rate dependent behavior and permanent residual

The symmetric snap-through response of a bistable structure, composed from two beams, coupled via a rigid truss at their midpoint, is studied when subjected to a distributed electrostatic load. Both beams are double clamped and initially curved. The analysis is based on a reduced order (RO) model, resulting from Galerkin’s decomposition. For the base functions, symmetric buckling modes are used for

Digital Light Synthesis (DLS) technology creates ample opportunities for making 3D printed soft polymers for a wide range of grades and properties. In DLS, a 3D printer uses a continuous building technique in which the curing process is activated by an ultra-violet (UV) light. In this contribution, EUP40, a recently invented commercially available elastomeric polyurethane (EPU) printed by the DLS technology

We consider a nonholonomic system that describes the rolling without slipping of a spherical shell inside which a frame rotates with constant angular velocity (this system is one of the possible generalizations of the problem of the rolling of a Chaplygin sphere). After a suitable scale transformation of the radius of the shell or the mass of the system the equations of motion can be represented as

The primary resonances of a pre-deformed rotating beam model including the quadratic and cubic nonlinearities are investigated in the presence of the 3:1 internal resonance. The steady state responses of the beam are analyzed in two cases of the primary resonance with the method of multiple scales. The original dynamic equation is integrated numerically in two frequency sweep directions. The theoretical

This paper introduces a homogenization-based constitutive model for the large-strain mechanical response of elastomeric syntactic foams subject to arbitrary quasistatic loading and unloading conditions. Based on direct observations from experiments, this class of emerging foams are considered to be made of a nonlinear elastic matrix filled with a random isotropic distribution of hollow thin-walled

This paper investigates the dynamic snap-through buckling of classical and non-classical curved beams subjected to a suddenly applied step load. The small scale effect prevalent in non-classical beams, viz, micro and nanobeam, is modeled using the nonlocal elasticity approach. The formulation accounts for moderately large deflection and rotation. The governing equilibrium equations are derived using

We study approximate Hamiltonian symmetries and related first integrals for perturbed Hamiltonian systems. The approximate Hamiltonian symmetry expressed in evolutionary form gives rise to an approximate first integral provided it satisfies certain criteria. We provide formulas to deduce an approximate first integral for any given approximate Hamiltonian symmetry in three ways. As applications, mainly

Aerospace vehicle structures in the supersonic regime flight have their outer skin subjected to unsteady aerodynamic and thermal loading, which may lead to aeroelastic instability. Typical aerospace structures are built as multiple adjacent panels, the so-called multi-bay configuration, but early efforts to predict the supersonic flutter were based on a single panel arrangement. This work evaluates

The nonlinear panel flutter behaviour of two-dimensional porous curved panel reinforced by graphene platelets exposed to a supersonic flow is investigated. A curved beam element developed based on the trigonometric shear deformation theory is employed. The formulation integrates the geometric nonlinearity with von Karman’s approximation. The effort to model the fluid–structure interaction is reduced

The nonlinear dynamics of a tip excited cantilevered beam with an end-mass attached to elastic-damping support is considered in this paper. This prototypical system is examined using a minimal two degree of freedom (DOF) model and its bifurcation characteristics, computed by AUTO software, is compared with the analytical solutions and that of the full system using multi-body dynamic simulation. The

Based on the continuum mechanics principles, a rigorous formulation is presented for the linearized stiffness equation of three-dimensional beam elements with account taken of the joint moment equilibrium in the deformed configuration C2. By sticking to the Bernoulli–Euler hypothesis of plane sections and elasticity definitions for stress resultants, the bending moments and torque of the element are

In the present work, the modeling of a human arm has been carried out in its antagonistic actuation mode. Here, the functions of the biceps and triceps muscles are replaced by a pneumatic artificial muscle (PAM) and a spring to lift the required mass. The governing nonlinear equation of motion has been derived considering the system as a single degree of freedom system. Here, the muscle force has been

A space–time conformal gauge theory is used to develop a unified continuum model describing myriad electromechanical and magnetomechanical coupling effects observed in solids. Using the pseudo-Riemannian Minkowski metric in a finite-deformation setup and exploiting the Lagrangian’s local conformal symmetry, we derive Cauchy-Maxwell (CM) equations that seamlessly combine, for the first time, Cauchy’s

In this investigation, three-dimensional nonreciprocal transmission is realized by the combination of structural asymmetry and material nonlinearity. Analytical solutions of the coupled quasi-longitudinal (qP) and quasi-shear (qS1 and qS2) waves are derived. According to Bloch’s law and the stiffness matrix method, we obtain the band gaps and the transmission coefficients of the fundamental and double

In this paper, the three-dimensional (3D) stress analysis of plate-type structures in instability conditions is presented The displacement-based and hybrid-mixed four-node quadrilateral elements are developed taking the advantages of the sampling surfaces (SaS) method. The SaS formulation is based on considering inside the plate N not equally spaced SaS parallel to the middle surface to specify the

Homogenization of mechanical properties of a heterogeneous material using analytical/semi-analytical micromechanics approaches is computationally less expensive than that through numerical techniques. However, analytical methods cannot be easily applied to a complex distribution of the microstructure in a unit cell (or a representative volume element). Here, we alleviate this by accommodating cuboidal

The mechanical response of a hollow circular cylinder to internal pressure represents an important theoretical model which can be helpful in the design of tubular structures, and in the biomechanical research of tissues like arteries. It has been shown that arteries in vivo, in addition to pressure loading, sustain significant axial extension. It is manifested as a retraction that is observed when

Wave propagation through nonlinear acoustic metamaterials has generated numerous scientific interests for their enormous potential in practical applications these years. This study focuses on the effects of nonlinearity on the band properties of diatomic mass-in-mass chain with active control. By applying the Lindestedt–Poincaré (L–P) perturbation method, analytical dispersion relations of the linear

This study presents the analytical and finite element formulation of a geometrically nonlinear and fractional-order nonlocal model of an Euler–Bernoulli beam. The finite nonlocal strains in the Euler–Bernoulli beam are obtained from a frame-invariant and dimensionally consistent fractional-order (nonlocal) continuum formulation. The finite fractional strain theory provides a positive definite formulation

The smart structures with the harmonic nonlinear vibration are used widely to broaden the frequency range of vibrations energy harvesting. In the paper, the potential of harvesting vibratory energy via a mono-stable Duffing energy harvester subjected to sub-harmonic excitation is investigated. The averaging method is used to derive the approximate solutions of the electromechanical linkage management

A plane turbulent mixing in a shear flow of an ideal homogeneous fluid confined between two relatively close rigid walls is considered. The character of the flow is determined by interaction of vortices arising at the non-linear stage of the Kelvin–Helmholtz instability development and by turbulent friction. In the framework of the shallow water theory and a three-layer representation of the flow,

Autonomous robots have several applications on industry, military and safety fields. The replacement of the conventional wheels by deformable ones improves the maneuverability, allowing it to trespass obstacles that goes from small fissures to step elevations. Besides, path control can be made by directly actuation on the wheel using a small number of actuators, reducing the structure weigh. This paper

Since Euler’s elastica, buckling of straight columns under axial compression has been studied for more than 260 years. A low width-to-length ratio column typically buckles at a critical compressive strain on the order of 1%, after which the compressive load continuously increases with the displacement. Here using a general continuum mechanics-based asymptotic post-buckling analysis in the framework

When drilling ultra-deep wells with polycrystalline diamond compact (PDC) bits, the drillstring suffered from severe vibrations that were responsible for the premature failure of drillstring components and the inefficient drilling process. In this paper, a field experiment was conducted in an ultra-deep well to measure the downhole tri-axial accelerations of the drillstring. The analyses of the acceleration

A constitutive relation is proposed for viscoelastic bodies that is a generalization of the classic Kelvin-Voigt model, wherein the left Cauchy Green tensor, the symmetric part of the velocity gradient, and the Cauchy stress tensor are implicitly related. The model developed includes several models that are being used in the literature to describe the elastic and viscoelastic response of bodies. In

The time-dependent deflection responses of the mechanically excited layered skew sandwich shell panels are computed numerically via a generic model developed mathematically using the higher-order shear deformation theory including the effects of the large displacement. The model includes the large displacements associated with the structural distortion under the small strain regime through Green–Lagrange

Dynamic systems, such as vibration isolators, rotor-bearing systems, are inherently nonlinear and their dynamic behaviour often cannot be sufficiently explained or predicted by simple linear models. Presence of nonlinearity leads to certain characteristic behaviours in the response such as jump phenomenon, limit cycle, super-harmonic resonances and such behaviours can be accurately predicted only if

The balance laws of Rational Extended Thermodynamics describe well the evolution of rarefied gases in non-equilibrium. Usually, it is necessary to approximate the theory in a neighborhood of an equilibrium state and consequently, its hyperbolicity property remains valid only in a neighborhood of the equilibrium state of the field variables, called hyperbolicity region. The goal of this paper is first

The phenomenon of mode localization is explored theoretically and experimentally on two mechanically or electrostatically coupled beam resonators. Lumped parameter models are used to simulate the response of the systems. The eigenvalue problems are solved for both case studies under different stiffness perturbations and coupling strengths. The influence of the side electrode bias on the veering points

The mechanical behavior of rubber-like materials is dominantly non-linear elastic. Their mechanical response is measured by numerous conventional techniques including the universal loading machines (tension and compression) and indentation. Recently, an unconventional technique based on cavitation rheology has been implemented to measure the mechanics of these materials. The loading mechanism of this

This paper is devoted to the study of the nonlinear model of the longitudinal deformations of an elastic rod in the presence of the non-stationary external source. The presence of the non-stationary external source greatly complicates the study of this model. By methods of the symmetry analysis, all basic models of the general model, having different symmetry properties are found. A basic model that

A variety of methods have been proposed to improve the performance of dielectric elastomer transducers, which lead to the anisotropic electromechanical behavior of the material. This paper theoretically analyzes the effect of material anisotropy on the diffuse modes of instability in dielectric elastomer plates. As a first step, a transversely isotropic material is considered in the present study.

The von-Kármán effect on the free torsional vibrations of carbon nanotube made of functionally graded materials (FGMs) is inspected in this research using the theory of nonlocal elasticity. The material properties are assumed to change continuously through the radius of the FGM carbon nanotube (FGM-CNT) according to a power-law distribution. Using Hamilton’s principle, the equations of nonlinear torsional

A typical quasi-zero-stiffness (QZS) vibration isolator composed of two lateral springs and a vertical spring has been widely studied in previous literature, in which the dynamic equation is usually formulated with linear viscous damping. However, in practical applications, the damping may be generated from many sources and thus deserves special study. In this paper, a dynamic model with consideration

This study presents a modified harmonic balance method, which is used to solve the force and displacement transmissibilities of a vibration isolator with both the quasi-zero-stiffness and geometrically nonlinear damping. The steady-state response of the nonlinear isolation system is obtained by Jacobi elliptic functions, and is used to modify the harmonic components of stiffness and damping force in

Soft materials with engineered microstructure support nonlinear waves which can be harnessed for various applications, from signal communication to impact mitigation. Such waves are governed by nonlinear coupled differential equations whose analytical solution is seldom trackable, hence emerges the need for suitable numerical solvers. Based on a finite-volume method in one space dimension, we here

In this work, the nonlinear dynamic and force transmissibility characteristics of a flexible shaft–disk rotor system supported by suspension system with nonlinear stiffness and damping are investigated numerically. The distributed variables representing the elastic motions of the shaft are discretized using the Assumed Mode Method (AMM) and the equations of motion (EOM) are subsequently obtained using