The overall behavior of an articulated beam structure constituted by elements arranged according to a specific chirality is studied. The structure as a whole, due to its slenderness and geometry, is called duoskelion beam. The name duoskelion is a neologism which is inspired by the Greek word δύοσκέλιον (two-legged). A discrete model for shearable beams, formulated recently, is exploited to investigate

We investigate the dynamical characteristics of a two degrees of freedom friction oscillator with constrained spring cushions. Based on the discontinuity resulted from the rough contact surface and the nonsmoothness resulted from fixed spring, different boundaries and domains are given in phase space. The G-functions are introduced to determine whether the passable, grazing, sliding and stick motions

The model of interaction of two strains of the virus is considered in the paper. The model is based on a nonstationary system of differential equations with delays and takes into account populations of susceptible, first-time and re-infected individuals across two strains. For small values of the delays, the conditions of global asymptotic stability are obtained with the help of Lyapunov functionals

Slow-fast analysis has been extensively used in the past to study the occurrence of bursting oscillations. Most bursting oscillations studies are performed on the low dimensional autonomous systems where only codimension-1 bifurcations take place at the transitions of quiescent and spiking states. However, in high dimensional slow-fast dynamical systems, there exist higher co-dimensional bifurcations

We present a new model within the class of generalised neo-Hookean strain energy functions for application to the finite deformation of incompressible elastomers. The model has a simple form with only two parameters, namely μ and N with structural roots, and is derived within the classical framework of statistical mechanics for freely jointed molecular chains in rubber elasticity Using existing experimental

In this paper, we propose a generalized strain energy density function based on invariants of stretch tensor with arbitrary exponents. We employ polynomial, logarithmic and exponential functions of these invariants to develop the strain energy functions. We also study characteristics and applications of the proposed model for isotropy, transverse isotropy, orthotropy with a special focus on initial/residual

Rolling element bearings are used as main supports and are key sources of vibrations for aero-engine rotor systems. Mainly including the inner and outer rings, cages, and balls or rollers, the complicated mechanical structures of rolling element bearings exhibit nonlinear behaviors due to the bearing clearance, nonlinear Hertzian contact forces, and defects. Due to imbalanced rotations, which are unavoidable

In this manuscript, we propose a novel reduction framework for obtaining Reduced Order Models (ROMs) of large-scale, nonlinear dynamical systems. We advocate the use of Nonlinear Moment Matching (NLMM) with the Dynamic Mode Decomposition (DMD) to get a much efficient dimensionality reduction scheme. While NLMM does not require the expensive computation of the time-displaced snapshot ensemble of the

Centrifugal governors play an important role in rotating machinery such as diesel engines and steam engines. This paper considers two impulse excitations of the freewheel. The feedback control issue of the Neimark–Sacker bifurcation design of the centrifugal governor system is studied. A feedback control method is addressed to realize the control objectives of the existence, stability and the mean

For problems with strong shock waves a modification of the Landau–Teller equation in the system of two-temperature gas dynamics is proposed. This allows for extending the admitted Lie algebra of the system by the generator of simultaneous scaling of the independent variables. On this basis a class of self-similar solutions of the one-dimensional unsteady flows of a vibrationally excited gas is obtained

Flexural tensegrity is a structural principle for which the integrity under flexure of a beam formed by a chain of segments in unilateral contact is provided by an unbonded prestressing tendon anchored to the end segments, with the possible interposition of linear springs and linear dashpots. These are activated by the inflexion of the beam as a consequence of the particular shape of the contact surfaces

This work proposes an alternative approach for the nonlinear analysis of 2D, thin-walled lattice structures. The method makes use of the well-established Carrera Unified Formulation (CUF) for the implementation of high order 1D finite elements, which lay along the thickness direction. In this manner, the accuracy of the mathematical model does not depend on the finite element discretization and can

Inverted pendulum (IP) has been broadly used to model locomotor systems. In this paper, we demonstrate that an IP-like model could simulate stable periodic handspring maneuvers with passive flight phases. The model is a 2-D symmetric rigid body which is merely controlled during the contact phase. To benefit from an open-loop sensorless strategy, the control policy is implemented only by an unvaried

This work investigates the primary sinusoidal bifurcation wrinkling response of single- and multi-layered magnetorheological elastomer (MRE) film–substrate systems subjected to combined transverse applied magnetic fields and in-plane biaxial pre-compression. A recently proposed continuum model that includes the volume fraction of soft-magnetic particles is employed to analyze the effect of the magnetic

Four nonlinear computational models for the surface wrinkling of curved shell-core systems under external pressure are presented. Three of the considered finite element models neglect the displacements tangential to the shell surface. Two of the models are static formulations and the other two are derived in the dynamic framework. For the latter, the energy-decaying time-stepping algorithm is applied

Growth-induced pattern formation in tubular tissues is intimately correlated to normal physiological functions. Moreover, either the microstructure or certain diseases can give rise to material inhomogeneity, which can lead to a change of shape in the tissue. Therefore, it is of fundamental importance to understand surface instabilities and pattern transitions of graded tubular tissues. In this paper

Excessive vibration of rotor-blade systems has been a main reason for the failure of rotating machinery. Therefore, methods capable of simultaneously suppressing vibrations rotor and blade are urgently needed. Considering this, a nonlinear energy sink (NES) with piecewise linear stiffness is used to satisfy the requirements. Firstly, the structure and working mechanism of the NES are introduced. And

A two-dimensional plate theory is derived for incompressible transversely isotropic fiber-reinforced materials with wavy fibers. Single-layer plates and two-layer laminates are considered. Numerical simulations of axially loaded rectangular sheets in the post-buckling regime illustrate the marked effect fiber waviness has on both the wrinkling patterns and the effective axial stiffness. For fibers

The complex buckling behavior of one of the simplest structures, an elastic thin strip under combined stretch and twist loading represents a fascinating example for structural stability analysis. For stretched-twisted strips, in contrast to solely stretched strips, not just the computation of the post-buckling process but also the simulation of the pre-buckling behavior and the determination of the

This works presents the theoretical analysis and experimental observations of the bidirectional motion of a millimeter-scale bristle robot (milli-bristlebot) with an on-board piezoelectric actuator. First, the theory of the motion, based on the dry-friction model, is developed and the frequency regions of the forward and backward motion, along with the resonant frequencies of the system are predicted

Dynamics of a periodically forced anharmonic oscillator with cubic nonlinearity, linear damping, and nonlinear damping, is studied. To begin with, the authors examine the dynamics of an anharmonic oscillator with the preservation of parity symmetry. Due to this symmetric nature, the system has two neutrally stable elliptic equilibrium points in positive and negative potential-wells. Hence, the unforced

Soft functionally graded materials have attracted intensive attention owing to their special material inhomogeneity and are realized as various applications. In this paper, we theoretically investigate the finite deformation and superimposed bifurcation behaviors of an incompressible functionally graded dielectric tube subject to a combination of axial stretch and radial voltage. The theoretical framework

Many biological tissues and organisms are in a state of residual stress, which should be considered rather than ignored as in many previous studies. In this work, we establish a theoretical model to study the growth and patterns of a residually stressed core–shell soft sphere. The effect of the initial residual stress is considered by employing a modified multiplicative decomposition growth model.

The Poisson’s ratio and the Young’s modulus play an important role in the characterization of nanomaterial mechanical properties. They are the vital parameters of understanding nanoscale material behavior. Here we report a method of quantitatively determining the values of the Poisson’s ratio and the Young’s modulus with a T-shape contact resonance atomic force microscopy. Unlike the cantilever of

In this paper, geometrically nonlinear analysis of functionally graded beams using the dual mesh finite domain method (DMFDM) and the finite element method is presented. The DMFDM makes use of a primal mesh of finite elements and associated approximation for the variables of the formulation and a dual mesh of control domains, which does not overlap the primal mesh, for the satisfaction of the governing

The present work deals with the progressive damage analysis of composite laminates subjected to low-velocity impact. We develop a numerical model using higher-order structural theories based on the Carrera Unified Formulation (CUF) with Lagrange polynomials and resulting in a 2D refined layer-wise model. To model damage, we use a combination of the continuum damage-based CODAM2 intralaminar damage

This paper presents a derivation of a hinged–hinged Euler–Bernoulli beam including cubic and quintic nonlinearities. Then, a three-mode Galerkin discretization technique has been utilized to generate a system of ordinary differential equations governing the temporal deflections of the first three modes of the studied beam. The pioneering work of Nayfeh and Mook (1995) has shown the absence of internal

Buckling instabilities of layered materials are an important phenomenon that has been analyzed both analytically and numerically, but generally only in the absence of surface pressure. In this study, we present a linear stability analysis of the wrinkling of an inhomogeneous bilayer made up of dissimilar neo-Hookean elastic materials, under uniaxial compression with pressure applied to the top surface

This paper presents an approach to obtaining higher order approximations to limit cycles of an autonomous multi-degree-of-freedom system with a single cubic nonlinearity based on a first approximation involving first and third harmonics obtained with the harmonic balance method. This first approximation, which is similar to one which has previously been reported in the literature, is an analytical

We consider a variant of the classical Biot problem concerning the wrinkling of a compressed hyperelastic half-space. The traction-free surface is no longer flat but has a localized ridge or trench that is invariant in the x1-direction along which the wrinkling pattern is assumed to be periodic. With the x2-axis aligned with the depth direction, the localized imperfection is assumed to be slowly varying

We examine stability of the polar vortex that initiates planetary-scale westerly (west to east) atmospheric flow that encircles the pole in middle or high latitude of a planet. In our studies, the polar vortex is modeled as an annular flow (zonal flow) extending radially from a rigid inner boundary to a free outer boundary on a Ek− plane, which is parallel to the equatorial plane but generally displaced

We investigate the entrance flow of a suspension modeled as a single inhomogeneous fluid. The inhomogeneity is due to non-uniform particles distribution on the vessel cross section. Our study aims to show that the particles migration towards the duct axis can also be explained as an entrance effect. The analysis is performed by generalizing the classical inertial terms linearization thus getting an

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

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–Planck–Kolmogorov (GFPK) equation for the stationary joint probability density of amplitude and phase difference are

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

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

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

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

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

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

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

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,

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 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

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

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

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

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

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

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 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 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

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 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

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

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