Dynamic systems, such as vibration isolators, rotor-bearing systems, are inherently nonlinear and their dynamic behaviour often can not 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 behviours 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 component 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

Investigated herein are the nonlinear vibration characteristics of a rectangular microsheet comprising micro fiber composite with graphene (GP) skin under coupled excitations. Owing to the good thermal conductivity of GP, the heat sink performance of the GP skin is also considered. In this study, the constitutive relation for the microsheet is established by applying the Eringen theory and the governing

Mechanical systems like the Centre Buffer Couplers, which connect railway coaches, are spring–dashpot mechanisms characterized by presence of dry friction and backlash and are subjected to large dynamic forces. While systems with individual characteristics mentioned above, have been studied by earlier researchers, a system where all of the above physical features are present simultaneously, is analysed

Dielectric elastomer actuators have attracted much attention in the application of soft robotics. In this work, we present a new design of electromechanical actuator using gel, dielectric elastomer and oil. Compared to the traditional dielectric elastomer actuator, we replace the electrodes with conductive gel and replace the dielectric elastomer with a combination of oil and elastomer. In our new

The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas dynamics equations can be rewritten in a variational form. Such a Lagrangian is found in the paper. Complete group analysis of the Euler–Lagrange equation is performed

A numerical approach is presented to find the equilibrium solutions of a soap film spanning a flexible but inextensible boundary (Giomi and Mahadevan 2012). Various shapes of the soap films are quantified in terms of a dimensionless parameter. Numerical stability and bifurcation analysis is performed. Specifically, estimates of two critical values of the bifurcation parameter responsible for the onset

The analysis of the affect of angular velocity on the geometry of the basins of convergence (BoC) linked to the equilibrium points in the restricted three-body problem is illustrated when the primaries are source of radiation. The bivariate scheme of the Newton–Raphson (N–R) iterative method has been used to discuss the topology of the basins of convergence. The parametric evolution of the fractality

Dynamics of nonlinear coupled driven oscillators is investigated. Recently, we have demonstrated that the amplitude profiles – dependence of the amplitude A on frequency Ω of the driving force, computed by asymptotic methods in implicit form as FA,Ω=0, permit prediction of metamorphoses of dynamics which occur at singular points of the implicit curve FA,Ω=0. In the present study we strive at a global

We model and investigate the response of a nonlinear cantilever beam under principal parametric excitation. The design is initially assessed, optimized, and tuned using three-dimensional finite element analysis (FEA) to ensure the presence of fundamental parametric resonance and the absence of other internal and higher-order parametric resonances. The derived governing differential equation represents

In this paper classes of double wave solutions of the 1D Euler system describing a ideal fluid in the non-homogeneous case have been determined. In order that the analytical procedure under interest to hold, suitable model laws for the source term involved in the governing model were characterized. Finally such a class of exact double wave solutions has been used for solving some problems of interest

In this work, two geometrically non-linear beam models which use different strain measures are investigated in problems with large rotations. The first is the Simo–Reissner model. The second is the Green–Lagrange model. The novel aspects of this work are: (1) the 1-D formulation of the second beam model which uses the Green–Lagrange strain tensor components so that is comparable to the Simo–Reissner

The problem of stability for classical Couette and Poiseuille flows (flows of a horizontal layer of fluid between plates in relative motion) is still open. Recently, Falsaperla et al. obtained values for critical linear and nonlinear energy Reynolds numbers which are in good agreement with the experiments of Prigent et al. and with the numerical simulation of Barkley and Tuckerman. Such critical values

Seismic Performance-based design demands reliable means for profound understanding of inelastic and non-linear dynamic behavior of civil structures. In this study, a hybrid experimental and numerical approach for seismic assessment of soil-nailed structures is introduced which incorporates simple static loading of a small-scale physical model and non-linear dynamic analysis of a two degree-of-freedom

In this paper, aeroelastic equations for a two-dimensional wing encountering a wind gust are presented and solved numerically. The indicial aerodynamic theory based on Wagner’s function is adopted to obtain aerodynamic forces and moments acting on the wing in the time domain. The dynamics of the wing is approximated via two degrees-of-freedom, i.e. pitch and plunge. The structural stiffness is modeled

The design of blast-resistant glazed façades can be required by building standards. The high-pressure generated by the blast wave air-front can lead to catastrophic failure of the glass panes and/or their load-bearing structure, with possible projection of fragments that constitutes a potential threat for human lives and properties. The time-dependent deformations-history is usually assessed via numerical

The numerical implementation of the complex rheology of blood, namely the viscoelastic property, in hemodynamic simulations is still a challenge. A more accurate numerical tool is essential for diagnosis, prevention and treatment of atherosclerotic disease in arteries. In particular, in small vessels or vessels with stenosis and aneurysms, the elastic effects of blood should not be neglected. Since

Among the most studied models in mathematical physics, Timoshenko beam is outstanding for its importance in technological applications. Therefore it has been extensively studied and many discretizations have been proposed to allow its use in the most disparate contexts. However, it seems to us that available discretization schemes present some drawbacks when considering large deformation regimes. We

As a basic structure and a fundamental vibration issue, the vibration of cantilever structures has been thoroughly studied, and there are some generally accepted conclusions, for example, internal resonance does not take place in the transverse vibration of a basic cantilever beam. In this study, by including 3:1 internal resonance caused by gravity, mode interactions of hanging cantilever beams are

Motivated by the complex rheological behaviors observed in small/micro scale blood vessels, such as the Fahraeus effect, plasma-skimming, shear-thinning, etc., we develop a non-linear suspension model for blood. The viscosity is assumed to depend on the volume fraction (hematocrit) and the shear rate. The migration of the red blood cells (RBCs) is studied using a concentration flux equation. A parametric

Lipid-bilayers are the fundamental constituents of the walls of most living cells and lipid vesicles, giving them shape and compartment. The formation and growing of pores in a lipid bilayer have attracted considerable attention from an energetic point of view in recent years. Such pores permit targeted delivery of drugs and genes to the cell, and regulate the concentration of various molecules within

Microstructure-based constitutive models have been adopted in recent studies of non-linear mechanical properties of biological soft tissues. These models provide more accurate predictions of the overall mechanical responses of tissues than phenomenological approaches. Based on standard approximations in non-linear mechanics, we classified the microstructural models into three categories: (1) uniform-field

An interpolating spline-based approach is presented for modeling multi-flexible-body systems in the divide-and-conquer (DCA) scheme. This algorithm uses the floating frame of reference formulation and piecewise spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body system undergoing large rotations and translations. The new approach is compared with the

The goal of this manuscript is to establish a novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits. Within the physiological regime, skin displays a reversible, highly nonlinear, stretch locking, and anisotropic behavior. We model these characteristics using a transversely isotropic chain network model composed of eight

The undamped, finite amplitude horizontal motion of a load supported symmetrically between identical incompressible, isotropic hyperelastic springs, each subjected to an initial finite uniaxial static stretch, is formulated in general terms. The small amplitude motion of the load about the deformed static state is discussed; and the periodicity of the arbitrary finite amplitude motion is established

A commonly used assay for studying cell - matrix interactions is the free-floating fibroblast populated collagen lattice, which was introduced in 1979. Briefly, fibroblasts are seeded within an initially thin, amorphous, untethered, circular gel consisting of reconstituted fibrillar collagen. Although the gel remains traction free and circular, the cells typically contract the gel to less than 50%

In this paper we use a modified form of the mixture theory developed by Massoudi and Rajagopal to study the blood flow in a simple geometry, namely flow between two plates. The blood is assumed to behave as a two-component mixture comprised of plasma and red blood cells (RBCs). The plasma is assumed to behave as a viscous fluid whereas the RBCs are given a granular-like structure where the viscosity

Motivated by applications to seed germination, we consider the transverse deflection that results from the axisymmetric indentation of an elastic membrane by a rigid body. The elastic membrane is fixed around its boundary, with or without an initial pre-stretch, and may be initially curved prior to indentation. General indenter shapes are considered, and the load-indentation curves that result for

A coordinate-free Lie-group formulation for generating ensembles of DNA conformations in solution is presented. In this formulation, stochastic differential equations define sample paths on the Euclidean motion group. The ensemble of these paths exhibits the same behavior as solutions of the Fokker-Planck equation for the stochastically forced elastica. Longer chains for which the effects of excluded

DNA looping plays a key role in the regulation of the lac operon in Escherichia coli. The presence of a tightly bent loop (between sequentially distant sites of Lac repressor protein binding) purportedly hinders the binding of RNA polymerase and subsequent transcription of the genetic message. The unexpectedly favorable binding interaction of this protein-DNA assembly with the catabolic activator protein