Perpetual points in mathematics defined recently, their significance, in systems dynamics is ongoing research. In linear unforced mechanical systems, the perpetual points are associated with rigid body motion, and they are not just a few points, but they form the perpetual manifolds. The mechanical systems with perpetual manifolds the rigid body motion are called perpetual mechanical systems. The concept

Motivated by a recent paper of Pennisi in the relativistic framework Pennisi (2021), we revisit the previous approach of two hierarchies of moments critically and propose a new natural physical hierarchy of moments to describe classical rarefied non-polytropic polyatomic gas in the framework of Molecular Rational Extended Thermodynamics. The differential system of the previous approach is proved to

A beam-like model is proposed to address nonlinear dynamic response of a thin pipe, under the action of a resonant transverse load. The mechanical model consists of a Timoshenko beam enriched with further kinematic and dynamic variables which, besides extension and bending, consistently describe local effects, related to ovalization and warping of the cross-section. The nonlinear equations of motions

An experimental investigation of the compressive response of unitized stiffened textile composite panels that are manufactured using two-dimensional triaxially braided composites loaded in axial compression well into the postbuckling regime is presented. The stiffened panels are unitized because the constituent material was a textile laminate with an alternative method to form the stiffener geometry

In this paper, nonlinear free vibration analysis of shear deformable functionally graded material (FGM) tubes conveying fluid with immovable support conditions resting on a Pasternak-type foundation is presented. Based on Hamilton’s principle, the equations of motion and boundary conditions are obtained by using a new high-order shear deformation tubular beam model with von Kármán nonlinearity and

A computational investigation of unitized stiffened textile composite panels that are manufactured from triaxially braided textile composites and loaded in axial compression into the postbuckling regime is presented. The stiffened panels are unitized because the textile nature of the constituent material, in conjunction with an alternative stiffener design, form a near-net shape one-piece stiffened

The contributions of various non-linearities to an automotive drum brake’s transient response has been studied analytically. A discrete system model with friction, contact, and kinematic non-linearities is formulated such that each of the non-linearities could be linearized independently. The contact between the brake shoes and the brake drum is modeled using Hertzian contact theory, supported by kinematic

The dynamical analysis of a quarter car suspension based on the Kelvin–Voigt​ viscoelastic model with fractional order derivative is analytically and numerically studied in this paper. Depending on the non-dimensional quadratic stiffness parameter, the potential configuration associated with the system under study is possible to obtain monostable and, asymmetric bistable configurations. Thanks to the

In this work, the nonlinear dynamic responses of a high-speed rotor-bearing system have been investigated to explore the safe operating regions (SORs) with stable parametric shelter. Here, a new large deflection model of a high-speed multi-disk rotating shaft mounted on a moving base has been developed accounting for nonlinear geometric curvature and gyroscopic effect. Viscoelastic rotating shaft has

The purpose of this work is the investigation of the dynamical behavior of a mechanical network consisting of discontinuous elastically coupled system oscillators with strong irrational nonlinearities. This mechanical network is consisted of a set of N nonlinear oscillators, elastically coupled where nonlinearity in each unit cell is just due to the geometric configuration, which is the inclination

Dissipative devices, interposed between a glazed surface and its supporting back structure, can efficiently contribute to safeguard the integrity of glass under the impinging action of a shock wave generated by an explosion. This is theoretically demonstrated with reference to a paradigmatic model problem, in which a glass pane is connected to a load-bearing structure via a dissipative unit. This is

In the paper, the potential of harvesting vibratory energy via a mono-stable Duffing energy harvester with base excitation in super-harmonic resonance is investigated. The averaging method is exploited to provide an approximate analytical solution for the system. The displacement and voltage responses are determined depending explicitly on the displacement amplitude and excitation frequency. The explicit

Nonlinear vibration of a fractional viscoelastic micro-beam is investigated in this paper. The Euler–Bernoulli beam theory and the nonlinear von Kármán strain are used to model the beam. The small-scale effects are considered by employing the Modified Couple Stress Theory (MCST). The viscoelastic material of the beam is modeled via the fractional Kelvin–Voigt model. Utilizing the Hamilton’s Principle

In this article, the forced vibration of double-curved nanocomposite shells under a time dependent excitation is studied using nonlinear shell theory and multi-scales method in primary resonance. The nanocomposite representative volume element consists of two phases, including carbon nanotube (CNT) and matrix. By generalizing the Ambartsumyan’s first order shear deformation shell theory (FSDT) to the

We show interaction between high- and low-frequency modes in periodic α-FPU chains with alternating large masses. This high-low frequency interaction is known if the number of particles N is a 4-fold, our treatment discusses the difficult case where the number of particles N=2p involves p prime. A key role is played by identifying symmetric invariant manifolds, thus reducing the dimension of the problems

Residual stresses may exist in different finitely deformed soft multifunctional materials such as in electro-active and magneto-active polymers. In order to develop accurate constitutive frameworks of these smart materials experiencing electro-magneto-mechanically coupled loads, the presence of residual stresses needs to be considered on the onset of the model development. In this contribution, a spectral

This paper deals with the equilibrium problem of the Mises truss, with out-of-plane lateral linear spring, analyzed as a three DOF system. It is shown that, as a consequence of the geometry of the structure, the system can undergo three buckling modes which are asymmetric in-plane buckling, symmetric out-of-plane buckling and asymmetric out-of-plane buckling. The analysis takes into account the influence

We study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and relaxation towards a traffic-dependent Optimal Velocity (OV) and we show that the resulting macroscopic models depend on the relative frequency between these two microscopic

Three-phase flow in porous media may appear in different scenarios during the production life of a hydrocarbon reservoir. The simultaneous flow of different phases is modeled by relative permeability curves which are fundamental to petroleum production analysis and forecast. Laboratory experiments are the main source of data for relative permeability curves. Mathematical solutions for multiphase flow

This work deals with the consequence of fitting hyperelastic material models to quasi-static multi-hysteresis test data with and without the correction of permanent deformation. Multi-hysteresis experiments are performed in different deformation states with equivalent amplitudes and equivalent strain rates. The investigations are performed on a carbon black filled ethylene propylene diene terpolymer

The motion of a heavy bead on a smooth ring is considered. The ring is rotating uniformly around an inclined diameter. The integrability of the equations is studied using the method of splitting separatrices. The Poincaré maps for the period are constructed. Some classes of periodic motion are identified, and their stability is investigated. The reaction is calculated, and its properties are discussed

This paper aims to investigate the local oscillations of a dielectric elastomer with emphasis on the effect of the second invariant of the deformation tensor in finite strain theory on such oscillations. Four hyperelastic constitutive models are utilized in this study, namely the classic Gent model, a modified Gent model, a modified version of the Pucci–Saccomandi model, and the Mooney–Rivlin model

Pressure can sometimes be utilized to increase or decrease the strength of adhesion. This phenomenon is analyzed for upward pull-off of (i) a flat, circular cylindrical punch from a circular plate and (ii) a long, flat, rectangular punch from a long rectangular plate. The pressure is applied, and then the punch is pulled upward. The pressure may act upward (positive) or downward (negative) on the plate

We develop some Gent-like limited extensible models for initial stress symmetry. The proposed models exhibit sharp strain-stiffening characteristics when the stiffening parameter approaches the maximum allowable limit. When this maximum allowable limit tends to infinity, these models reduce to some other existing models for initial stress. We perform a micro-mechanical investigation which agree with

The membrane–membrane contact mechanics plays an important role in several biological processes, such as drug delivery, cell infection, cell destruction, etc. at microscales. The problem at macroscales is relevant to air inflated and air supported structures. In this work, we have chosen a simple system in which contact mechanics of two inflated membranes (initially flat circular membranes parallelly

Based on the simplified aero-engine rotor system, a new nonlinear response prediction model of rotor bearing rub-impact system is established. Different from the traditional rotor system rub-impact model, based on the detailed characteristics of the blade–disc system, this paper considers the influence of the number of blades and the dynamic to static clearance on the rub-impact force. In addition

Presence of dry friction and clearance discontinuities in various dynamic systems, such as friction wedge dampers in a three-piece railway freight-vehicle bogie, centre buffer coupler connecting two coaches, originate significant jerks. While nonlinear dynamics of systems, with these individual and combined discontinuities has received some attention, behavior of jerks remains unexplored. This study

We consider the problem of an impenetrable Kirchhoff rod in self-contact. The contact is assumed to be frictionless and of point-contact type. The self-contacted rod is modeled as a set of contact-free segments each having unknown length and connected in series with each other through frictionless hard-contact condition. The Landau–Lifshitz approach is used to express analytically the centerline of

This work concerns the generalized Hopf bifurcation analysis of a piecewise-smooth wheel system with higher order discontinuities. Center manifold reduction is used to reduce the towed caster wheel system to a planar dynamical system, in which the non-smoothness factor is considered. The analysis can be divided into two cases by the coefficient of quadratic term. If the coefficient of quadratic term

The nonlinear modulation of waves in a metamaterial mass-in-mass lattice model is studied. The governing continuum nonlinear equation is obtained from the original discrete model. The important differences in the modulated nonlinear wave dynamics on the acoustic or optical bands are described analytically. It is shown that the choice of the band can affect the shape of the modulated nonlinear wave

The development of a constitutive representation for predicting the durability of filled rubbers upon aggressive environmental conditions is crucial for numerous technical examples but still remains largely an open issue. This paper presents a constitutive model for the prediction of thermal aging effects on the inelastic response of filled rubbers. A network alteration theory is proposed for the thermally

Derived in this paper are evolution equations for the thickness and surface surfactant concentration pertaining to a thin liquid layer that is laden with a soluble surfactant as it flows under the influence of gravity down a heated incline. These equations account for variations in surface tension with surfactant concentration and temperature. A linear stability analysis and numerical simulations are

We study the influence of residual stress on the static and dynamic characteristics of a spherical structure. We consider a shrink-fitted compound sphere, where residual stress is developed due to the interference between outer and inner spherical layers. We calculate this residual stress and model the residually stressed material with suitable hyperelastic strain energy satisfying Initial Stress Reference

The nonlinear behaviour of a simply supported granular column loaded by an axial force is studied in this paper. The granular column is composed of rigid grains (discs) elastically connected by some shear and rotational springs. The in-plane buckling and post-buckling analysis in a geometrically exact framework is numerically investigated from a nonlinear difference eigenvalue problem. The granular

The nonlinear vibration analysis of cracked structures could be a suitable indicator for diagnosing defects. When breathing cracks appear on the beam, its behavior can be modeled as a bilinear oscillator. In this paper, the nonlinear vibration behavior of a cantilever beam with multiple breathing cracks is investigated. For this purpose, the multi-cracked beam’s stiffness is calculated by introducing

An electromechanical coupling model (EMCM) is constructed, and a contact-separation mode triboelectric nanogenerator (CS-TENG) is analyzed. In consideration of the contact-impact force between the moving and fixed electrodes, a piecewise linear differential equation of the moving electrode is derived and combined with the equivalent circuit differential equation to establish the EMCM of a CS-TENG with

An incremental harmonic balance (IHB) method with two time-scales is presented and used for calculating accurate quasi-periodic responses of a one-degree-of-freedom Van der Pol–Mathieu equation with coupled self-excited vibration and parametrically excited vibration with 1:2 resonance. For periodic responses of the Van der Pol–Mathieu equation with only one basic frequency, the traditional IHB method

In this paper, we study the nonlinear response of a bistable van der Pol–Mathieu–Duffing (VMD) oscillator under the influence of two periodic excitations of widely different frequencies. We have shown that by systematically modulating the strength of the high-frequency drive as well as the strength of the parametric oscillation, a symmetrically oscillating bistable potential can be converted to a symmetrically

The article deals with the problem of computing efficiently the nonlinear response of a rod involving a fractional constitutive model, and exposed to random excitation. The constitutive model is a three-parameter model comprising an instant elasticity modulus, a prolonged elasticity modulus, and a relaxation parameter. The nonlinear term is a linear-plus-cubic force of the Winkler kind. The resulting

A computational algebraic geometry technique is developed for determining nonlinear normal modes (NNMs) of multi-degree-of-freedom (MDOF) nonlinear dynamic systems. Specifically, resorting to computational algebraic geometry concepts and tools, such as Gröbner basis, it is shown that the complete solution set of a nonlinear algebraic system of coupled multivariate polynomial equations is determined

In this work, passive vibration absorbers are used to obtain a metamaterial vibrating plate. For this purpose, a set of linear and nonlinear passive absorbers are used. The plate is modeled based on Mindlin’s theory in which the effects of rotary inertia and shear deformation are considered. The metamaterial plate is considered to be both linear and nonlinear, with a set of linear, nonlinear, and viscous

Recently, scientists have utilized self-excited oscillations in many mechanical and micromechanical applications and accordingly, several experimental and theoretical research activities have been undertaken with the objective of artificially inducing self-excited oscillation in mechanical systems. This paper considers some theoretical aspects of generation of self-excited oscillation in a two degrees-of-freedom

Multiscale based finite element model developed in the framework of the Cauchy–Born rule is employed to investigate the nonlinear response of some noncarbon nanosheets considering geometric and material nonlinearities. The Tersoff–Brenner type interatomic potentials with newly calibrated empirical parameters are employed to model the atomic interactions. The quadratic-type Cauchy–Born rule is used

The present study aims to investigate the synchronization characteristics of a pitch–plunge aeroelastic system subjected to coupled structural free-play and dynamic stall-induced aerodynamic nonlinearities. The semi-empirical Leishman–Beddoes (LB) aerodynamic model is used to capture the dynamic stall phenomena at large angles-of-attack (AoA). A bifurcation analysis, considering the flow-speed as the

This paper deals with the equilibrium problem of slender beams inflexed under variable curvature in the framework of fully nonlinear elasticity. For the specific case of uniform flexion, the authors have recently proposed a mathematical model. In that analysis, the complete three-dimensional kinematics of the beam is taken into account and both deformations and displacements are considered large. In

Studying the large-amplitude forced vibration characteristics of micropolar shell-type structures is the main objective of this paper. In order to obtain the full geometrically nonlinear model of micropolar theory, the micromorphic seven-parameter shell kinematic is first developed. Via a nonlinear micro-motion map, the extracted formulation is fitted for the micropolar continuum. As a result, possessing

In the assessment of breathing cracks, it is assumed that both sides of the crack will contact each other along with the vibration, causing the blades to exhibit nonlinear behaviors. Therefore, nonlinear approaches are much more sensitive to the cracks and are also capable of detecting their location and size. Recently, a nonlinearity measure-based damage location method was proposed for the distributed

The response enhancement (autoresonance) in a weakly dissipative nonlinear chain subjected to harmonic forcing with a slowly-varying frequency may be of interest for both a fundamental standpoint as well as practical applications. However, the cumulative effect of dissipation and forcing parameters on the emergence and stability of autoresonance in an anharmonic array has not been discussed thus far

In this article we generalize to polyatomic gases the moment closure of the relativistic Anderson–Witting model proposed by Cercignani and Kremer in the monatomic case, that uses the four-velocity in the Landau–Lifshitz description. A moment model is derived and compared with that recently proposed by Pennisi and Ruggeri using a variant of the Anderson–Witting model in an Eckart frame, obtaining that

The onset of thermal convection in a uniformly rotating and horizontally isotropic bi-disperse porous medium, taking into account the Vadasz term, is investigated. Via linear instability analysis, it has been proved that the Vadasz term allows the onset of convection via an oscillatory state but does not affect convection via a stationary motion.

The deformation of an initially straight elastic strip can be determined by prescribing the two end angles and the distance between the two ends. At certain end angles and end distance, snapping motion of the elastica may occur. A collection of these end angle pairs is called the snap boundary of the planar elastica. In the snap boundary theory developed previously (Cazzolli and Corso, 2019) self-intersection

In this paper, we provide a method for developing the FENE-P constitutive relation and generalizations of such constitutive relations from a totally different perspective than that used to develop such constitutive relations. The thermodynamic framework within which the constitutive relations are generated is a generalization of the structure within which rate type fluid models to describe the viscoelastic

The purpose of the current study is the nonlinear vibration analysis of an axially moving truncated conical shell. Based on the classical linear theory of elasticity, Donnell’s nonlinear theory assumptions with Von Kármán nonlinear terms, Hamilton principle, and Galerkin method, the nonlinear motion equations of axially moving truncated conical shells are derived. Then, a set of nonlinear motion equations

Hard magnetic materials belong to a novel class of soft active materials with the capability of quick, large, and complex deformation via applying an external actuation. They have an extensive range of potential applications in soft robots, biomedical devices, wearable devices, and stretchable electronic devices. Recently, investigation of experimental and theoretical nonlinear mechanics of hard magnetic

We present a constitutive framework for modeling the nonlinear elastic behavior of α-Germanium (Ge). Starting with all possible phase changes Ge sustains under compression, we correspond to each space group of every phase the arithmetic symmetry group by viewing Ge as a multilattice. We then focus on the mother α phase of Ge. Confining ourselves to weak transformation neighborhoods and adopting the

This paper presents a meshless model for quasi-static and dynamic analysis of a three-dimensional Timoshenko beam with geometric nonlinearity. A general mathematical formulation is constructed based on the corrective smoothed particle method (CSPM), which can correct the low precision and completeness deficiency of the standard smoothed particle hydrodynamics(SPH) method. The discrete governing equations

In this paper, equilibrium and stability of the von Mises truss subjected to a vertical load are analyzed from theoretical, numerical and experimental points of view. The bars of the truss are composed of a rubber material, so that large deformations can be observed. The analytical model of the truss is developed in the fully nonlinear context of finite elasticity and the constitutive behavior of the

A non-classic double bifurcation of discrete static systems, occurring along a non trivial equilibrium path, is studied. It occurs when, by varying a parameter, a pair of eigenvalues of the tangent stiffness matrix first merge and then disappear. A paradigmatic 2 degrees of freedom system with some symmetry, consisting of an inverted extensible pendulum, so far studied in literature in the linear range