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

The Oberbeck–Boussinesq (OB) approximation for a compressible fluid in Bénard’s problem geometry is studied. We present a new derivation of the classical and ’extended’ OB models for a fluid obeying the ideal gas state equation by means of an asymptotic limit for vanishing temperature difference. The ‘extended’ OB approximation takes account of the compressibility effects in the energy balance, due

Nonlinear analysis of two base isolated tall buildings, close to each other, coupled at the tip with a nonlinear viscous device and under the effect of wind, is addressed. The partial differential equations of motion are written with reference to a system constituted by two equivalent beam-like elements, and the modal features are evaluated both in presence and absence of wind which, besides nonlinear

Different one-phase Stefan problems for a semi-infinite slab are considered, involving a moving phase change material as well as temperature dependent thermal coefficients. Existence of at least one similarity solution is proved imposing a Dirichlet, Neumann, Robin or radiative–convective boundary condition at the fixed face. The velocity that arises in the convective term of the diffusion–convection

In this work, mathematical models of physically nonlinear beams (and plates) are constructed in a three-dimensional and one-dimensional formulation based on the kinematic models of Euler–Bernoulli and Timoshenko. The modeling includes achievements of the deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the Birger theory of elasticity. The

The current paper focuses on investigating the effect of different distribution types of single-walled carbon nanotube (SWCNT) reinforcement and the volume fraction of CNTs on the nonlinear vibration of simply supported nanocomposite circular cylindrical shells. The governing equations are derived for uniform and three kinds of FG distribution of CNTs utilizing the extended mixture rule and Hamilton

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

Recently, for high-power ultrasonic beams, it was experimentally found that as a result of self-action, their self-focusing occurs. With self-focusing, a powerful ultrasonic beam is noticeably narrowed, has a nonlinear narrowing, and it is significantly amplified at the focus. A generalization of the three-dimensional Khokhlov–Zabolotskaya–Kuznetsov model in a cubic nonlinear medium in the presence

This work investigates the interaction between adjacent bays and the effect of the curvature ratio in the nonlinear response of cross-stream curved panels. The study presents a numerical investigation of shallow shells’ linear and nonlinear dynamic behavior exposed to supersonic flutter. The finite element model embedding the aerodynamic piston theory and the Newmark method for direct time-domain integration

The present paper proposes a new Strain Energy Function (SEF) for modeling​ incompressible orthotropic hyperelastic materials with a specific application to the mechanical response of passive ventricular myocardium. In order to build our SEF, we have followed a classical strategy based on exponential functions, but we have chosen to work with polyconvex invariants instead of the standard ones. Actually

This paper deals with the frequency–amplitude response of superharmonic resonance of second order (order two) of electrostatically actuated Micro-Electro-Mechanical System (MEMS) cantilever resonators. The structure of MEMS resonators consists of a cantilever resonator over a parallel ground plate, with a given gap in between, and under AC voltage. This resonance results from hard excitations and AC

A gravity-driven, thin, incompressible liquid film flow on a non-uniformly heated, slippery inclined plane is considered within the framework of the long-wave approximation method. A mathematical model incorporating variation in surface tension with temperature has been formulated by coupling the Navier–Stokes equation, governing the flow, with the equation of energy. For the slippery substrate, the

In this paper, we investigate the pulsatile flow of a cement slurry in a pipe. The constitutive relation for the viscous stress tensor is based on the power-law model, where the shear viscosity not only depends on the shear rate but also the volume fraction of the cement particles. To solve for the volume fraction field, a convection–diffusion equation is used. The dimensionless form of the governing

In this paper, we explore the Riemann problem for the equations of constant pressure fluid dynamics with nonlinear damping. By introducing a variable substitution of exponential type, the Riemann problem is solved and the solutions involving delta shock wave and vacuum state are obtained. Then, we solve the generalized Riemann problem for such equations with nonlinear damping when the initial data

This article investigates the large deflection and post-buckling of composite plates by employing the Carrera Unified Formulation (CUF). As a consequence, the geometrically nonlinear governing equations and the relevant incremental equations are derived in terms of fundamental nuclei, which are invariant of the theory approximation order. By using the Lagrange expansion functions across the laminate

A new bistable impact oscillator with bilateral rigid constraints under periodic excitations is established and the global dynamics are studied in detail respectively by the extended analytical Melnikov method for non-smooth systems and dynamical experiments. Firstly, the Melnikov method is extended from a new viewpoint of geometry for an abstract non-smooth dynamical system denoting a class of bistable

A dynamic model with two discontinuously coupled bi-nonlinear oscillators and multiple non-smooth constraints is presented, which increases the complexity of the system. The dynamic behaviors of the system with asymmetric clearances are investigated by the continuation platform Computational Continuation Core (abbreviated as COCO) and rich bifurcation phenomena are revealed. In the case of bilateral

A nonlinear vibration absorber (NVA) is used to suppress the nonlinear response of a panel flutter in supersonic airflow. The nonlinear aeroelastic equations of a three-dimensional (3-D) panel with an NVA are established using Galerkin’s method, with the aerodynamic load being based on the piston aerodynamic theory. We use the aeroelastic equations to study the nonlinear aeroelastic response behaviors

This work investigates the thin film instability of a non-Newtonian second-grade fluid flowing down a heated inclined plane subject to linear variation of physical properties such as density, viscosity, thermal diffusivity, and surface tension concerning temperature. A nonlinear evolution equation for the description of the free surface is derived using long-wave approximation. The critical conditions

In this study, we computationally corroborate the flow of rock glaciers against borehole measurements, within the context of a model previously developed (2020). The model is, here, tested against the simulation of the sliding motion of the Murtel-Corvatsch alpine glacier, which is characterized in detail in the literature with internal structure description and borehole deformations measurement. The

A nonlinear static analysis of the sandwich plate using variational techniques and the Ritz method is presented. The kinematic description developed for a sandwich plate undergoing small strains and moderate rotations within the framework of Extended Higher Order Sandwich Panel Theory is considered. Employing the Ritz method, the total potential energy of the system is developed. Four different cases

This research article investigated the rotor-casing contact phenomena of a high-speed rotor-bearing system under mass unbalance situation. Here, large deflection rotor-bearing model with a flexible shaft, a rigid disk loaded with an unbalance mass and contact phenomenon between a disk and casing of the rotating system has been used. A nonlinear mathematical model of a rotating system has been developed

We propose to use a shallow arched microbeam to design a compact 2D energy harvesting device using a single electrostatic transducer. The proposed design can transform any in-plane applied acceleration into motion of a variable capacitor whose movable electrode is linked to the shallow arched microbeam. A secondary electrode is placed to directly apply a force on the microbeam in order to tune its

By using a Pontryagin’s principle, we study the optimal shape of a rotating nano rod and determine the optimal cross-section that is stable against buckling due to centrifugal forces. We generalize the results of the earlier studies focused on the constant cross-sectional area of nano rods. The problem of the optimal shape of a Bernoulli–Euler rotating rod is analyzed first. The optimal nano rod with

Working in the context of hyperbolic reaction–diffusion–acoustic theory, we present a detailed study of singular surface shock phenomena under two hyperbolic versions of the Fisher–KPP equation, both of which are based on flux laws originally used to describe the phenomenon of second-sound. Employing both analytical and numerical methods, we investigate the propagation, evolution, and qualitative behavior

This paper is about the role of the fluid in supporting the overall compressive stress applied to nonlinear elastic fluid-saturated porous material. The case of large deformation and compressible hyperelastic matrix material is considered. Due to complexity of the problem, a simple model of the porous medium consisting of an assemblage of fluid-filled cylinders is studied in more detail. The procedure

In this work, a new class of discrete Bonhoeffer–van der Pol (BVP) system with an odd function is proposed and investigated. At first, the necessary and sufficient conditions on the existence and stability of the fixed points for this system are given. We then show the system passes through various bifurcations of codimension one, including pitchfork bifurcation, saddle–node bifurcation, flip bifurcation

In this study, the stochastic dynamic response of a spur gear pair model under the excitation of filtered noise is investigated. The spur gear pair is modeled as a single degree of freedom (SDOF) system in which nonlinear and non-smooth backlash and time-varying mesh stiffness as well as stochastic excitation are concurrently considered. Four cases are addressed, based on how the noise is incorporated

A collocation technique based on the use of Bernstein polynomials to approximate the field variable is assessed in Boundary Value Problems (BVPs) of beams with governing non-linear differential equations. The BVPs are transformed into unconstrained optimization problems by means of an extended cost function which leverages the properties of the Bernstein basis to enforce the boundary conditions. The

This study performs an experimental and numerical investigation on the nonlinear aeroelastic response of cantilever high-aspect-ratio beam-like wings with a ballast at their free tips, emulating the effects of a store. As an extent, the effects of different chord-wise ballast positions are experimentally examined for two highly flexible rectangular wings. Furthermore, the numerical model proposed brings

This work presents a new numerical integration method for determining dynamics of a class of multibody systems involving impact and friction. Specifically, these systems are subject to a set of equality constraints and can exhibit single frictional impact events. Such events are associated to significant numerical stiffness, appearing in the equations of motion. The new method is a time-stepping scheme

One of the problems of periodic FPU-chains with alternating large masses is whether significant interactions exist between the so-called (high frequency) optical and (low frequency) acoustic groups. We show that for α-chains with 2n particles we have significant interactions caused by external forcing of the acoustic modes by a stable or unstable optical normal mode. In the proofs an embedding theorem

In this paper, the efficacy of velocity feedback based nonlinear resonant controller is proposed to control the free and forced self-excited vibration of a nonlinear beam. The velocity signal obtained from the sensor is fed through a second-order filter and the nonlinear function of the derivative of the filter variable is used to obtain the control force. The resulting control system being a band-pass

The motion of a polytropic compressible fluid or gas in a non-uniform channel with elastic walls and a specified cross-section A(x,p) depending on a given point x and the pressure p is examined. The form of a cross-section A=kxαpβ is considered in this paper. Particular cases arising from the analysis that lead to an exact solution of the equations of the hydraulic longitudinal waves are given. For

Nonlinear vibro-acoustic behavior of cylindrical shell excited by an oblique incident plane sound wave under primary resonances is analytically examined in this paper. Donnell’s nonlinear shallow shell theory is used to model the cylindrical shell. Coupled nonlinear differential equations of the system are analytically derived using Galerkin’s approach. The Multiple Scales Method is hence, employed

Nonlinear shell modeling is always accompanied by simplifying assumptions on some computational parameters. In the latest nonlinear model based on eight parameters, that considers the displacement field as third-order polynomials in all three directions of curvilinear system, rotational inertia and shear deformations are also included; however, nonlinear terms are eliminated from some dependent variables

In this paper, the internal resonance response of two nonlinearly coupled micro beams with frequency ratio approximately 1:3 is investigated and an interesting phenomenon called frequency locking is observed experimentally. A nonlinear dynamic model of the coupled system is established and solved using multi scale method to explain this phenomenon, and the amplitude region for triggering frequency

We examine theoretically the dynamic inflation and finite amplitude oscillatory motion of inhomogeneous spherical shells and cylindrical tubes of stochastic hyperelastic material. These bodies are deformed by radially symmetric uniform inflation, and are subjected to either a surface dead load or an impulse traction, uniformly applied in the radial direction. We consider composite shells and tubes

The increasing complexity of the constructive forms and shell elements structure leads to the need to develop both the theory and methods for solving static and dynamic problems for non-homogeneous (heterogeneous) shells. By the shell heterogeneity, we mean heterogeneity in a broad sense: these are inclusions in the shell body of the different rigidity elements and, as a special case, these are holes;

Many civil structures and facilities can be modeled using cable-stayed cantilever beams. This study is to investigate the nonlinear dynamic response and dynamic behavior of a cable-stayed cantilever beam subjected to two different external excitations through theoretical analyses. First, the equations of motion of the cable and the beam are established. Then, based on the Galerkin method, dynamic structural

This paper is concerned with the analysis of the influence of the friction model on the existence of additional integrals of motion in a system describing the sliding of a spherical top on a plane. We consider a model in which the friction is described not only by the force applied at the point of contact, but also by an additional friction torque. It is shown that, depending on the chosen friction

This paper presents exact solutions for the buckling loads and postbuckling states of extensible, shear deformable beams. The governing equation for the large-amplitude lateral deformation of beams in compression is expanded in Taylor series up to the cubic nonlinearity. Closed-form solutions in terms of the axial and shear stiffnesses are developed for statically determinate and statically indeterminate

In a recent paper in this journal by Anssari-Benam and Bucchi (2021), the authors have proposed a new two-parameter constitutive model for isotropic incompressible hyperelastic generalized neo-Hookean materials. The model reflects the limiting chain extensibility characteristic of non-Gaussian molecular models for rubber. A major contribution of Anssari-Benam and Bucchi (2021) is in showing that the

This work explores the modelling of soft tissues, particularly the Achilles tendon, using the absolute nodal coordinate formulation (ANCF).The anisotropic Gasser–Ogden–Holzapfel (GOH) potential energy function provided the necessary anisotropic elastic feature descriptions. A generalized one-dimensional Maxwell model described the viscoelastic effects. Finally, a parameter-based damage model characterized

Nano and micro electro-mechanical systems (NEMS and MEMS) have been attracting a large amount of attention recently as they have extensive current/potential applications. However, due to their scale, molecular interaction and size effects are considerably high which needs to be considered in the theoretical modelling of their electro-mechanical behaviour. Both nano- and micro-scale electrically actuated

In this paper, the nonlinear three-dimensional (3D) stress analysis of shell structures in buckling and snapping problems is presented. The exact geometry or geometrically exact (GeX) hybrid-mixed four-node solid-shell element is developed using a sampling surfaces (SaS) method. The SaS formulation is based on the choice of N SaS parallel to the middle surface to introduce the displacements of these

Coupling nonlinear dynamical systems can lead to a host of phenomena, one of which leads to the complete cessation of their oscillations. This phenomenon is referred to as amplitude death (AD) in the dynamical systems literature. Recently, there is a growing interest to mitigate oscillatory or dynamic instabilities in a variety of engineering systems using AD. Deriving impetus from the same, we investigate

We consider a single degree freedom oscillator in order to accurately represent some modeling with ship roll damping. The proposed oscillator is a nonsmooth Rayleigh–Duffing equation ẍ+aẋ+bẋ|ẋ|+cx+dx3=0. The main goal of this paper is to study the global dynamics of the nonsmooth Rayleigh–Duffing oscillator in the case d<0, i.e., the saddle case. The nonsmooth Rayleigh–Duffing oscillator is only

In the second part of the article, the nonlinear dynamics and stability of nonhomogeneous variable thickness axisymmetric shells are analyzed. The mathematical model is based on the Kirchhoff–Love kinematic hypothesis. The resulting system of partial differential equations is reduced to an algebraic equations system by the Ritz method. The convergence of the applied numerical methods is investigated

The present article studies the nonlinear dynamics and effects of high-frequency excitations (HFE) on a forced 2-D coupled beam and wake oscillator model ascribing vortex-induced vibrations. Oscillatory strobodynamics (OS) theory is employed for studying the characteristics of the system in slow time-scale. Linear stability analysis is performed near the equilibrium point of the system for both with

Nonlinear aspects of aeroelastic stability are here investigated for two and three dimensional panels in high subsonic and low supersonic flows. The effects of edge constraints and initial conditions on post-flutter behaviour are also studied. Such phenomena are crucial for spatial launchers development, that has renewed interest due to a larger number of commercial companies in the frame of space

This paper deals with the uncertainty analysis of the cardiac system described by a mathematical model. The model is composed of three-coupled nonlinear oscillators with time-delayed connections. The main idea is to investigate heart dynamics using the Random Matrix Theory, modeling uncertainties and establishing the impact of the probabilistic model on the dynamic response of the system Two advantages

The equation describing surface waves in a one-dimensional magnetohydrodynamic discontinuity involves the Hilbert transform and is therefore nonlocal. It is found that by taking the analytic function whose real part is the first order perturbation one obtains a local equation. This equation yields several integral equalities which may be studied with the help of certain classical results of the theory

In a rapidly moving multiphase mass flow, drag and virtual mass forces are important interfacial forces. However, in many existing literatures, virtual mass force has often been ignored or employed empirically. In this contribution, we construct analytical, full and explicit expressions for the virtual mass coefficients in the true three-phase typical debris flow consisting of coarse-solid, fine-solid

The Riemann problem for isentropic drift-flux model of compressible two-phase flow in a variable cross-section duct is considered. First, the two-phase duct flow model is established based on the balance laws. Then, by averaging the equations of single phase flow, the drift-flux model in a variable cross-section duct is deduced. The model includes two parts: mass conservation and momentum conservation