Dynamic Instability Regions Research Articles

Dynamic buckling of magnetorheological fluid integrated by visco-piezo-GPL reinforced plates

This paper deals with the dynamic buckling analysis of sandwich plates with magnetorheological (MR) fluid core and piezoelectric nanocomposite facesheets. The core is subjected to magnetic field and the facesheets are exposed to 3D electric field. Due to the piezoelectric properties of the facesheets, the top and bottom layers can be used as actuator and sensor, respectively. Hence, a proportional-derivative (PD) controller is employed to control the dynamic buckling and vibration responses of the structure. In addition, the facesheets are reinforced by with non-uniform graphene platelets (GPLs) which their equivalent material properties are obtained using Halpin-Tsai micromechanics model. The structural damping of the piezoelectric layers is considered according to Kelvin-Voigt theory. The sandwich structure is rested on orthotropic viscoelastic model with normal, shear and damping forces. Based on the sinusoidal shear deformation theory (SSDT) and piezoelasticity theory, the motion equations are derived utilizing Hamilton's principle. Applying differential cubature method (DCM), the motion equations are solved for calculating the dynamic instability region (DIR) of the structure. The influences of various parameters such as magnetic field, applied voltage, structural damping, viscoelastic medium, volume fraction and distribution of GPLs, boundary conditions and geometric parameters of the structure are shown on the dynamic buckling behavior of the system. The results are validated with other published work for indication the accuracy of the obtained results. The results reveal that by applying the magnetic field to the MR fluid core, the DIR with be happened at higher excitation frequencies.

Dynamic stability of a size-dependent micro-beam

The effect of variation of the geometrical dimensions on dynamic instability regions (DIRs) of a rectangular cross-sectioned micro-beam with simply supports is discussed in this study based on modified coupled stress theory. A set of linear equations are derived on basis of the Lagrange method and trial series expansions for vertical displacement and rotation of the Timoshenko micro-beam model while longitudinal displacement is neglected due to the stretching effect of the micro-beams mid-plane. The first approximation of the dynamic stability analysis is done by the application of the Bolotin method besides obtaining the Mathieu-Hill equations. The numerical results demonstrate how the cross section's height and micro-beams length are the only effective parameters on DIRs somehow that when the geometrical dimensions are increased the DIRs are going to coincide.

On the Lack of Circumbinary Planets Orbiting Isolated Binary Stars

Abstract We outline a mechanism that explains the observed lack of circumbinary planets (CBPs) via coupled stellar–tidal evolution of isolated binary stars. Tidal forces between low-mass, short-period binary stars on the pre-main sequence slow the stellar rotations transferring rotational angular momentum to the orbit as the stars approach the tidally locked state. This transfer increases the binary orbital period, expanding the region of dynamical instability around the binary, and destabilizing CBPs that tend to preferentially orbit just beyond the initial dynamical stability limit. After the stars tidally lock, we find that angular momentum loss due to magnetic braking can significantly shrink the binary orbit, and hence the region of dynamical stability, over time, impacting where surviving CBPs are observed relative to the boundary. We perform simulations over a wide range of parameter space and find that the expansion of the instability region occurs for most plausible initial conditions and that, in some cases, the stability semimajor axis doubles from its initial value. We examine the dynamical and observable consequences of a CBP falling within the dynamical instability limit by running N-body simulations of circumbinary planetary systems and find that, typically, at least one planet is ejected from the system. We apply our theory to the shortest-period Kepler binary that possesses a CBP, Kepler-47, and find that its existence is consistent with our model. Under conservative assumptions, we find that coupled stellar–tidal evolution of pre-main sequence binary stars removes at least one close-in CBP in 87% of multi-planet circumbinary systems.

Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study

We study the nonlinear dynamics of solitary and optically injected two-element laser arrays with a range of waveguide structures. The analysis is performed with a detailed direct numerical simulation, where high-resolution dynamic maps are generated to identify regions of dynamic instability in the parameter space of interest. Our combined one- and two-parameter bifurcation analysis uncovers globally diverse dynamical regimes (steady-state, oscillation, and chaos) in the solitary laser arrays, which are greatly influenced by static design waveguiding structures, the amplitude-phase coupling factor of the electric field, i.e. the linewidth-enhancement factor, as well as the control parameter, e.g. the pump rate. When external optical injection is introduced to one element of the arrays, we show that the whole system can be either injection-locked simultaneously or display rich, different dynamics outside the locking region. The effect of optical injection is to significantly modify the nature and the regions of nonlinear dynamics from those found in the solitary case. We also show similarities and differences (asymmetry) between the oscillation amplitude of the two elements of the array in specific well-defined regions, which hold for all the waveguiding structures considered. Our findings pave the way to a better understanding of dynamic instability in large arrays of lasers.

Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: Dynamic buckling analysis

Dynamic buckling of viscoelastic sandwich truncated nanocomposite conical shell subjected to moisture, temperature and magnetic field is presented in this paper. This class of structures is of great interest due to its extensive use in aerospace applications. The layers of the structure are made from a multiphase nanocomposite consist of polymer-carbon nanotubes (CNT)-carbon fibers. The micromechanics and Halpin–Tsai equations in hierarchy are applied for calculating the effective material properties of the multiphase nanocomposite layers. The structural damping effects are considered based on Kelvin–Voigt theory. The surrounding medium is simulated using visco-Pasternak model. Utilizing the first order shear deformation theory (FSDT), energy method and Hamilton's principle, the motion equations are derived. Differential quadrature method (DQM) and Bolotin's method are applied for solution of the motion equations to obtain the dynamic instability region (DIR) of the structure. The effects of various parameters such as structural damping, viscoelastic medium, magnetic field, number of layers, volume fraction of CNTs, temperature and moisture changes as well as boundary conditions on the DIR of the structure are studied. The results reveal that by increasing the moisture and temperature changes, the DIR will be happened at lower excitation frequencies.

Dynamic instability response in nanocomposite pipes conveying pulsating ferrofluid flow considering structural damping effects

This paper deals with the dynamic stability of nanocomposite pipes conveying pulsating ferrofluid. The pipe is reinforced by carbon nanotubes (CNTs) where the agglomeration of CNTs are considered based on Mori-Tanaka model. Due to the existence of CNTs and ferrofluid flow, the structure and fluid are subjected to axial magnetic field. Based on Navier-Stokes equation and considering the body forced induced by magnetic field, the external force of fluid to the pipe is derived. For mathematical modeling of the pipe, the first order shear deformation theory (FSDT) is used where the energy method and Hamilton\'s principle are used for obtaining the motion equations. Using harmonic differential quadrature method (HDQM) and Bolotin\'s method, the motion equations are solved for calculating the excitation frequency and dynamic instability region (DIR) of the structure. The influences of different parameters such as volume fraction and agglomeration of CNTs, magnetic field, structural damping, viscoelastic medium, fluid velocity and boundary conditions are shown on the DIR of the structure. Results show that with considering agglomeration of CNTs, the DIR shifts to the lower excitation frequencies. In addition, the DIR of the structure will be happened at higher excitation frequencies with increasing the magnetic field.

Dynamic stability of nanocomposite Mindlin pipes conveying pulsating fluid flow subjected to magnetic field

In this work, the dynamic stability of carbon nanotubes (CNTs) reinforced composite pipes conveying pulsating fluid flow is investigated. The pipe is surrounded by viscoelastic medium containing spring, shear and damper coefficients. Due to the existence of CNTs, the pipe is subjected to a 2D magnetic field. The radial induced force by pulsating fluid is obtained by the Navier-Stokes equation. The equivalent characteristics of the nanocomposite structure are calculated using Mori-Tanaka model. Based on first order shear deformation theory (FSDT) or Mindlin theory, energy method and Hamilton\'s principle, the motion equations are derived. Using harmonic differential quadrature method (HDQM) in conjunction with the Bolotin\'s method, the dynamic instability region (DIR) of the system is calculated. The effects of different parameters such as volume fraction of CNTs, magnetic field, boundary conditions, fluid velocity and geometrical parameters of pipe are shown on the DIR of the structure. Results show that with increasing volume fraction of CNTs, the DIR shifts to the higher frequency. In addition, the DIR of the structure will be happened at lower excitation frequencies with increasing the fluid velocity.

On the Dynamic Stability of a Reinforced Concrete Plate, Taking into Account the Material Creep

The problem of the dynamic stability of a reinforced concrete plate armoured in two directions parallel to its edges is considered. To describe the viscoelastic properties of concrete, an integral dependence was adopted with an exponential kernel. The use of this dependence led to a linear differential equation of plate vibration. In addition to the creep of concrete, the work of the reinforcement was taken into account. The solution of the differential equation of vibrations of a plate in the form of a series with separated variables is considered, which satisfies the plate fastening conditions. Differential equations are obtained for the time function by the Bubnov-Galerkin method. The task was to find the main areas of dynamic instability. For this, the critical frequency equation was obtained. The influence of the coefficients entering into the equation of critical frequencies on the position of the main regions of dynamic instability is investigated.

Dynamic instability of variable angle tow composite plates with delamination

In this paper, the dynamic instability of variable angle tow (VAT) plates with a single rectangular delamination is studied using an analytical model. The analytical model is derived from the principle of potential energy based on the classical laminated plate theory. Both global and local behavior of delaminated VAT plates in the dynamic instability analysis are accurately captured by the use of multiple Legendre polynomial series. The equations for the motion in dynamic instability problem are derived using Hamilton’s principle. The dynamic instability regions are determined from the resulting Mathieu differential equations, which are solved using Bolotin’s approach. To validate the proposed analytical model, both critical buckling loads and natural frequencies of delaminated VAT plates are evaluated and compared with FEM results. The influence of delamination on the buckling load, natural frequency and dynamic instability region (DIR) of delaminated VAT plates is examined by numerical examples. A parametric study is subsequently carried out to analyze the effect of linearly varying fibre orientation angles on the dynamic instability response of delaminated VAT plates. Finally, the mechanism of applying variable angle tows to improve the dynamic stability performance of delaminated composite plates is studied.

Dynamic buckling of polymer–carbon nanotube–fiber multiphase nanocomposite viscoelastic laminated conical shells in hygrothermal environments

This paper deals with the dynamic buckling of a sandwich truncated conical shell composed of polymer–carbon nanotubes–fiber multiphase nanocomposite layers. The structure is located in hygrothermal environments. The equivalent material properties of the multiphase nanocomposite layers are obtained using fiber micromechanics and Halpin–Tsai equations in hierarchy. According to Kelvin–Voigt theory, the realistic behavior of the structure is considered by considering the viscoelastic properties. The surrounding medium is simulated using visco-Pasternak model. The governing equations of the system are derived based on the classical theory by employing Hamilton’s principle. To obtain the dynamic instability region of the system, the differential quadrature method, and Bolotin’s method are utilized. The influences of various parameters such as structural damping, viscoelastic medium, number of layers, volume fraction of carbon nanotubes, temperature, and moisture changes on the analysis of the dynamic instability region of the structure are studied. The results reveal that by increasing the volume percent of carbon nanotubes, the dynamic instability region moves to higher frequencies.

Dynamic buckling response of temperature-dependent functionally graded-carbon nanotubes-reinforced sandwich microplates considering structural damping

This research deals with the nonlocal temperature-dependent dynamic buckling analysis of embedded sandwich micro plates reinforced by functionally graded carbon nanotubes (FG-CNTs). The material properties of structure are assumed viscoelastic based on Kelvin–Voigt model. The effective material properties of structure are considered based on mixture rule. The elastic medium is simulated by orthotropic visco-Pasternak medium. The motion equations are derived applying Sinusoidal shear deformation theory (SSDT) in which the size effects are considered using Eringen\'s nonlocal theory. The differential quadrature (DQ) method in conjunction with the Bolotin\'s methods is applied for calculating resonance frequency and dynamic instability region (DIR) of structure. The effects of different parameters such as volume percent of CNTs, distribution type of CNTs, temperature, nonlocal parameter and structural damping on the dynamic instability of visco-system are shown. The results are compared with other published works in the literature. Results indicate that the CNTs have an important role in dynamic stability of structure and FGX distribution type is the better choice.

Dynamic Stability of Woven Fiber Laminated Composite Shallow Shells in Hygrothermal Environment

The dynamic stability of bidirectional woven fiber laminated glass/epoxy composite shallow shells subjected to harmonic in-plane loading in hygrothermal environment is considered. An eight-noded isoparametric shell element with five degrees of freedom is used in the analysis. In the present finite element formulation, a composite doubly curved shell model based on first-order shear deformation theory (FSDT) is used for the dynamic stability analysis of shell panels subjected to hygrothermal loading. A program is developed using MATLAB for the parametric study on the dynamic stability of shell panels under the hygrothermal field. The effects of various parameters like static load factor, curvature, shallowness, temperature, moisture, stacking sequence and boundary conditions on the dynamic instability regions of woven fiber glass/epoxy shell panels are investigated. The location of dynamic instability regions is shown to affect significantly due to presence of the hygrothermal field.

Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method

This research deals with the nonlocal dynamic buckling analysis of embedded microplates reinforced by single-walled carbon nanotubes (SWCNTs). The material properties of structure are assumed viscoelastic based on Kelvin–Voigt model. Agglomeration effects are considered based on Mori–Tanaka approach. The elastic medium is simulated by orthotropic visco-Pasternak medium. The motion equations are derived applying higher-order shear plate model based on sinusoidal kinematic in which the size effects are considered using Eringen’s nonlocal theory. The Navier method in conjunction with the Bolotin’s methods is applied for calculating resonance frequency and dynamic instability region of structure. The effects of different parameters such as volume percent of SWCNTs, agglomeration, volume percent of SWCNTs in volume, nonlocal parameter and structural damping on the dynamic instability of visco-system are shown. The results are compared with other published works in the literature. Results indicate that the agglomeration effects have an important role in dynamic stability of structure. In addition, increasing volume percent of SWCNTs leads to higher resonance frequency.

Dynamic stability of FG-CNT-reinforced viscoelastic micro cylindrical shells resting on nonhomogeneous orthotropic viscoelastic medium subjected to harmonic temperature distribution and 2D magnetic field

This paper deals with the dynamic stability of embedded functionally graded (FG)-carbon nanotubes (CNTs)-reinforced micro cylindrical shells. The structure is subjected to harmonic non-uniform temperature distribution and 2D magnetic field. The CNT reinforcement is either uniformly distributed or FG along the thickness direction where the effective properties of nano-composite structure are estimated through Mixture low. The viscoelastic properties of structure are captured based on the Kelvin–Voigt theory. The surrounding viscoelastic medium is considered nonhomogeneous with the spring, orthotropic shear and damper constants. The material properties of cylindrical shell and the viscoelastic medium constants are assumed temperature-dependent. The first order shear deformation theory (FSDT) or Mindlin theory in conjunction with Hamilton\'s principle is utilized for deriving the motion equations where the size effects are considered based on Eringen\'s nonlocal theory. Based on differential quadrature (DQ) and Bolotin methods, the dynamic instability region (DIR) of structure is obtained for different boundary conditions. The effects of different parameters such as volume percent and distribution type of CNTs, mode number, viscoelastic medium type, temperature, boundary conditions, magnetic field, nonlocal parameter and structural damping constant are shown on the DIR of system. Numerical results indicate that the FGX distribution of CNTs is better than other considered cases. In addition, considering structural damping of system reduces the resonance frequency.

Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects

Based on nonlocal Timoshenko beam theory, dynamic stability of functionally graded (FG) nanobeam under axial and thermal loading was investigated. Surface stress effects were implemented according to Gurtin-Murdoch continuum theory. Using power law distribution for FGM and von Karman geometric nonlinearity, governing equations were derived based on Hamilton's principle. The developed nonlocal models have the capability of interpreting small scale effects. Pasternak elastic medium was employed to represent the interaction of the FG nanobeam and the surrounding elastic medium. A parametric study was conducted to focus influences of the static load factor, temperature change, gradient index, nonlocal parameter, slenderness ratio, surface effect and springs constants of the elastic medium on the dynamic instability region (DIR) of the FG beam with simply-supported boundary conditions. It was found that differences between DIRs predicted by local and nonlocal beam theories are significant for beams with lower aspect ratio. Moreover, it was observed that in contrast to high temperature environments, at low temperatures, increasing the temperature change moves the origin of the DIR to higher excitation frequency zone and leads to further stability. Considering surface stress effects shifts the DIR of FG beam to higher frequency zone, also increasing the gradient index enhances the frequency of DIR.

Parametric Instability of Laminated Composite Plates Using Third Order Shear Deformation Theory

Parametric instability as compared to force resonance may occur in a structure when the frequency of loading is at a fraction of the natural frequency of the structure. As such the structure may experience fatigue failure due to parametric instability merely at loading less than its critical load. In this paper, parametric instability analysis of composite plate subjected to periodic compressive loading has been conducted using finite element method (FEM). The FEM formulation is based on the third order shear deformation theory. The Mathieu-Hill type equation that described the parametric instability of the composite plate was developed using the Hamilton’s principle. This equation was solved using the Bolotin’s method that reduces the Mathieu-Hill equation to a couple of eigen-value problems. Using the developed FEM source codes, the instability chart or the Strut-Ince diagrams were drawn to show the instability regions for several cases of composite types and parameters. The results of the dynamic instability region were validated with the results from past literatures. It was found that as the static load parameter is increased, the center for dynamic instability region is shifted to the left and in the case of symmetric angle-ply composite plate, the orientation angle of θ = 45° gives the highest frequency at the center of the instability chart.

Nonlinear size-dependent dynamic buckling analysis of embedded micro cylindrical shells reinforced with agglomerated CNTs using strain gradient theory

This article presents an analysis on the nonlinear dynamic buckling of a micro cylindrical shell reinforced by carbon nanotubes (CNTs) with considering agglomeration effects. The structure is surrounded by an elastic medium and is subjected to magnetic field and harmonic mechanical load. Mindlin theory is employed to model the structure and the modified strain gradient theory (SGT) is also used to capture the size effect. Mori–Tanaka approach is used to estimate the equivalent material properties of the nanocomposite cylindrical shell and consider the CNTs agglomeration effect. The motion equations are derived using Hamilton’s principle and the differential quadrature method (DQM) along with Bolotin method is employed to solve them for obtaining the dynamic stability region. The effect of different parameters including magnetic field, CNTs volume percent and agglomeration effect, boundary conditions, elastic medium, size effect and length to thickness ratio on the dynamic buckling behavior of the system is studied. The results indicate that considering elastic medium, magnetic field and size effects, increases the stiffness of the structure and so, the dynamic instability region occurs at higher frequency while considering the CNTs agglomeration effect has inverse effect. Also, by increasing the CNTs volume percent and considering the clamped–clamped boundary condition, the dynamic behavior of the system improves.

Effect of coolant flow rate on the dynamics of delayed recycle continuous stirred tank reactor

Abstract Numerical bifurcation analysis of delayed recycle stream in a continuous stirred tank reactor was studied using DDE-BIFTOOL. A first-order irreversible exothermic reaction s 1 → k 2 , 1 s 2 was considered for analyzing effect of delay on the stability of the delayed recycle system. The non-isothermal CSTR was operated at both infinite and finite coolant inlet flowrates. A constant delay was considered in the recycle stream of CSTR for concentration of reactant, and temperature. DDE-BIFTOOL solver was used for finding dependency of delays on the bifurcation parameters, and its stability characteristics. The bifurcation parameters considered were: (i) fresh feed flowrate, (ii) coolant temperature, and (iii) coolant inlet flowrate. In the absence of delay, the system exhibits the region of dynamic instability for both infinite and finite coolant inlet flowrates. For infinite coolant flowrate, the region of dynamic instability on the reactor temperature was modified as a result of delay by varying either fresh feed flowrate or coolant temperature. The steady-state multiplicity was observed on the coolant temperature by varying fresh feed flowrate at finite coolant inlet flowrate. In the absence of delay, the fold and Hopf bifurcations were observed on the multiple steady-states of coolant temperature. The concentration and temperature delays do not alter substantially the dynamic characteristics of coolant temperature at Tc,in = 298 K. However, delays can alter the region of dynamic instability for coolant temperature when coolant inlet temperature is higher than 298 K. These are the main result of present work.

Floquet Instability of Gravity-Modulated Salt Fingering in a Porous Medium

Fingering convection in a horizontal doubly stratified fluid-saturated porous medium is examined under the influence of modulating gravitational field. The Brinkman model of momentum transfer is considered, and the Boussinesq approximation is assumed for natural convection. Floquet theory is employed to determine the onset condition within the framework of linear theory. Continued fractions that can handle arbitrary modulational parameters has been used to predict the dynamic instability regions at the marginal state and critical instability boundaries. Certain combinations of solutal Rayleigh and Schmidt numbers give rise to the occurrence of doubly unstable regions. An increase in the modulation amplitude always encourages instability. The competition between synchronous and subharmonic instability modes is observed for a certain range of values of the parameters. Solutal convection is found to introduce closed disconnected instability loops at the marginal state. It is seen that gravity modulation effe...

Assessment of lateral dynamic instability of columns under an arbitrary periodic axial load owing to parametric resonance

The paper presents a method for assessing the dynamic stability of simply supported columns with damping under arbitrary periodic axial loading owing to parametric resonance. The equation for determining critical excitation frequencies causing lateral parametric instability of columns is derived using the Bolotin′s method. A method of matrix transformation is developed to solve the ill-condition problem in the even regions of dynamic instability of the column caused by inclusion of damping. The accuracy of the proposed method is carefully verified by comparing the results with those in the literature. New findings of this investigation are: (1) the critical excitation parameter for inducing dynamic instability under arbitrary periodic loading increases with increasing damping ratio; (2) in difference from columns under a simple harmonic load, the width of instability regions of columns under an arbitrary periodic load does not necessarily decrease as the number of region increases, so the instability regions can cover most of the parametric plane, and thus the dynamic instability is more likely to occur; (3) under an arbitrary periodic axial load, the first region of instability of columns may not be the critical one, and the number of harmonic waves adopted in the computation is important for the location of the most critical region of instability and the distribution of instability regions in the parametric plane; and (4) the dimension of determinant in the equation of boundary frequencies rather than the number of harmonic waves is responsible for computation efficiency, and the sufficient large dimension of determinant should be retained to achieve the computational accuracy.