Functionally graded materials are well-known composite materials, characterized by a continuously varying mixture of materials’ phases, tailored to meet structures operating requirements while ...contributing to minimize abrupt stress transitions at dissimilar materials’ interfaces, as occur in composite laminates. Hence, designing a functionally graded material to comply with these objectives constitutes an important modelling tool to improve structures’ functionality. These graded composite materials present more commonly a mixture variation through the structures’ thickness direction. However, when dealing with thin structures this solution may present evident limitations, both from the manufacturing perspective as well as from the through-thickness distribution influence on the structure response. It is therefore important to explore other spatial mixture distributions’ possibilities.
To this purpose, the present work considers thin graded materials’ plates which constitution is defined by a set of different in-plane volume fraction distributions. The influence of these distributions on the free vibrations and dynamic instability of thin plates is assessed through a comprehensive set of parametric studies. The free vibration problem and the dynamic instability problem’ solutions are respectively obtained by Rayleigh-Ritz and Bolotin’s methods. As a complementary analysis contribution, image correlation studies are also developed for a set of fundamental mode shapes.
•The mode shape functions for out-of-plane displacement of arches with different elastic rotational restraints are analytically determined.•Analytical solution for instability regions with elastic ...rotational restraints under a localized uniform radial periodic load is presented.•The analytical solution of dynamic instability regions are verified by frequency sweep transient finite element analyses (FEA).•Affected parameters on dynamic instability regions are comprehensively analyzed.
Out-of-plane dynamic instability of a circular arch with elastic rotational constraints under localized uniform radial periodic load is studied in this paper which has not been yet reported in the literature. In the out-of-plane dynamic instability analysis, the coupled equation of motion associated with lateral displacement and twist angle is derived by using an energy method and Hamiltonian principle. Then the mode shape functions of arches with different elastic rotational restraints are deduced and analytical solution for unstable regions with a period of 2T are obtained by using Bolotin’s method. Finite element numerical analysis is employed to justify the dynamic unstable regions by frequency sweeping simulation and the results show a desirable agreement. It is found that when the flexibility of out-of-plane elastic rotational restraints decreases, the unstable region moves towards the direction of higher frequencies owing to the increase in rigidity of the arch, with the out-of-plane dynamic stability of the arch being improved. The load localized parameter significantly impacts the dynamic stability for the arches with various flexibility of out-of-plane restraints. These results give us a deep understanding of the instability mechanism of engineering structures with arches and provide insight into the effective design of arch structures.
A small external excitation can trigger a strong auto-parametric internal resonance response in underwater structure. Currently, research on auto-parametric internal resonance primarily relies on ...theoretical methods and experimental approaches involving the simulation of water flow forces using vibrators. To more realistically reflect the auto-parametric internal resonance of structures in water, this study investigates the phenomenon of auto-parametric internal resonance of a Γ-shaped frame structure induced by vortex-induced vibration in a laboratory flume. The results indicate that the auto-parametric internal resonance can be excited by water flow in the flume and the Γ-shaped frame structure is more prone to experience normal resonance than auto-parametric internal resonance. However, the vibration intensity caused by auto-parametric internal resonance is significantly greater than that of normal resonance. The range of h/L (the ratio of water depth to the length of the vertical beam) for auto-parametric internal resonance in both the clamped-pined joint system (CPJS) and the pined-pined joint system (PPJS) is 0.307–0.364, but the flow velocity range for auto-parametric internal resonance in CPJS is broader than that in PPJS. When h/L is 0.307, the reduced velocity Ur ranges for the auto-parametric internal resonance of CPJS and PPJS are 4.839–5.375 and 4.904–5.256, respectively. When h/L is 0.364, the Ur ranges for the auto-parametric internal resonance of CPJS and PPJS are 4.587–4.742 and 4.507–4.660, respectively.
•The auto-parametric internal resonance is excited by water flow in the flume.•Reveal the mechanism of vortex-induced auto-parametric internal resonance.•Obtain water depth and velocity ranges of structural internal resonance instability.
The stability characteristics of closed supercritical natural circulation loop has hardly been explored owing to the mathematical complexity and absence of explicit boundary condition. Present ...numerical study investigates the nature of both static and dynamic instability in a rectangular loop with carbon dioxide as the working medium. Sharp deterioration in the steady-state circulation rate can be observed, consistent to existing multidimensional analyses. Loop exhibits Ledinegg instability for an intermediate range of heater power, characterized by multiple steady-state solutions. Appearance of static instability has been substantiated following the pressure drop versus mass flow rate profiles, leading to the development of the stability maps. Dynamic instability has also been identified by introducing perturbation during transient simulations, and the range of both static and dynamic instabilities conforms well with each other. A novel approach of approximating the location of the stability threshold using time-series data has also been proposed.
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•Static and dynamic stability analysis of supercritical CO2-driven closed NCL.•Appearance of Ledinegg instability with multiple steady-states at intermediate power.•Transient simulation identifies unstable oscillation growth on imposing perturbation.•Excellent agreement between static and dynamic stability maps on multiple planes.•Detailed appraisal of effect of operating and geometric parameters on stability maps.
•Analytical solution for critical instability regions of arches is presented.•Influenced factors on instability regions are thoroughly analyzed.•In-plane dynamic instability of modal superposition is ...investigated.•Analytical solutions are justified by FE and Newmark-β methods.
This paper presents an analytical investigation on the in-plane dynamic instability of a shallow circular arch subjected to a vertical-periodic load uniformly distributed along the arch axis, which has not been previously reported in the literature hitherto. Equations of motion of the arch in the radial and tangential directions are derived by employing the Hamilton's principle. The trigonometric and hyperbolic functions are utilized as the mode shapes for the tangential and radial displacements. A method for determining critical instability regions bounded by the periodic solutions with the period T or 2T is presented for the antisymmetric and symmetric dynamic instability of the arch. Frequency sweep transient finite element analyses (FEA) are conducted to verify the analytical solution. Through comparisons, it is observed that analytical solutions agree well with the FEA results. It is shown that the bandwidth of instability regions bounded by the periodic solutions with a period 2T is significantly greater than that bounded by the periodic solutions with a period T. Effects of the rise-span ratio, damping ratio and static component of the periodic load on the dynamic instability are explored. It is found that the dynamic instability behavior of an arch is significantly influenced by the rise-span ratio and damping ratio and their increases lead to the decrease of the bandwidth of the dynamic instability region. It is also found that when the static component of the periodic load is considered, the dynamic instability region undergoes significant variations and moves towards to the lower excitation frequency owing to the decrease of vibration frequency of the arch. The bandwidth of the instability regions, however, increases with an increase of the static component. In addition, it is shown that dynamic instability of modal superposition may occur under a periodic load with a period between T and 2T and symmetric and antisymmetric instability modes are alternately changed during the dynamic instability of modal superposition.
In-plane dynamic instability of the fixed arch under a vertical periodical load uniformly distributed along the arch axis Dynamic instability regions Display omitted
In this article, nonlinear vibration and dynamic stability analyses of simply supported laminated composite circular cylindrical shells subjected to periodic edge loading are carried out. A ...third-order shear deformation shell theory that considers all the nonlinear terms in all five kinematic parameters and rotary inertia is used to develop the present mathematical model so that the model is also valid for thick cylindrical shells. Hamilton’s principle, an energy-based approach, is used to obtain the governing partial differential equations (PDEs) of motion of the cylindrical shell. Further, these equations are reduced into ordinary differential equations by employing Galerkin’s method. The incremental harmonic balance (IHB) method in conjunction with the pseudo-arc-length method is used to obtain the frequency-amplitude response of the system. For obtaining the zone of instability regions, Bolotin’s method is adopted. For more practical significance, analysis of results is also extended by considering damping into account for the composite cylindrical shells. Time history response and phase portrait are plotted by adopting Newmark-beta method. The effects of the static load factor, dynamic load factor, modal damping coefficient, and stacking sequence on nonlinear vibration, instability regions and time history responses are also examined.
This paper reports an energy-based method for the dynamic pull-in instability analysis of a spherical dielectric elastomer (DE) balloon subjected to a quasi-statically applied inflation pressure and ...a Heaviside step voltage across the balloon wall. The proposed technique relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle, followed by the imposition of an instability condition for extracting the threshold parameters. The material models of the Ogden family are employed for describing the hyperelasticity of the balloon. The accuracy of the critical dynamic pull-in parameters is established by examining the saddle-node bifurcation in the transient response of the balloon obtained by integrating numerically the equation of motion, derived using the Euler–Lagrange equation. The parametric study brings out the effect of inflation pressure on the onset of the pull-in instability in the DE balloon. A quantitative comparison between the static and dynamic pull-in parameters at four different levels of the inflation pressure is presented. The results indicate that the dynamic pull-in instability gets triggered at electric fields that are lower than those corresponding to the static instability. The results of the present investigation can find potential use in the design and development of the balloon actuators subjected to transient loading. The method developed is versatile and can be used in the dynamic instability analysis of other conservative systems of interest.
Abstract
Regarding the experimental observation that microtubule (MT) catastrophe can be described as a multistep process, we extend the Dogterom–Leibler model for dynamic instability in order to ...discuss the effect that such a multistep catastrophe mechanism has on the distribution of MT lengths in the two regimes of bounded and unbounded growth. We show that in the former case, the steady state length distribution is non-exponential and has a lighter tail if multiple steps are required to undergo a catastrophe. If rescue events are possible, we detect a maximum in the distribution, i.e. the MT has a most probable length greater than zero. In the regime of unbounded growth, the length distribution converges to a Gaussian distribution whose variance decreases with the number of catastrophe steps. We extend our work by applying the multistep catastrophe model to MTs that grow against an opposing force and to MTs that are confined between two rigid walls. We determine critical forces below which the MT is in the bounded regime, and show that the multistep characteristics of the length distribution are largely lost if the growth of an MT in the unbounded regime is restricted by a rigid wall. All results are verified by stochastic simulations.
The initial geometric imperfections in manufacturing structure are unavoidable. Critical buckling load and dynamic instability of the rotating cantilever cross ply laminate thin walled twisted plate ...with exponential function type initial geometric imperfection are investigated for the first time. The mode shapes are obtained by using Rayleigh-Ritz method and shallow shell theory including the influence of rotational speed and imperfection. Based on the Lagrange equations and the obtained mode shape function, motion equations considering the first three modes of the system are derived. The mode shapes, critical loads and dynamic instability obtained in present have been verified by comparing them with other researcher results. The detail studies about the effect of rotating speed, twisted angle, stacking sequence and imperfection factors of the rotating thin walled twisted plate subjected to the in-plane load on the static critical buckling load and dynamic instability are carried out.
The Front Cover represents an energy landscape of kinetically trapped chemical‐fueled fibers, which reminds of a mountain landscape. Our work unravels how tuning the kinetic trapping in ...chemical‐fueled self‐assemblies can recover dynamic instabilities, such as microtubule‐like growth and shrinkage. This opens the door to the creation of new adaptive nanotechnologies. More information can be found in the Research Article by Job Boekhoven and co‐workers.
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