Nonlinear model updating of frictional structures through frequency–energy analysis

Nonlinear Dynamics - Recently, some researchers have suggested using frequency–energy representations of nonlinear normal modes (NNMs) for nonlinear model updating of conservative systems....     

Analytical modeling of static behavior of electrostatically actuated nano/micromirrors considering van der Waals forces

In this paper,the effect of van der Waals(vdW)force on the pull-in behavior of electrostatically actuatednano/micromirrors is investigated.First,the minimum potential energy principle is utilized to find the equation governing the static behavior of nano/micromirror under electrostatic and vdW forces.Then,the stability of static equilibrium points is analyzed using the energy method.It is foundthat when there exist two equilibrium points,the smaller oneis stable and the larger one is unstable.The effects of different design parameters on the mirror’s pull-in angle andpull-in voltage are studied and it is found that vdW forcecan considerably reduce the stability limit of the mirror.Atthe end,the nonlinear equilibrium equation is solved numerically and analytically using homotopy perturbation method(HPM).It is observed that a sixth order perturbation approximation can precisely model the mirror’s behavior.The results of this paper can be used for stable operation design andsafe fabrication of torsional nano/micro actuators.     

Variation of constant formula for the solution of interval differential equations of non-integer order

In the recent years some efforts were made to propose simple and well-behaved fractional derivatives that inherits the classical properties from the first order derivative. Therefore, we propose in this research a new strategy to acquire interval solution of fractional interval differential equations (FIDEs) under interval fractional conformable derivative. This scheme is developed based on a variation of the constant formula to achieve the solution explicitly. The important characteristic of this technique is that it helps us to find a solution with decreasing length of its support which is critical for the solutions based on the interval or fuzzy notions. Two examples are experienced to illustrate our approach and validate it.     

Identification of Iwan distribution density function in frictional contacts

Mechanical contacts affect structural responses, causing localized nonlinear variations in the stiffness and damping. The physical behaviors of contact interfaces are quite complicated and almost impossible to model at the micro-scale. In order to establish a meaningful understanding of the friction effects and to predict the contact behavior, a robust parametric friction model is usually employed. This paper employs an Iwan-type model to predict the nonlinear effects of a frictional contact interface. The Iwan model is characterized by its distribution density function which is commonly identified by double differentiation of the experimentally obtained joint interface restoring force. Direct measurement of restoring forces at the contact interface is impractical and estimating it using an inverse approach introduces considerable uncertainties in identification of the density function. This paper develops a more reliable procedure in identification of the Iwan model by relating the density function to the joint interface dissipated energy. The energy dissipated in a contact interface is easily obtained from measurement and it is shown that the dissipation is uniquely defined using the density function and the vibration amplitude. In an experimental case study Iwan distribution density function in a frictional contact is obtained using measured dissipations at different vibration levels.     

Modeling squeezed film air damping in torsional micromirrors using extended Kantorovich method

The current paper uses the Extended Kantorovich Method (EKM) to analytically solve the problem of squeezed film damping in micromirrors. First a one term Galerkin approximation is used and following the extended Kantorovich procedure, the solution of the Reynolds equation which governs the squeezed film damping in micromirrors is reduced to solution of two uncoupled ordinary differential equation which can be solved iteratively with a rapid convergence for finding the pressure distribution underneath the micromirror. It is shown that the EKM results are independent of the initial guess function. It is also shown that EKM is highly convergent and practically one iterate is sufficient for obtaining a precise response. Furthermore using the presented closed form solutions for the squeezed film damping torque, it is proved that when the tilting angle of the mirror is small, the damping is linear viscous one, while when the tilting angle is finite, the damping would be linearly proportional with the angular velocity of the mirror and at the same time it is a nonlinear function of the tilting angle of the mirror. Results of this paper can be used for accurate dynamical simulation of micromirrors with presence of the squeezed film damping.     

Stabilizing network bargaining games by blocking players

Cooperative matching games (Shapley and Shubik) and Network bargaining games (Kleinberg and Tardos) are games described by an undirected graph, where the vertices represent players. An important role in such games is played by stable graphs, that are graphs whose set of inessential vertices (those that are exposed by at least one maximum matching) are pairwise non adjacent. In fact, stable graphs characterize instances of such games that admit the existence of stable outcomes. In this paper, we focus on stabilizing instances of the above games by blocking as few players as possible. Formally, given a graph G we want to find a minimum cardinality set of vertices such that its removal from G yields a stable graph. We give a combinatorial polynomial-time algorithm for this problem, and develop approximation algorithms for some NP-hard weighted variants, where each vertex has an associated non-negative weight. Our approximation algorithms are LP-based, and we show that our analysis are almost tight by giving suitable lower bounds on the integrality gap of the used LP relaxations.     

Preparation of titanium dioxide nanostructure from ilmenite through sulfate-leaching process and solvent extraction by D<Subscript>2</Subscript>EHPA

In this study, TiO₂ nanoparticles have been obtained from low-grade ilmenite ore via two consecutive acid digestion and solvent extraction processes. The as-extracted TiO₂ (Anatase phase) product was characterized using techniques such as XRD, XRF, FESEM, FTIR and BET surface area. Diluted sulfuric acid and D₂EHPA (bis-(2-ethyl-hexyl) phosphoric acid) were used as digester agent and an extraction solvent, respectively. The effects of main parameters such as recycling capacities and D₂EHPA concentration, as well as the extraction time and temperature on TiO₂ extraction were investigated. The results demonstrated that the best performance and efficiency for titanium and total iron uptake were 99 and 3.8%, respectively, at the lowest concentration of D₂EHPA.     

Influence of hybrid nanofluids and heat generation on coupled heat and mass transfer flow of a viscous fluid with novel fractional derivative

Journal of Thermal Analysis and Calorimetry - In this paper, it has been discussed a nonlocal fractional model of viscous nanofluid holding a hybrid nanostructure. Hybridized copper (Cu) and...     

An experimental and numerical study of packing,compression, and caking behaviour of detergent powders

This paper presents an experimental and numerical study of the packing, compression, and caking behaviour of spray dried detergent(SDD) powders with a two-fold aim: an experimental process of observation and evaluation of the packing, compression and caking behaviour of SDD powders, and a numerical approach based on discrete element modelling(DEM). The mechanical properties, including the stress–strain response and the corresponding porosity change as a function of consolidation stress in a confined cylinder, the stress–strain response during unconfined shearing and the cake strength as a function of consolidation stress, were evaluated and compared for different SDD powders using an extended uniaxial tester(Edinburgh Powder Tester – EPT). The experiments using EPT showed excellent reproducibility in the measurement of packing, compression and caking behaviour and were therefore very useful for describing the handling characteristics of these powdered products including screening new products and different formulations. It was found that the sample with higher moisture had lower bulk porosity but higher compressibility and cake strength. The porosity, compressibility and cake strength were found to vary across different size fractions of the same sample. The larger sieve-cut samples had higher initial bulk porosity, compressibility and cake strength. It is revealed that moisture plays a significant role in packing, compression, and shearing behaviour of the powder. Three-dimensional DEM modelling using a recently developed elasto-plastic adhesive-frictional contact model showed that the contact model is able to capture the detergent behaviour reasonably well and can be used to model complex processes involving these powders.     

Vibrational analysis of electrostatically actuated microstructures considering nonlinear effects

The vibrational behavior of electrostatically actuated microstructures subjected to nonlinear squeeze film damping and in-plane forces is investigated. First-Order Shear Deformation Theory is used to model dynamical system by means of finite element method, while finite difference method is applied to solve the nonlinear Reynolds equation of squeeze film damping simultaneously. Vibrational analysis of microplates is performed by solving eigenvalue problem, after validating the model by pull-in phenomenon and transient behavior. In addition, considering nonlinear squeeze film damping and step-input actuations, response frequencies of microplates are calculated. Effect of ambient pressure and in-plane forces on dynamic pull-in phenomenon is also studied. Results for simplified models are verified and are in good agreement with the published literature. This investigation can reveal nonlinear vibrational behavior of microstructures.