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Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

Abstract

We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

Open access
Numerical Solutions for Nonlinear High Damping Rubber Bearing Isolators: Newmark’s Method with Netwon-Raphson Iteration Revisited

Abstract

Numerical methods for the solution of dynamical problems in engineering go back to 1950. The most famous and widely-used time stepping algorithm was developed by Newmark in 1959. In the present study, for the first time, the Newmark algorithm is developed for the case of the trilinear hysteretic model, a model that was used to describe the shear behaviour of high damping rubber bearings. This model is calibrated against free-vibration field tests implemented on a hybrid base isolated building, namely the Solarino project in Italy, as well as against laboratory experiments. A single-degree-of-freedom system is used to describe the behaviour of a low-rise building isolated with a hybrid system comprising high damping rubber bearings and low friction sliding bearings. The behaviour of the high damping rubber bearings is simulated by the trilinear hysteretic model, while the description of the behaviour of the low friction sliding bearings is modeled by a linear Coulomb friction model. In order to prove the effectiveness of the numerical method we compare the analytically solved trilinear hysteretic model calibrated from free-vibration field tests (Solarino project) against the same model solved with the Newmark method with Netwon-Raphson iteration. Almost perfect agreement is observed between the semi-analytical solution and the fully numerical solution with Newmark’s time integration algorithm. This will allow for extension of the trilinear mechanical models to bidirectional horizontal motion, to time-varying vertical loads, to multi-degree-of-freedom-systems, as well to generalized models connected in parallel, where only numerical solutions are possible.

Open access
Powered Upper Limb Orthosis Actuation System Based on Pneumatic Artificial Muscles

Abstract

The actuation system of a powered upper limb orthosis is studied in the work. To create natural safety in the mutual “man-robot” interaction, an actuation system based on pneumatic artificial muscles (PAM) is selected. Experimentally obtained force/contraction diagrams for bundles, consisting of different number of muscles are shown in the paper. The pooling force and the stiffness of the pneumatic actuators is assessed as a function of the number of muscles in the bundle and the supply pressure. Joint motion and torque is achieved by antagonistic actions through pulleys, driven by bundles of pneumatic muscles. Joint stiffness and joint torques are determined on condition of a power balance, as a function of the joint position, pressure, number of muscles and muscles

Open access
Spatial Rack Drives Pitch Configurations: Essence and Content

Abstract

The practical realization of all types of mechanical motions converters is preceded by solving the task of their kinematic synthesis. In this way, the determination of the optimal values of the constant geometrical parameters of the chosen structure of the created mechanical system is achieved. The searched result is a guarantee of the preliminary defined kinematic characteristics of the synthesized transmission and in the first place, to guarantee the law of motions transformation. The kinematic synthesis of mechanical transmissions is based on adequate mathematical modelling of the process of motions transformation and on the object, realizing this transformation. Basic primitives of the mathematical models for synthesis upon a pitch contact point are geometric and kinematic pitch configurations. Their dimensions and mutual position in space are the input parameters for the processes of design and elaboration of the synthesized mechanical device. The study presented here is a brief review of the theory of pitch configurations. It is an independent scientific branch of the spatial gearing theory (theory of hyperboloid gears). On this basis, the essence and content of the corresponding primitives, applicable to the synthesis of spatial rack drives, are defined.

Open access
Calculation of Stress-Deformed Condition in Polymer Nanocomposites Filled with Microcapsules with Lubricant

Abstract

The article suggests the technology of modifying a polymer matrix by microencapsulation, i. e. the introduction of microparticles (lubricants with nano-additives in polymer shells) into nanocomposites matrix, to form multilevel structures on the tribounit surface. Besides, it suggests the method of predicting the operational elastic properties of multicomponent matrix composites with microcapsules, filled with a liquid substance. The method is based on the generalized singular approximation of the theory of random fields and allows, taking into account the geometric dimensions of the inclusions in the shell. It contains the results of numerical modelling of the effective elastic characteristics (Young’s modulus and Poisson’s ratio) of composites, based on phenylone with dispersed inclusions (microcapsules), which are glycerin-filled spherical shells of the kapton. The paper investigates the effect of the geometric dimensions of microcapsules and the volumetric content of components on the operational elastic properties of tribocomposites. The developed antifriction nanomaterials with microcapsules are able to create an oriented lubricating coating on the friction surfaces, apply lubrication to a certain friction area and carry out the lubrication portion wise precisely in the necessary contact zone of the bodies.

Open access
Development of Hand-Held Surgical Robot ODRO-2 for Automatic Bone Drilling

Abstract

This paper represents the development of a prototype robotic system for automatic bone drilling in orthopaedic surgery. A new design of the mechanical structure is proposed, answering the surgical requirements for the robot dimensions and weight to be as small as possible. The new structure design is based on idea of parallelism of the axis of the linear actuator and the axis of the rotary one. The control system is improved by using a new micro-controller. A new type of linear drive and a new force sensor (load cell) are built in, so that the quality characteristics of the “Orthopaedic bone Drilling Robot” (ODRO) are not only the same as previous its two versions, but becomes better.

An experimental setup is arranged and experiments are executed to test and to verify the robot quality features and functional capabilities.

Open access
Experimental Research of Rotational-and-Frictional Boring of Big Holes in Large Parts

Abstract

When producing large-dimensional parts of heavy machines, the largest specific weight in the general labour input is made by the operations, connected with machining the main holes, i. e. holes of large diameter. To the holes of large diameter of large-dimensional parts, there are specified high requirements in the aspect of accuracy of the size, shape and arrangement. Machining of holes still remains one of the topical problems of present day mechanical engineering, in particular machine-building enterprises of the Republic of Kazakhstan.

Solving the problem of ensuring accuracy and quality of machining large holes of large-dimensional parts requires the development of new resource-saving technologies of machining. In this work there are presented the results of studying a resource-saving method of rotation-friction boring of large diameter holes. There has been achieved good results in providing the quality indicators, when machining by the proposed method of rotation-friction boring with the use of the tool (a disk cutter) made of steel 90CrSi5 in comparison with well-known boring of holes. The diagram of chip formation of cutting and the results of studying the zone of chip formation by the metallographic method is also presented.

Open access
Finding the Optimal Parameters for Robotic Manipulator Applications of the Bounded Error Algorithm for Iterative Learning Control

Abstract

This paper continues previous research of the Bounded Error Algorithm (BEA) for Iterative Learning Control (ILC) and its application into the control of robotic manipulators. It focuses on investigation of the influence of the parameters of BEA over the convergence rate of the ILC process. This is performed first through a computer simulation. This simulation suggests optimal values for the parameters. Afterwards, the estimated results are validated on a physical robotic manipulator arm. Also, this is one of the first reports of applying BEA into robots control.

Open access
Novel Dynamic Model Updating Technique for Damped Mechanical System

Abstract

Response surface method and Derringer’s function approach have been combined together to develop novel structural dynamic model updating technique for a damped mechanical system. Response surface models have been incorporated instead of finite element models, in order to increase computational efficiency of proposed technique. Derringer’s function approach is useful in dealing successfully with multi-objective optimization type model updating problems. Few such undamped techniques have been recently developed for undamped mechanical systems by combining the benefits of response models with Derringer’s function approach. This paper presents the theory and numerical application of a damped updating technique, which is based upon response models and Derringer’s function approach. In this technique, updating process is formulated as an optimization problem, wherein desirability functions are formulated, based on natural frequencies, modal-assurance-criterion values, resonance and anti-resonance points of frequency response functions. Desirability functions are then optimized to evaluate updated elastic parameters in stage one and updated damping constants in stage two of proposed technique. By using this technique, total absolute errors in natural frequencies, modal-assurance-criterion values, elastic parameters and frequency response functions have been reduced to 0.02%, 0.00%, 3.69% and 0.11%, respectively.

Open access
Torsional Wave Propagation in a Pre-Stressed Structure with Corrugated and Loosely Bonded Surfaces

Abstract

An analytical model is presented to study the behaviour of propagation of torsional surface waves in initially stressed porous layer, sandwiched between an orthotropic half-space with initial stress and pre-stressed inhomogeneous anisotropic half-space. The boundary surfaces of the layer and halfspaces are taken as corrugated, as well as loosely bonded. The heterogeneity of the lower half-space is due to trigonometric variation in elastic parameters of the pre-stressed inhomogeneous anisotropic medium. Expression for dispersion relation has been obtained in closed form for the present analytical model to observe the effect of undulation parameter, flatness parameter and porosity on the propagation of torsional surface waves. The obtained dispersion relation is found to be in well agreement with classical Love wave equation for a particular case. The cases of ideally smooth interface and welded interface have also been analysed. Numerical example and graphical illustrations are made to demonstrate notable effect of initial stress, wave number, heterogeneity parameter and initial stress on the phase velocity of torsional surface waves.

Open access