• Structural Engineering and Mechanics
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• v.71 no.4
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• pp.351-361
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• 2019

Present article deals with the static stability analysis of compositionally graded nanocomposite beams reinforced with graphene oxide powder (GOP) is undertaken once the beam is subjected to an induced force caused by nonuniform magnetic field. The homogenized material properties of the constituent material are approximated through Halpin-Tsai micromechanical scheme. Three distribution types of GOPs are considered, namely uniform, X and O. Also, a higher-order refined beam model is incorporated with the dynamic form of the virtual work's principle to derive the partial differential motion equations of the problem. The governing equations are solved via Galerkin's method. The introduced mathematical model is numerically validated presenting a comparison between the results of present work with responses obtained from previous articles. New results for the buckling load of GOP reinforced nanocomposites are presented regarding for different values of magnetic field intensity. Besides, other investigations are performed to show the impacts of other variants, such as slenderness ratio, boundary condition, distribution type and so on, on the critical stability limit of beams made from nanocomposites.

• Nuclear Engineering and Technology
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• v.54 no.1
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• pp.275-282
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• 2022

The aim of this work is to develop the fractional Bateman equations, which can model memory effects in successive isotopes transformations. Such memory effects have been previously reported in the alpha decay, which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alpha decays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations, which can reproduce the standard ones when the fractional order is equal to one. The proposed fractional model preserves the mathematical shape and the symmetry of the standard equations, being the only difference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a very important result, because allows the implementation of the proposed fractional model in burnup and activation codes in a straightforward way. Numerical experiments show that the proposed equations predict high decay rates for small time values, in comparison with the standard equations, which have high decay rates for large times. This work represents a novelty approach to the theory of successive transformations, and opens the possibility to study properties of the Bateman equation from a fractional approach.

• Nuclear Engineering and Technology
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• v.54 no.5
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• pp.1644-1651
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• 2022

This paper focuses on the power-level control of nuclear power plants (NPPs) in the presence of lumped disturbances. An adaptive second-order nonsingular terminal sliding mode control (ASONTSMC) scheme is proposed by resorting to the second-order nonsingular terminal sliding mode. The pre-existing mathematical model of the nuclear reactor system is firstly described based on point-reactor kinetics equations with six delayed neutron groups. Then, a second-order sliding mode control approach is proposed by integrating a proportional-derivative sliding mode (PDSM) manifold with a nonsingular terminal sliding mode (NTSM) manifold. An adaptive mechanism is designed to estimate the unknown upper bound of a lumped uncertain term that is composed of lumped disturbances and system states real-timely. The estimated values are then added to the controller, resulting in the control system capable of compensating the adverse effects of the lumped disturbances efficiently. Since the sign function is contained in the first time derivative of the real control law, the continuous input signal is obtained after integration so that the chattering effects of the conventional sliding mode control are suppressed. The robust stability of the overall control system is demonstrated through Lyapunov stability theory. Finally, the proposed control scheme is validated through simulations and comparisons with a proportional-integral-derivative (PID) controller, a super twisting sliding mode controller (STSMC), and a disturbance observer-based adaptive sliding mode controller (DO-ASMC).

• Structural Engineering and Mechanics
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• v.80 no.6
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• pp.727-736
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• 2021

In this work, mathematical modeling of the passive vibration controls of a three-layered sandwich beam under hard excitation is developed. Kelvin-Voigt Viscoelastic model is considered in the core. The formulation is based on the higher-order zig-zag theories where the normal and shear deformations are taken into account only in the viscoelastic core. The dynamic behaviour of the beam is represented by a complex highly nonlinear ordinary differential equation. The method of multiple scales is adopted to solve the analytical frequency-amplitude relationships in the super-harmonic resonance case. Parametric studies are carried out by using HSDT and first-order deformation theory by considering different geometric and material parameters.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.247-263
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• 2023

The paper deals with the study of the mechanical time-harmonic forced vibration of the hydro-piezoelectric system consisting of the piezoelectric plate and compressible viscous fluid with finite depth. The exact equations of motion of the theory of linear electro-elasticity for piezoelectric materials are employed for describing the plate motion, however, the fluid flow is described by employing the linearized Navier-Stokes equations for a compressible (barotropic) viscous fluid. The plane-strain state in the plate and the plane flow of the fluid are considered and the corresponding mathematical problems are solved by employing the Fourier transform with respect to the space coordinate which is on the coordinate axis directed along the platelying direction. The expressions of the corresponding Fourier transform are determined analytically, however, the inverse transforms are found numerically. Numerical results on the interface pressure and the electrical potential are obtained for various PZT materials and these results are discussed. According to these results, in particular, it is established that the electromechanical coupling effect can significantly decrease the interface pressure.

• Steel and Composite Structures
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• v.44 no.3
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• pp.371-388
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• 2022

The present study tackles the problem of forced vibration of imperfect axially functionally graded shell structure with truncated conical geometry. The linear and nonlinear large-deflection of the structure are considered in the mathematical formulation using von-Kármán models. Modified coupled stress method and principle of minimum virtual work are employed in the modeling to obtain the final governing equations. In addition, formulations of classical elasticity theory are also presented. Different functions, including the linear, convex, and exponential cross-section shapes, are considered in the grading material modeling along the thickness direction. The grading properties of the material are a direct result of the porosity change in the thickness direction. Vibration responses of the structure are calculated using the semi-analytical method of a couple of homotopy perturbation methods (HPM) and the generalized differential quadrature method (GDQM). Contradicting effects of small-scale, porosity, and volume fraction parameters on the nonlinear amplitude, frequency ratio, dynamic deflection, resonance frequency, and natural frequency are observed for shell structure under various boundary conditions.

• Steel and Composite Structures
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• v.43 no.2
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• pp.229-240
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• 2022

The main objective of this work is presenting a mathematical model for the concrete slab with fiber reinforced polymer (FRP) layer under the impact load. Impacts are assumed to occur normally over the top slab and the interaction between the impactor and the structure is simulated using a new equivalent three-degree-of-freedom (TDOF) spring-mass-damper (SMD) model. The structure is assumed viscoelastic based on Kelvin-Voigt model. Based on the sinusoidal shear deformation theory (SSDT), energy method and Hamilton's principle, the motion equations are derived. Applying DQM, the dynamic deflection and contact force of the structure is calculated numerically so that the effects of mass, velocity and height of impactor, boundary conditions, FRP layer, structural damping and geometrical parameters of structure are shown on the dynamic deflection and contact force of system. Results show that considering structural damping leads to lower dynamic deflection and contact force. In addition, increasing the impact velocity of impactor yields to increases in the maximum contact force and deflection while the contact duration is decreased. The result shows that the contact force and the central deflection of the structure decreases and the contact time decreases with assuming FRP layer.

• Smart Structures and Systems
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• v.29 no.2
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• pp.279-286
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• 2022

In this article, a novel propagation formulation of Rayleigh waves in a compressible isotropic half-space with impedance boundary condition is proposed by embedding the normal stress. In a two-dimensional case, it is assumed that a design boundary is free of normal traction and a shear traction depends on linearly a normal component of displacements multiplied by frequencies. Therefore, impedance boundary conditions affect the normal stress, where the impedance parameters correspond to dimensions of stresses over velocity. On the other hand, vanished impedance values are traction-free boundary conditions. The main purpose of this article is to present theoretically the existence and uniqueness of a Rayleigh wave formulation relying on secular equation's mathematical analyses. Its velocity varies along with the impedance parameters. Moreover, numerical experiments with different values for the velocity of Rayleigh waves are carried out. The present Rayleigh waves study is a fundamental step in analyzing the cause and effect of physical states such as building or structure damages resulting from natural dynamics. The results of the study generate a basic design formulation theory to test the effects of Rayleigh waves affecting structures when an earthquake occurs. The presence and uniqueness of the proposed formulation is verified by mutual comparisons of several numerical examples.

• Steel and Composite Structures
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• v.48 no.6
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• pp.625-639
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• 2023

In this paper, a Taguchi-based finite element method (FEM) has been proposed and implemented to assess optimal design parameters for minimum static deflection in laminated composite plate. An orthodox mathematical model (based on higher-order shear deformation plate theory and Green-Lagrange geometrical nonlinearity) has been used to compute the nonlinear central deflection values of laminated composite plates according to Taguchi design of experiment via a self-developed MATLAB computer code. The lay-up scheme, aspect ratio, thickness ratio and the support conditions of the laminated composite plate structure were designated as the governable design parameters. Analysis of variance (ANOVA) is used to investigate the effect of diverse control factors on the nonlinear static responses. Moreover, regression model is developed for predicting the desired responses. The ANOVA revealed that the lay-up scheme alongside the support condition plays vital role in minimizing the central deflection values of laminated composite plate under uniformly distributed load. The conformity test results of Taguchi analysis are also in good agreement with the numerical experimentation results.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.1
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• pp.174-184
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• 1997

This paper presents a robust force tracking control of a smart flexible gripper featured by a piezoceramic actuator characterizing its durability and quick response time. A mathematical governing equation for the proposed gripper structure is derived by employing Hamilton's principle and a state space control model is subsequently obtained through model analysis. Uncertain system parameters such as frequency variation are included in the control model. A sliding mode control theory which has inherent robustness to the sys- tem uncertainties is adopted to design a force tracking controller for the piezoceramic actuator. Using out- put information from the tip force sensor, a full-order observer is constructed to estimate state variables of the system. Force tracking performances for desired trajectories represented by sinusoidal and step func- tions are evaluated by undertaking both simulation and experimental works. In addition, in order to illustrate practical feasibility of the proposed method, a two-fingered gripper is constructed and its performance is demonstrated by showing a capability of holding an object.