فهرست مطالب عطیه اندخشیده

Metallic pipelines are mainly corroded and damaged in operation that replacing damaged lines or their local welding is sometimes not feasible or economical, so for resolving the corrosion and functional damage of metallic pipelines, localized repair using composites as one of the most effective and cost effective solutions is used. The connection of composite repair to the metal substructure in this method is one of the most important design parameters. Therefore, deriving the important parameters at the junction will help engineers in designing and predicting the interlaminar crack initiation and propagation at the joint interface of composite repair to the metal substrate. Therefore, to investigate the second mode of failure in this method, the strain energy release rate is calculated experimentally and numerically in a steel/GFRP bond. According to an experimental standard for calculating the second mode strain energy release rate, ASTM-D7905, experimental tests are accomplished for three symmetric and asymettric unlike end-notched flexure specimens and a relationship for the thickness of each material to have symmetric specimens is proposed. To validate the thickness calculation relationship, the finite elemental modeling of unlike samples using virtual crack closure technique is used which indicates the good agreement of experimental and numerical results. Compareing the experimental results obtained in force-displacement diagrams of symmetric and asymmetric samples in crack propagation showed that the second mode strain energy release rate of symmetric samples are more than asymmetric and about 1.6 times as large.

In this paper, the nonlinear forced vibrations of nonlocal Euler-Bernoulli nanobeam that is utilized in nanoelectromechanical systems are studied using the analytical method of multiple time scales. Based on non-linear strain gradient elasticity theory, governing equation of Euler-Bernoulli nanobeam with von-karman geometric nonlinearity is derived using Hamilton principle. In the next step, using the Galerkin method, the partial differential governing equations for simply supported boundary conditions are reduced to time variable ordinary nonlinear differential equation. Subsequently, the nonlinear forced vibration equation is solved using a multiple time scalar method. After solving the nonlinear excited equation, primary and secondary resonances of nonlocal nanobeam are studied. The region of acceptable sub-harmonic responses is identified and for different values of nonlocal parameter, the frequency response curves and response amplitudes versus excitation amplitude is plotted in all resonances as primary, super-harmonic and sub-harmonic. These results show that using nonlocal strain gradient theory is a fundamental necessity for analyzing nonlinear vibration of nanobeams. The results of this paper can be used to improve the design and optimization of nanoelectromechanical systems.

In this study, nonlinear dynamics of non-classical Kirchhoff plate is analyzed for the first time and the region of chaotic behavior is predicted and controlled by designing the robust adaptive controller. Virtual displacement principle is employed to derive the governing equation of Kirchhoff micro-plate resting on nonlinear elastic foundation. In the governing equation, von Karman geometrical nonlinearity and couple stress theory is considered. Solving the eigen value governing equation for fully simply supported boundary conditions, results are validated. Next, Galerlkin method considering harmonic excitation of first mode is used to derive micro-plate forced vibration equation. Regardless of modal interaction, the chaos threshold is then investigated. Homoclinic orbits of unperturbed system is plotted and stable and unstable manifold transversely cut that is criteria to predict chaos according to Melnikov’s method is studied. Using maximum Lyapunov exponents numerical method, size-dependent chaos is also locally identified. Phase portrait, Poincare mapping and time response are plotted for different values of size ratios and the important effect of size on the chaotic behavior of micro-plats is presented. The results of this study show that chaos in the micro-plats is size dependent and using the non-classical theories to analyze the chaos of micro-plats is necessary. Subsequently, designing the robust adaptive fuzzy controllers, chaotic vibrations are completely eliminated from the system and the robust adaptive fuzzy controller is introduced as an effective method for controlling chaos in these systems. Results of this research can be used in the production process, optimization and control of nanoelectromechanical systems.

In this paper, an atomic force microscope is modeled based on non-classical nonlocal theory and nonlinear vibration of the system is analyzed and controlled. In this modeling, the Hamilton principle is used to derive the governing equation of Euler-Bernoulli nanocantilever based on the Eringen nonlocal elasticity theory considering Von-Karman geometric non-linearity. In the next step, using the Galerkin method, the governing dynamics differential equation of the atomic force microscope is obtained in the presence of attractive and repulsive van der Waals forces. The governing nonlinear equation is solved by employing multiple time scales method, and primary and secondary resonance of the atomic force microscope is studied. In this regard, the frequency response and excitation amplitude curves of primary, superharmonic and subharmonic resonances are plotted for different values ​​of the nonlocal parameter. Accordingly, it is shown that primary, superharmonic and subharmonic resonances of atomic force microscope are significantly affected by the nonlocal parameter. The results show that the use of nonlocal theory is a fundamental necessity for analyzing nonlinear vibrations of the atomic force microscope. Then, in addition to dynamic analysis, the chaotic vibrations are completely controlled and removed in the nonlocal model of the atomic force microscope by designing and implementing the robust adaptive fuzzy controller. For this task, the robust adaptive fuzzy controller which is considered as a powerful method of chaos controlling is used in the nonlocal model of atomic force microscope. The obtained results are used in the design and control process of the atomic force microscope.

One of the applications of composite materials in the oil and gas industry is to repair worn metal pipelines. Calculating the strain energy release rate of the first failure mode is an important criterion for testing the bond strength and predicting the failure of these types of structures. In this paper, the rate of strain energy release during crack growth in bonding a composite patch to a steel substrate is investigated. In this regard, using the theory of elastic beam first, a new method is proposed to calculate the thickness of the metal and composite for Unlike Double Cantilever Beam (UDCB). This is due to the fact that the standard for experimental test procedure of strain energy release rate (ASTM-D5528) is for symmetric double cantilever beams. In this study, samples are fabricated from composite consisting of unidirectional fiberglass/ epoxy resin with harder in the upper and steel in the lower half of the beam. After sample fabrication, the strain energy release rate of UDCB and Asymmetric Unlike Double Cantilever Beam (AUDCB) are calculated experimentally. In addition, for the separation of first and second failure modes in symmetric and asymmetric samples, finite element simulation based on the virtual crack closure technique is presented. This analysis is to qualify the accuracy of the proposed equation for the thickness of unlike beams to achieve the first failure pure mode of symmetric samples. Also, it calculates the contribution of the first and second modes of failure in the strain energy release rate of AUDCB samples.

In this research, the behavior of functionally graded micro-beams under electrostatic excitation is investigated. The system model is developed based on Euler-Bernoulli beam theory. In the developed model, the effects of electrostatic excitation and mid-layer stretching are considered. In order to solve the nonlinear governing equation, Generalized Differential Quadrature method and the Newton-Raphson method are used. To develop the pull-in voltage through the numerical results, a novel algorithm is developed. For numerical integration, Generalized Integral Quadrature is also used. Finally, the major problem of this method that prevent it from being used more frequently is discussed and a solution of that problem is suggested. In numerical results of this research, the pull-in voltage variation with respect to the functionally graded micro-beam stiffness distribution and initial gap of micro-beam is studied. Results show that increasing the micro-beam equivalent stiffness or beams initial gap, will increase the pull-in voltage. The boundary conditions effect on the micro-beam pull-in voltage is also studid in the numerical results.

In this article, for the first time, the effect of non-uniformity of microbeam cross section and various boundary conditions on the nonlinear vibration of microbeam is investigated considering the size dependent behavior based on modified couple stress theory. Using the Hamilton’s principle, the governing equation of Euler–Bernoulli microbeam with von Karman geometric nonlinearity based on the modified couple stress theory is derived. The nonlinear vibration governing equation is then solved using the Generalized Differential Quadrature method (GDQ) and direct iterative method to obtain the nonlinear natural frequencies. In this step, the Galerkin method is used to reduce the nonlinear PDE governing the vibration into a time-dependent ODE of Duffing-type. The time domain is then discretized via spectral differentiation matrix operators which are defined based on the derivatives of a periodic base function. Next, the nonlinear parametric equation is solved using pseudo arc-length method and the frequency–response curves of microbeam nonlinear forced vibration is obtained. Finally, nonlinear natural frequency and frequency response of microbeam with various non-uniformity of cross sections and boundary conditions are obtained. Present results show that, the nonlinear free and forced vibration of microbeam is size dependent. Moreover, this size dependency is more significant for non-uniform microbeam and is deferent for various boundary conditions. The result of present method for simple case including uniform section and simply supported boundary condition is validated with that of exact method and have good agreement.

Dual laminate pipes made of thermoset polymer composite structure and thermoplastic liner are the only alternative in pipelines conveying high temperature corrosive fluids. Investigating the bonding between thermoset composite and thermoplastic liner is very important in these pipelines. Calculating the strain energy release rate of first mode of failure is very important criteria in bonding strength and failure of doulas pips. ASTM-D5528 is the standard for experimental test procedure of strain energy release rate of symmetric double cantilever beam. In this study, using the classical laminates theory, the general equation for determination the laminates thicknesses in unlike double cantilever beam is presented, for the first time. To study the validity of the equation, in unlike double cantilever beam samples consists of laminates with different thicknesses are manufactured for the experimental tests. Upper, lower and bonding regions consist of composite made of unidirectional fiberglass/Vinylester resin, PVCU and epoxy or Vinylester primers, respectively. The samples of this study are manufactured base on the practical case studies of chemical fluid pipelines with chlor-alkali process like Arvand Petrochemical units. The main aim of this work is to help manufacturers of these unites equipment to have practical guideline. To qualify the efficiency of the proposed equation, finite element simulation base on the virtual crack closure technique is presented. Good agreement is achieved in comparing the numerical and experimental results that shows the efficiency and accuracy of the proposed equation.