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In this study, the active control of the three-degree-of-freedom quarter-car suspension system passing over the bridge, which can be modeled as an Euler-Bernoulli beam, is studied. The mathematical model of the bridge and the vehicle was determined and the equations of motion were derived using the Lagrangian method. The obtained equations of motion were solved in Matlab using the fourth-order Runge-Kutta method. By giving the wheels two different road profiles along with the oscillations of the bridge beam, the vehicle's handling and passenger comfort are ensured to be optimal by using the classical PID and Sliding mode control (SMC) method. The accuracy of the proposed method in the study was compared with other studies in the literature. The simulation results showed that thanks to the active suspension controllers, the result of the passenger displacement and acceleration values improved significantly compared to the passive one. [ABSTRACT FROM AUTHOR]

In this study, axial vibration of a nano rod in an elastic media is discussed using the non-local elasticity theory. Equations of motion of the problem are obtained by means of equilibrium conditions and solved analytically. The expressions giving the free vibration frequencies of the fixed-fixed nanorod and fixed-free nanorod were found depending on the non-local parameter and the elastic medium parameters. For fixed-fixed and fixed-free boundary conditions, the relationships between vibration frequencies and elastic medium parameter and nonlocal parameter are examined and the results are shown on graphs. Physical and material properties of the carbon nanotube were used for numerical results. With the results, it was seen that free vibration frequencies are remarkably be subject to size and the size effect is more effective in high modes. The frequency values which obtained using the classical elasticity theory are very distinct than obtained using the non-local elasticity theory. [ABSTRACT FROM AUTHOR]

In this study, the dynamic instability region of cracked composite plates subjected to periodic axial loading has been investigated numerically by using the finite element method. A composite plate based on classical lamination theory is modeled by using the finite element method. It is assumed that the boundary condition of the composite plate is fixed on one side and the other sides are free. The composite plate is divided into square plate elements, each having four nodes. Each node has one translational and two rotational degrees of freedom, therefore, the square plates have twelve degrees of freedom. Mathieu-Hill type motion equation, which is used to calculate the dynamic instability region of the plate is created by using energy expressions obtained from the Lagrange equation. The developed MATLAB finite element code is used to examine the effect of crack on dynamic instability region for composite plates. [ABSTRACT FROM AUTHOR]

Crank – connecting rod mechanisms are a movement system with a wide area of use and these mechanisms are highly preferred in multi-ply materials cutting machines due to their simple and usefulness. Simulation was carried out with Matlab/Simulink to see the effects of changing the crank length, which is one of the parameters that increase the cutting speed, on the system in cutting systems based on this mechanism. The kinematic of the cutting mechanism of a cutting machine used to cut multi-ply materials were investigated and its motion was analysed. The optimum dimensions of the crank-connecting rod have been obtained using equations created from complex numbers. These dimensions and motion equations have been modelled with Matlab / Simulink and characteristic curves have been obtained. As a result of the analysis, the crankconnecting rod length suitable for the cutting machine of multi-layered materials has been obtained. [ABSTRACT FROM AUTHOR]

In this study, free vibration and buckling analyses of functionally graded (FGM) sandwich beams is investigated by Navier's method. Displacement field is defined according to the first order shear deformation theory, and the equations of motion are derived by the Lagrange's principle. Volumetric ceramic ratio is defined by a power-law rule. In the analytical solution, different trigonometric series functions are used for each end conditions considered. Two cases of functionally graded sandwich beams are considered: a) Homogeneous ceramic core and FGM faces (Type A), and b) FGM core and homogeneous faces (Type B). Natural frequencies and buckling loads are obtained for different boundary conditions, power-law indices and slenderness. Numerical results are compared with the available literature, and a good agreement are obtained between the results. [ABSTRACT FROM AUTHOR]

On September 26, 2019 at 13:59 Turkish local time, on the Kumburgaz segment of the North Anatolian fault-line, an offshore event, Silivri (Marmara Sea) Earthquake with a magnitude of Mw 5.8 at the depth of 6.99 km occurred. The earthquake was felt especially in the nearby cities Tekirdag and Istanbul, and other cities Yalova, Kocaeli, Bursa and Kırklareli in the region, as well. The September 26 Silivri earthquake is important because, it is the biggest earthquake affecting the region after 1999 Kocaeli (Mw 7.6) and 1999 Duzce (Mw 7.1) earthquakes and their aftershocks. In this study, Mw 5.8 Silivri earthquake ground motion records were examined. The ground motion parameter, Peak Ground Acceleration (PGA), was evaluated using the 2014 Next Generation Attenuation Relations (Ground Motion Prediction Equations (GMPEs). In addition, distribution maps of ground motion parameters (MMI, PGA, Sa 0.2 s, Sa 1.0 s) were generated and compared with the recorded ground motions. The amount of energy released during the earthquake has been compared with the past large-scale earthquakes. [ABSTRACT FROM AUTHOR]

In this study, a simple method is proposed to obtain the optimum design parameters of vibration absorbers consisting of several tuned mass damper units connected each other in parallel. The method is essentially the extension of the formulas proposed by Den Hartog for single degree-of-freedom tuned mass dampers to multiple tuned mass dampers. To demonstrate the effectiveness of the proposed method, an application to high-speed rail bridges are made. The bridge is modeled as a simple Euler-Bernoulli beam, and the train is modeled as a series of moving loads. The equations of motion are solved numerically by the Newmark method. The results of the study showed that multiple tuned mass dampers designed by the proposed method show good performance in reducing the resonance vibrations in high-speed rail bridges. [ABSTRACT FROM AUTHOR]

Nonlinear Oscillation of a Mass Attached to a Stretched Elastic Wire is considered. Equation of motion of the system is obtained. The classical multiple scales method (MS) and multiple scales Lindstedt Poincare (MSLP) method are applied to the equation of motion. Approximate analytical solutions of the equation of motion are obtained using the stated methods. Obtained solutions are compared with numerical solution of the equation of motion. MSLP method gives better results for strong nonlinearities. [ABSTRACT FROM AUTHOR]

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Secondary braking system is used to keep the vehicle speed at a constant value for commercial vehicles in down hill position. Retarder braking systems is applied on the vehicle driveline, and when the retarder engaged it creates the variable braking moment effect between vehicle chassis and driveline. This type of braking moment that is created by retarder is occurred moment peaks on driveline during the moment transmissions. In this study, a mathematical model of vehicle driveline is established with generated equations of motion. The retarding effect is calculated theoretically and compared these theoretical results with test studies. [ABSTRACT FROM AUTHOR]

The stability of cutting system in machine tools is not only dependent on the structural but also dependent on the process damping ratio (PRD), which is generated by the chip formation process. In this study, the effects of the cutting process damping in a turning system with two degree of freedom on the cutting system were investigated. For this purpose, the equations of motion for this turning system were derived as linear and nonlinear in the (t) -decomposition form. Changing of the cutting process damping was obtained by numerical solution of the nonlinear differential equations. [ABSTRACT FROM AUTHOR]

The problem of harmonic wave propagation in prestressed or stress free elastic or viscoelastic tubes filled or not filled with a viscous or an ideal fluid, became an interesting subject since the time of Thomas Young (1773-1829) who first obtained the speed of the pulse wave in arteries, and found important applications in many fields of engineering. The historical evolution of the subject can be found in the papers by Lambossy (1951) and Skalak (1966) and in the book by Fung (1984). In the present work, the problem that we consider is to investigate the pulsating wave propagation in large blood vessels. The importance of the present problem from the bioengineering point of view is that the wave speed and the transmission coefficient depend on the initial deformation and the material coefficients. The measurement of these parameters makes it possible to observe the variation of them with material properties. For the historical evolution of the subject the reader may refer to Morgan and Kiely (1954), Womersley (1957) who used the theory of small deformations, Atabek and Lew (1966) who were the first to introduce the effect of prestress, Mirsky (1967) who took into account the orthotropic properties of the arterial wall, Rachev (1980), Kuiken (1984) and Nayfeh (1966) who considered the blood as a two phase system consisting of plasma and blood cells and investigated the flow of the two phase flow in a rigid tube. The fluid (blood) is taken as incompressible and viscous with dusty particles in it, and the governing equations of motion are obtained in the cylindrical coordinates. On the other hand, to obtain the equations of motion of the tube (artery) which is assumed to have elastic, fibrous and incompressible material, the theory of "superimposing small deformations on large static deformations" is employed and, the incremental equations of motion and incremental constitutive equations that characterize the arisen dynamical state are given. These equations are expressed in the cylindrical coordinates and the boundary conditions to be satisfied are given. Then, assuming that the cylindrical shell (artery) is under the effect of both constant, axial stretch and inner pressure (initial equilibrium state), the incremental equations of the motion are given for this prestressed state. The solutions of these incremental equations of motion both for fluid and solid phases are obtained for the axial symmetric motion. The closed form solutions to the differential equations of the fluid were accomplished but, because the coefficients of the field equations are complex functions of the radial coordinate, it could not be accomplished to obtain closed solutions to the equations of the solid phase. For this reason and to obtain the effect of the tube's thickness on the wave characteristics, numerical solutions with method of finite differences are sought to the equations and the corresponding boundary conditions that govern the solid phase. Then, in the long wave approximation, assuming that the thin tube filled with a non-viscous fluid is non prestressed, the dispersion relation is investigated, wave speeds and transmission coefficients are obtained. As the last, again in the long wave approximation, the dispersion relation for the thick walled prestressed elastic tube filled with a viscous fluid is obtained, the wave velocities and the transmission coefficients are computed and the results are given with graphs. The obtained results are in agreement with the results of Ercengiz (2005) and Nag and Jana (1981). The obtained results reveal that the primary and the secondary wave speeds become higher with the increase of the fibre parameter of the tube's elastic material. On the other hand, the increase of the mass concentration of the dusty particles in the fluid decreases the primary wave velocity though only for the small values of the Womersley parameter, again decreases the secondary wave speed for all the values of the Womersley parameter. With the increase of the fiber parameter, while transmission coefficient for the primary wave increases, the transmission coefficient for the secondary wave decreases. The increase of the mass concentration of the dusty particles in the fluid decreases the transmission coefficients of both the primary and the secondary waves. The increase of the axial stretch increases the primary wave speed, but decreases the secondary wave speed and the transmission coefficient for the primary wave. The variation of the axial stretch doesn't change the transmission coefficient for the secondary wave. [ABSTRACT FROM AUTHOR]

This work focuses on the evaluation of critical control times in the optimal control of linear quantum systems. The linearity is used to imply the existence of only linear intra forces in the system. This means that the system under consideration is composed of harmonic oscillators. The linearity is not only in the forces. The external field's dipole polarizability function is also taken linear in spatial variables. Beyond that the objective operator whose expectation value's deviation from its target value should be minimized in square and the penalty operator whose expectation value is to be suppressed are also linear in position and momentum operators. We assume that the system has 3N degree of freedom and the cost functional for the optimal control is composed of four terms: (1) objective term which is the square of the objective operator whose expectation value's deviation from its prescribed target; (2) penalty term for getting finiteness in external field; (3) penalty term for an operator whose norm is to be suppressed ; (4) dynamical constraint term which enters the quantum motion of the system to the optimisation. This cost functional depends on five unkowns: (1-2) wave function and its complex conjugate; (3-4) costate function which is in fact the Lagrange multiplier of the dynamical constraint term. It varies in time and space and somehow describes the backward motion of the system from the final instant of the control. It is a complex valued function hence its complex conjugate is the companion unknown to itself; (5) The external field amplitude within the dipole the polarizability approximation. It is temporal and real valued. There may be a shorthand notation for the deviation of the expectation value of the objective operator from its target value. In that case, this entity can be considered as another unknown and can be handled by adding its definition as an extra condition. The equations of motion can be optained by setting the first variation of the cost functional to zero. Four partial differential equations are obtained for them-selves and complex conjugates of the wave and costate functions. The equations for the wave function are accompanied by initial conditions while the costate function related partial differential equations are right hand sided and accompanied by final conditions. This for equations two by two, describes forward and backward evolutions for the system and these evolutions are connected by the algebraic however functional relation obtained for the external field amplitude. All these equations are non line-ar for the general case. However for the present linearity assumptions they become linear. The equations of motion mentioned above are not attempted to be solved. Instead, ordinary differential equations for the expectation values of position and momentum operators on the wave function and the transition terms between the states decscribed by the wave and costate functions are constructed. These temporal ODEs are linear but may be timevariant in the coefficients if the weight functions of the penalty terms are temporally varying. The simplest case involves the cases where these weights are constansts and the ODEs can be analytically solved in terms of an exponentials matrix. This results in analytic expressions for the unknowns. These expressions de-pend not only on time but also control time (T). As can be shown by rigorous analytical analysis and verified by the numerical implementations, there are certain critical values of the control time where the extressions grow up to infinity or vanishes. Vanishing values mean exact achievement of the target value by the expectation value of the objective operator. These are the best control instants where the goal is exactly achieved. On the other hand, control times causing infinite jumps, are just the time instants the control becomes infeasible. The critical control times creating infinite jumps are called "Critical Control Times for Uncontrollability" and it is important to know these values before attempting the experimentation to avoid uncontrollability. Otherwise, experiment is wasted out. The critical control times which make the deviation of the expectation values of the objective operator from its target value are called "Critical Control Times for Exact Achievement" and they are useful to get the best control. Paper contains all important issues about these points. [ABSTRACT FROM AUTHOR]

To find a non-trivial field theoretical model is one of the outstanding problems in theoretical high energy physics. The perturbatively nontrivial f 4 theory in four dimensions was shown to go to a free theory as the cut-off was lifted a while ago. The Nambu-Jona- Lasinio model, which is non-renormalizable perturbatively, was also shown to go to a trivial model. There are claims that the gauged Nambu-Jona- Lasinio model may give a non-trivial theory for a non realistically large number of flavors. All these examples show that the search for non-trivial models may be an interesting endeavor. On the other hand, there are two-dimensional models with infinite number of local and non-local charges. These models were shown to give scattering matrices without particle production indicating a behavior not expected from fully interacting theories. When the symmetry present in these models is broken, these models give rise to particle production in perturbative calculations. Another class of models are those with zero scattering amplitudes for the constituent fields, even though their Lagrangians seem to have non-zero interaction terms. These interactions arise from constraints. An example of them is taking a product of the constituent field equal to a power of the auxiliary field, i.e. forming composites of the constituent fields. The interaction of the constituent field with the composite field is defined. The Lagrangian contains the kinetic part of only the constituent spinor fields and the kinetic terms for the composites are formed as a result of vacuum polarizations of the composite field due to its interaction with the constituent field. Such models simulate the models with only spinors. The first work on models with only spinors goes back to the work of Heisenberg. Gürsey proposed his model as a substitute for the Heisenberg model in the fifties. This spinor model is important since it is conformally invariant classically and has classical solutions which may be interpreted as instantons and merons, similar to the solutions of pure Yang- Mills theories in four dimensions. This original model can be generalized to include vector, pseudovector and pseudoscalar interactions. A while ago, Akdeniz et al. claimed to have written a polynomial Lagrangian equivalent to the one given by Gürsey. Now we know that the models studied are only naively equivalent to these spinor models. He, with his collaborators, has also shown that in some of these models, the interaction of the spinor field with other spinors goes to zero. The model is not only asymptotically free, it is actually free, meaning that the coupling constant goes to zero as the cut-off is removed. We could not find physical processes which give results indicative of an interacting theory. With this motivation we want to give a new interpretation of the old work of Akdeniz et al.. First of all we see that the polynomial form of the original Gürsey model really does not correspond to it in the exact sense. The two versions obey different symmetries.… [ABSTRACT FROM AUTHOR]