The dynamic response of shape memory alloy (SMA) systems and structures often exhibits a complex behavior due to their intrinsic nonlinear characteristics. The key characteristics of SMAs stem from adaptive dissipation associated with the hysteretic loop and huge changes in mechanical properties caused by the martensitic phase transformation. These exceptional properties have attracted attention of many researchers in various engineering fields from biomedicine to aerospace. One of the possible responses that may happen in SMA structures is the chaotic response, which can lead to a massive change in the system behavior. Moreover, such a system is highly sensitive to initial conditions. Therefore, its analysis is essential for a proper design of SMA structures. The present article discusses nonlinear dynamics and chaotic behavior in a one-degree-of-freedom (1DoF) oscillator connected to SMA at constant working temperature and pseudo elastic region. Equation of motion is formulated, using the Brinson constitutive model. Combination of structural equations of SMA and dynamical and kinematic relations, as well as forth-order Runge-Kutta scheme are employed to solve the equation governing the oscillator motion. Free and forced vibrations under the influence of harmonic stimulation force and in a wide range of excitation frequencies are presented in the form of various numerical examples. Different tools for detecting chaos, including, phase plane, time response, frequency response, Lyapunov exponent, and Poincare map are used to determine the type of motion. Numerical simulations demonstrate a wide range of periodic, quasi periodic, and chaotic responses for certain values of excitation frequencies, which is a reason for the proper understanding of the behavior of these systems.

Vibration of various types of structures such as beam, plate, shell, and rod have been investigated by researchers for their application in a wide range of mechanical systems. The longitudinal vibration of the rods is of great interest, so that the researchers have performed them numerically or analytically and precise or approximate. In this research, the nonlinear longitudinal free vibration of rod with variable cross-section under finite strain has been investigated. First, the governing equations of the rod with variable cross-section were obtained, which are partial differential equations; then, they were transformed to nonlinear ordinary differential equations, using the Galerkin method with considering one mode shape. The problem was investigated for two boundary conditions. Using the multiple scales method, the equations were analytically solved. The differential equations are solved by Runge-Kutta numerical method of order 4, and then compared with the analytical solutions. The effect of the amplitude and rate of changing cross-section on the ratio of linear to nonlinear frequency and also the effect of different initial condition, rate of changing cross-section and coefficient of damper were shown in figure. The results show that the tapered cross-sectional area has a significant effect on the ratio of linear to nonlinear frequency to vibrations amplitude. The coefficient of damper has a little effect and initial condition has a considerable effect on the process of problem.

Nonlinear behavior of an initially curved fully clamped microbeam is investigated in this paper. The microbeam is laminated between two thin piezoelectric layers along its length. Applying voltage to the piezoelectric layers induces a lengthwise force in the microbeam which, in turn, changes the initial rise and the bending stiffness of the microbeam. This feature is used to tune the frequency and the bistability band of the initially curved microbeam for the first time in this paper. The microbeam is electrostatically actuated as well. The governing equation of motion is obtained, using the Hamilton’s principle and the size effect is considered in the formulation of the problem utilizing the strain gradient theory. Static response of the system is obtained, using the Newton-Raphson numerical approach. The natural frequency of the system is obtained for various electrostatic voltages. The influence of piezoelectric actuation and size effect is studied on the static behavior and the frequency of the microbeam. Dynamic response of the microbeam in the vicinity of the primary resonance is obtained, using shooting technique and in some cases by the method of multiple scales. The effect of size and piezoelectric excitation on the primary resonance is investigated. The secondary resonance of the microbeam subjected to subharmonic resonance of order 1/2 and the influence of size on it is also studied.
 

The structural vibrations are the important sources of the energy harvesting, which can be produced from the harmonic excitation. The piezoelectric structure behavior is simulated by the electromechanical coupling. The flexible beam has the large strain. The results of linear theories are not proper. The large strains effect on the results response and the nonlinear behavior must be considered. The Newmark method is used to solve the equations of motion and coupled equations. Regarding the type of proportional damping, the nonlinear hardness effect is also applied to the damping calculation. This paper presents the electric response of the piezoelectric nonlinear beam with the harmonic base excitation by the numerical and experimental methods. The program of finite elements is developed for the numerical results and the electric response is obtained. The theories results are verified by the results of experimental. The experimental results are used for the piezoelectric bimorph beam with the change of concentrated mass position. The effect of piezoelectric property in the frequency response of nonlinear beam is presented. The results show the effect of piezoelectric properties on the frequency response of the nonlinear beam and the effect of the concentrated mass position on the output voltage, and the most suitable position of the concentrated mass position is presented to obtain the highest voltage response.

In this study, effect of shroud on dynamic characteristics of a rotating multi blade system is investigated. The main aim of this study is to investigate the effect of shroud stiffness and shroud configuration on the system natural frequency. For this purpose, natural frequencies of various systems (in terms of the position, where the blade is connected to the shroud and number of blades, which are connected together with a shroud) via different degrees of shroud stiffness and different configurations of shroud have been compared to show how this parameters affect the natural frequencies of the system. In this study, the shrouds have been considered as the discrete springs with corresponding stiffness values. The vibration frequency characteristics have been analyzed, using assumed mode method along with Hamilton’s law. Since in multi blade systems such as turbines it is crusial to keep the system working frequencies far away from natural frequencies (in order to prevent the resonance phenomenon), based on the results of this paper, it is shown how the parameters of shroud can remove the natural frequencies associated with some of the modes of the system from the work area.

The present paper applies a multi-objective genetic algorithm for optimally design of a vehicle suspension. The vehicle model considers three-dimensional movements of vehicle body. In this full vehicle model having 8 degrees of freedom, vertical movement of passenger seat, vehicle body, and 4 tires as well as rotational movements of vehicle body create the degrees of freedom of the model. In this paper, applicable suspension parameters, consisting of passenger seat acceleration, vehicle body pitch angle, vehicle body roll angle, dynamic tire force, tire velocity, and suspension deflections are considered and optimized in optimization process. Different pairs of these parameters are selected as objective functions and optimized in multi-objective optimization processes, and Pareto solutions are obtained for pair of objective functions. In final optimization process, the Pareto solution related to the summation of dimensionless parameters in one suspension parameters group versus other group, is derived. In these Pareto solutions, there are important optimum points and designers can choose any optimum points for a particular purpose. Pareto optimization is better than other multi-objective optimization methods because there are more optimum points on Pareto front, where each point represents a level of optimization for the pairs of objective functions, and designers can choose any of the points to specific purpose.

In this paper, the CFD-MBD numerical coupled model has been proposed for an accurate evaluation of the behavior of the partially filled railway tank wagon. The vibration response of the wagon has been obtained by the fourth-order Runge-Kutta method based on the three-dimensional multibody dynamic (MBD) model with 19 degrees of freedom comprising car-body, two bogies, and four wheel-sets. The model of transient fluid sloshing inside the tank has been analyzed using the computational fluid dynamics (CFD) method combined with the volume of fluid (VOF) technique for solving the Navier-Stokes equations and tracing the fluid free surface, respectively. Validation of the numerical results has been carried out using experimental data. Then, the simultaneous interaction of the transient fluid slosh and the wagon dynamics has been considered through the development of the numerical process of coupling CFD and MBD models. The dynamic characteristics of a partially filled tank wagon have been derived in braking conditions using parametric study on the filled-volume, tank cross-section shape, and fluid viscosity. The results indicate that the filled-volume increase decreases the amplitude of the fluid's center of gravity coordinate. The lowest fluid slosh in the different filled-volumes has been related to the modified-oval cross-section. The fluid viscosity has a slight effect on the longitudinal fluid slosh force and the stopping distance of the railway tank wagon.
 

Galloping is a large-amplitude, low frequency, wind-induced oscillation of overhead power transmission lines with one or multi loops of standing waves per span which occurs due to wind flow. Based on the field data, numerous galloping oscillations occurs in the form of one loop oscillation which whereby high dynamic loads are imported to the support structures. In this research, the results of wind tunnel tests have been performed on a two-span distorted scale model with an ice-accreted cross-section under uniform and non-uniform aerodynamic loadings. Dead-end and suspension insulators have been applied to the support points. Then, based on identifying the most critical state of the lines oscillation, a solution has been proposed based on increasing their bending strength through the application of hardening local covering. The results showed that the most critical state of the cables oscillation in the galloping is related to the one-loop oscillation, which occurs as a result of interactions between the cables of adjacent spans under uneven aerodynamic loading and the use of suspended insulators, and the dynamic forces applied to the supports are about 20% more than the case when the cables oscillate due to the dead-end connections attached to the support structure. Also, applying the local covering with a length of 20% of cable span leads to a 27% reduction in dynamic support reaction of one-loop galloping.

This paper focuses on 3-D dynamic modeling of a transport quadrotor with cable in the presence of load generating stochastic forces. In many practical cases, we are dealing with payloads that generate oscillating forces with random amplitude and frequency by their inherent dynamics or interacting with the environment. These forces can greatly affect the dynamics of the transport system. The innovation of the present study is to consider these forces and show their impact on quadrotor’s dynamics. Furthermore, in order to make the model more compatible with the real system, it is assumed that the connection point of cable and quadrotor is not located on the center of gravity of flying vehicle and the cable's inertia is considered in the modeling process. To this end, the systems’ equations of motion are derived based on both Euler-Lagrange and Newton-Euler methods. After obtaining equations of motion, the verification of the model is investigated in three steps. In the first step, by performing simulation, the validity of the nonlinear model is investigated and dynamical analysis is expressed. In the next step, by evaluating the structure of the model, it is shown that the equations of motion satisfy some structural features of a desirable dynamic model. Then, by setting some parameters and variables to zero, it is shown that simpler models provided in some references can be achieved from this comprehensive model. At the end, the conclusion of this work is presented.