Vibration behavior of an orthotropic cracked plate embedded in a nonlinear Winkler–Pasternak elastic foundation is studied in this paper. The plate’s imperfection is due to an inclined crack started ...on the surface and continued in the depth of the plate. Crack is located at the center of the plate and has an arbitrary angle of orientation with respect to its side edge. The harmonically excited plate is modeled based on the Kirchhoff’s plate theory. Galerkin’s procedure is applied to develop the time-dependent ordinary differential equations of the system, and multiple timescales method is used to obtain the solution. Two different phenomena, namely first primary resonance and the primary resonance with the 1:3 internal resonance, are investigated from the frequency responses of the system. The first four natural modes of vibration for the case of external forced vibration are studied, and for the combined primary and 1:3 internal resonances, the four-to-one internal resonances are considered. The effects of various parameters on these phenomena have been examined, and the results are discussed in detail.
Non-classical beam theory is employed to study higher modes of free vibration of a microtube conveying fluid. The modified couple stress theory is utilized to model the size-dependent vibration of ...the microtube structure. It is proposed that the midplane stretching of the microtube needs to be taken into account, and subsequently, the nonlinear partial differential equation of motion in a non-dimensional form has been derived. Three modes of vibration are considered in this study, and the Galerkin procedure is utilized to obtain the nonlinear equations of motion. Analytical expressions for the nonlinear frequencies are developed, and the time responses of the structural model employing the variational iteration method are presented. Results obtained from the analytical procedure were compared with those computed by using numerical method, and close agreements are observed. A parametric sensitivity study is carried out to evaluate the performance and the accuracy of the proposed analytical method from an engineering application point of view.
A multi-actuation model predictive controller is designed to improve the stability of the performance vehicles during high-speed maneuvers. The actuators included in this study are four electric ...motors for the wheels and two active aerodynamic wings at the front and rear of the vehicle. The designed controller integrates optimal corner torque allocation with an optimal active aerodynamics control system. A model predictive control scheme is used to adjust the air wings angle of attack and optimize the corner torques. A high-level constraint adjustment module is added to the controller to observe nonlinear tire behavior and optimize aerodynamic wings activation as required. Nonlinear tire behavior and actuator dynamics are considered and included in the prediction model. The controller performance is verified in simulation with MATLAB/Simulink and CarSim.
Vibration control of flexible structures has always been one of the most important issues and Among variant available control methods, active vibration control using piezoelectric sensors and ...actuators has become popular due to its high efficiency and flexibility for designing a control system. The main concern in designing a control system with piezoelectric patches is finding best position for patches. On the other hand, number of used sensors and actuators is another important issue which affects the costs of the project as well as the performance. The main goal of the present study is to control oscillation of a rectangular plate using minimum number of piezoelectric sensors and actuators (i.e., objective one) and finding their optimum placement to get the maximum possible performance (i.e., objective two); the mentioned two objectives are in conflict. The plate have been mathematically modeled using the Kirchhoff-Love theory. By considering the piezoelectric sensor-actuators effects, the control equation of the cantilever plate has been obtained. In order to find the optimum number and placement of the sensors and actuators, the multi-objective genetic algorithm (GA) has been used and the objective functions have been defined based on maximization of observability and countability indexes of the cantilever plate. After conducting the optimization process, a few thumb rules have been extracted using the innovization technique. The results have been verified by implementing the designed controller using the optimum solution found by optimization method. The importance of the rules found by innovization technique have been illustrated in the numerical discussion.
Free vibration analysis of a double-walled carbon nanotube (DWCNT) is performed where the surrounding medium has been modeled employing a Winkler model. The nonlinear differential equation of motion ...is derived for both layers of the nanotube by using an analytical method. In order to solve the coupled nonlinear differential equations of the system, the variational iteration method is utilized. By applying this method, analytical expressions are derived to predict the vibration characteristics of the model and the nonlinear frequencies and responses of the double-walled carbon nanotube are obtained. Results obtained for the nonlinear frequencies are also compared with the frequencies found by the numerical method. It has been shown that the results determined by these two procedures are in an excellent agreement. Finally, a parametric study is carried out and the effects of different parameters, namely, the amplitudes, boundary conditions, and the geometrical dimensions on the frequencies of the system have been examined.
