In this research dynamic instability and nonlinear vibration of a clamped-clamped micro-beam sandwiched with piezoelectric layers based on parametric EXCITATION in sub-HARMONIC region is investigated. The equation of motion is derived based on Hamiltonian principle, and nondimensionalized using appropriate non-dimensional parameters. Applying a HARMONIC AC voltage to the piezoelectric layers results in the time varying of the linear stiffness of the micro-beam. The resultant motion equation in non-dimensional form is discretized to single degree of freedom model using Galerkin technique. The governing equation is a nonlinear Mathieu type ODE, and the periodic attractors are captured based on the shooting technique. The nonlinearity of governing equation is due to the geometric nonlinearity which originates from the clamped-clamped boundary conditions. The effect of various parameters including magnitude of the nonlinear stiffness, damping coefficient, the frequency and the amplitude of the HARMONIC EXCITATION on the parametric resonance region is investigated. The results depict that increased damping coefficient leads to the decreased aria of the parametric resonance region. It is concluded that the magnitude of the nonlinear stiffness, does not affect on the area of the resonance region, however it considerably influences on the amplitude of the parametric resonance.

Electrical energy can be harvested from the vibrations of piezoelectric plates. The behavior of the piezoelectric plate is simulated using electromechanical coupling. Given the large strain experienced by the flexible plate, the linear theory is inadequate; therefore, the effect of Von Karman strain must be considered. This paper investigates and validates the vibrational behavior of a piezoelectric nonlinear plate. Specifically, it employs coupled equations for a multilayered plate, incorporates Von Karman’s nonlinear strain, and applies Mindlin’s first-order shear deformation theory. The electrical response is obtained through finite element analysis of the piezoelectric nonlinear plate in Matlab. Different boundary conditions are considered to verify the results, including clamped edges, simply supported edges, and a combination of two simply supported and two clamped edges. The electrical response of the open-circuit case under HARMONIC EXCITATION is presented. Furthermore, the phenomenon of voltage cancellation during plate vibrations is studied, and a method for enhancing energy harvesting performance using separated electrodes is proposed. The results indicate that, across all cases, the voltage response with a continuous electrode is lower than with segmented electrodes at the first natural frequency.

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 paper, the nonlinear vibration of a Euler–Bernoulli nanobeam resting on a non-linear viscoelastic foundation is investigated. It is assumed that the nanobeam is subjected to a HARMONIC EXCITATION that can be representative of an electrostatic field. The non-linear viscoelastic foundation is considered for both hardening and softening cases. By neglecting of the in-plane inertia, Eringen's nonlocal elasticity theory is used to model and derive the equation of motion of the nanobeam. Using the Galerkin method and the first mode shape, the obtained partial differential equation is reduced to the ordinary differential equation. Calculating the system's equilibrium points lead to heteroclinic bifurcation and the heteroclinic orbits are obtained. Then, using the Melnikov integral method, the chaotic motion of the system is studied analytically, and the safe region of the system is determined respect to the parametric space of the problem. When the viscoelastic foundation has a hardening characteristic, the chaotic behavior in the system does not occur. It has been observed that the use of nonlocal elasticity theory is necessary to investigate the chaotic behavior of nanobeam, and using the classical theory of elasticity may place the system in the chaotic region.

Risers are one of the main vessel structural members. So, non-linear vibration analysis of risers, is particularly important. To achieve a proper design, understanding how the transverse vibrations of risers and obtain their frequency response is very useful. In this paper, the transverse vibrations analysis of risers under variable axial load are investigated. The effects of mid-plane stretching is also considered. For this study, the method of multiple time scale is used. In order to verify the accuracy of this method, the results are compared with the results of four order Runge-Kutta numerical method, which has a good accuracy. The frequency response of the system is represented Bifurcation phenomenon. Study of frequency response indicating that there is bifurcation phenomenon in vibrational system, and also the mid-plane stretching of riser will create a hardening behavior. Parametric study is also performed that the effect of various parameters is review on the starting point of the bifurcation phenomenon.

Dynamic equation of a simply supported beam with a lump mass in the midspan subjected to HARMONIC axial EXCITATION, whose one end can move along the beam freely, is a nonlinear differential equation with no explicate solution. In this article we start extracting the equation of motion. Existence of periodic solution, under some condition, are investigated and proved using green function and Schaunders fixed point theorem; also noting into the structure of differential equation of motion, existence of oscillating response investigated, independently. By this analysis, it becomes possible to predict whether the solution converges to a point (zero) or a periodic answer

Sloshing phenomenon is one of the complex problems in free surface flow phenomena. Numerical meshless methods as a new method can be used to solve this problem. In these methods, the lack of a mesh and complex elements for the domain of problems due to the change in geometry of the solution over time provides a lot of flexibility in solving numerical problems. In the previous researches, the sloshing problem in reservoirs was solved, using the Laplace equation with respect to the velocity potential, but the solution to this problem with pressure equations has not much considered; therefore, using the pressure equations and a suitable lagrangian time algorithm, generalized exponential basis function method has been developed for dynamic stimulation reservoirs. The approximation is solved, using a meshless method of generalized exponential basis functions and the entire domain of problem will discrete to a number of nodes and then with appropriate boundary conditions, the unknowns are approximated. In this study, linear and nonlinear examples have been solved under HARMONIC stimulation, in two-dimensional form of rectangular cube tanks, and the results of them have been compared with the analysis solving methods, other numerical methods, and experimental data. The results show that the present method in two-dimensional mode is very noticeable compared with other available lagrangian methods because of accuracy in solving problem and spending time.

In the present research, performance of HARMONIC components identification and elimination techniques in practical operational modal data is investigated. Firstly, classical modal testing has been carried out on a cantilever steel beam and modal data are extracted. Four bending modes were available in the frequency band of interest. Afterwards, the same structure underwent operational modal tests with simultaneous random and HARMONIC EXCITATION forces. In OMA, measurement data obtained from the operational responses are used to estimate the parameters of models that describe the system behavior. Extracted modal parameters from these data compared with baseline parameters. Extraction of modal parameters from operational data was fulfilled through different common OMA techniques. Each set of obtained results was evaluated in comparison with reference results. Accuracy and capability of each method in eliminating spurious modes caused by HARMONIC input components have been studied. For data analysis, in addition to developed MATLAB codes, commercial software of PULSE has been utilized in parallel as a tool for verification. The results of this survey demonstrate that the accuracy of the Stochastic Subspace Identification method is higher compared to Frequency Domain Decomposition and Enhanced Frequency Domain Decomposition methods. However, when the system has low modal damping, Frequency Domain Decomposition methods provide better estimates.

In this work, the nonlocal elastic waves in a fluid conveying armchair thermo elastic single walled carbon nanotube under moving HARMONIC load is studied using Eringen nonlocal elasticity theory via Euler Bernoulli beam equation. The governing equations that contains partial differential equations for single walled carbon nanotube is derived by considering thermal and Lorenz magnetic force. The small scale interactions induced by the nano tubes are simulated by the non-local effects. The time domain responses are obtained by using both modal super position method and Newmarks’ s direct integration method. The effect of nonlocal parameter, thermal load, magnetic field of the moving HARMONIC load on the dynamic displacement of SWCNT is discussed. The results obtained show that the dynamic displacement of fluid conveying SWCNT ratio is significantly affected by the load velocity and the EXCITATION frequency. This type of results presented here, will provide useful information for researchers in structural nano science to understand the small scale response of elastic waves coupled with thermo elasticity and some field forces.

This paper analyzes the nonlinear dynamic response of truncated conical shells reinforced with carbon nanotubes with functional graded ceramic-metal matrix subjected to HARMONIC EXCITATION. Carbon nanotubes are distributed with three different patterns along the length and thickness of the conical shell. The matrix material of the shell is considered to be a combination of metal and ceramic, whose properties change as a power function along the thickness of the shell. In order to analyze the dynamic of this system, firstly, the nonlinear dynamic equations of the conical shell are derived based on the first order shear deformation theory and von Karman's strain-displacement relations. Then, with the help of Galerkin discretization method, partial differential equations of the system are converted into time-dependent ordinary differential equations. Adams-Bashforth numerical method is used to solve the system of nonlinear differential equations. Finally, a parametric study is presented to investigate the effects of some parameters of the system, such as the power index, volume fraction and distribution pattern of carbon nanotubes, the geometric characteristics of the shell, and amplitude of the EXCITATION force on the nonlinear dynamic response of the conical shell. In order to validate, the results of this article are compared and presented with the results of previous valid references.