Papers by Keyword: Nonlinear Vibration

Abstract: Analysis of vibration stability of simply supported Euler-Bernoulli functionally graded (FG) nanobeam embedded in viscous elastic medium with thermal effect under external parametric excitation is presented in this work. An attempt has been made for the first time is investigating the effect of thermal load on dynamic behavior, amplitude response, instability region and bifurcation points of functionally graded nanobeam. Thermal loads are supposed to be uniform, linear or nonlinear distribution along the thickness direction. Nonlocal continuum theory and the principle of the minimum total potential energy are applied to derive the governing equations. The partial differential equations (PDE) are transported to the ordinary differential equations (ODE) by using the Petrov-Galerkin method and the multiple time scales method are manipulated to solve the motion equation. To study the effect of external parametric excitation and thermal effect, different temperature distributions along the thickness such as uniform, linear, and nonlinear distribution are considered. Moreover, stable and unstable regions and bifurcation points are determined. It is obtained that the thermal load can affect the amplitude response of FG nanobeam. Also, it is observed that the instability of the system is affected by the detuning parameter and the parametric excitation amplitude plays great role in the instability of system. Nanobeams are used in many devices like nanoresonators, nanosensors and nanoswitches. This paper is helpful for designing and manufacturing nanoscale structures specially nanoresonators under different thermal loads.

Abstract: This paper aims to analyze the nonlinear vibration of clamped-clamped buckled beams made of Aluminium alloy (Al-alloy) reinforced with uniformly dispersed Single Walled Carbon Nanotube (SWNT). The mean field homogenization technique is used to predict the effective material properties of the beams. The equation of motion governing the nonlinear behavior is solved using an exact method. The effects of various parameters including axial load, vibration amplitude, SWNT volume fraction, SWNT aspect ratio and beam slenderness ratio on the nonlinear frequency and on the phase trajectory plots for pre- and post-buckling states are studied.

Abstract: The problem of geometrically nonlinear free vibration of a clamped-clamped functionally graded beam containing an open edge crack in its center is studied in this paper. The study is based on Euler-Bernoulli beam theory and Von Karman geometric nonlinearity assumptions. The cracked section is modeled by an elastic spring connecting two intact segments of the beam. It is assumed that material properties of the functionally graded composites are graded in the thickness direction and estimated through the rule of mixture. The homogenisation method is used to reduce the problem to that of isotropic homogeneous cracked beam. Direct iterative method is employed for solving the eigenvalue equation for governing the frequency nonlinear vibration, in order to show the effect of the crack depth and the influences of the volume fraction on the dynamic response.

Abstract: Dynamic characteristics of a dielectric elastomer based micro beam resonator are investigated by taking into consideration of squeeze-film damping, large deformation and electrical voltage. The analysis shows that the resonant frequency of the resonator can be tuned through changing applied electrical voltage. It is observed that the natural frequency of the resonator increases with the increase of the vibration amplitude. In addition, the ambient pressure can significantly alter the resonant frequency of the resonator. The analysis is envisaged to provide qualitative predictions and guidelines for design and application of DE-based micro resonators.

Abstract: In this paper, the Hamilton theory was applied to describe the dynamic model of Thermal Power Pipeline nonlinear fluid solid coupling vibration. The model includes the control equation of axial vibration and the transverse vibration of the pipeline, taking full account of the vibration characteristics of the fluid in the pipeline, effect of thermal deformation and constant support, as well as the friction coupling, Poisson coupling and junction coupling. The model is an attempt to the heating pipes and need to be further improved.

Abstract: In the torque converter, a damper with a piecewise-linear spring is used to reduce the forced vibration, and the subharmonic vibration occurs when the spring restoring torque characteristics approach the switching point. This research analyzed the effect of stiffness ratio between the neighboring piecewise-linear springs on the occurrence of the subharmonic nonlinear vibration in automatic transmission powertrain. The powertrain is modeled with multi degree-of-freedom nonlinear system as an actual vehicle. The result shows higher value of the stiffness ratio between the neighboring springs creates larger value of the subharmonic vibration.

Abstract: The free vibration along with the vertical direction of the symmetric double spring –mass system has been studied with experimental method. It is discovered that when the distance between two suspending points is not zero, the vibration of symmetrical double spring mass system along the vertical direction is nonlinear. The period of the system increases with the increase of the amplitude and distance of suspending points. The equivalent mass coefficient of the system vibrating nonlinearly is greater than that of the system vibrating harmonically and is related to inclination degree and relative elongation of the spring.

Abstract: The aim of this study is to examine the complicated dynamics behavior of nonlinear vibrations of bistable cantilevered piezoelectric beam. The base excitation on the beam is assumed to be harmonic load. The Galerkin’s approach is adopted to disperse the energies and the virtual work. Dynamic equation of the bistable piezoelectric system is established by using Hamilton’s principle. The averaged equations in the polar form is obtained by using the method of multiple scales. Based on the actual work situation of the cantilevered piezoelectric beam, it is known that base excitation and the size parameter of the beam play the important roles in the nonlinear vibration of the cantilevered piezoelectric beam. The quality of the permanent magnet, the thickness of the base layer and the length of the beam all affect the amplitude of the beam. The thickness of the piezoelectric layer can make the frequency response curve shift in frequency domain.

Abstract: In the present study, nonlinear free vibration behavior of nanobeam subjected to magnetic field is investigated based on Eringen's nonlocal elasticity and Euler–Bernoulli beam theory. The Hamilton's principle is adopted to derive the governing equations together with Euler–Bernoulli beam theory and the von-Kármán's nonlinear strain–displacement relationships. An approximate analytical solution is obtained for the nonlinear frequency of the nanobeam under magnetic field by using the Galerkin method and He's variational method. In the numerical results, the ratio of nonlinear frequency to linear frequency is presented. The effect of nonlocal parameter on the nonlinear frequency ratio is studied; furthermore, the effect of magnetic field on the nonlinear free vibration behavior of nanobeam is investigated.

Abstract: For effectively harvesting the broadband and low-frequency vibration energies in real environment, a micro bistable piezoelectric generator, without containing magnet, is designed. On the basis of analysis the nonlinear behavior of the stiffness, damping and the electromechanical coupling coefficient about the bistable vibration system, a precise mechanical-electric transfer model is built. The output characteristic of the piezoelectric generator is simulated and tested. The results showed that the piezoelectric generator can effectively harvest the broadband and low frequency vibration energies. And the output voltage can meet the electricity demand of a wireless sensor network node. The structure of the piezoelectric generator does not contain magnets, and it is easy to realize miniaturization and integration.