Nonlinear Vibration Of Nanobeam Research Articles

Simultaneous effects of material and geometric nonlinearities on nonlinear vibration of nanobeam with surface energy effects

Simultaneous effects of material and geometric nonlinearities on nonlinear vibration of nanobeam with surface energy effects

Magnetic field effect on nonlinear vibration of nonlocal nanobeam embedded in nonlinear elastic foundation

The history of modern humanity is developing towards making the technological equipment used as small as possible to facilitate human life. From this perspective, it is expected that electromechanical systems should be reduced to a size suitable for the requirements of the era. Therefore, dimensionless motion analysis of beams on the devices such as electronics, optics, etc., is of great significance. In this study, the linear and nonlinear vibration of nanobeams, which are frequently used in nanostructures, are focused on. Scenarios have been created about the vibration of nanobeams on the magnetic field and elastic foundation. In addition to these, the boundary conditions (BC) of nanobeams having clamped-clamped and simple-simple support situations are investigated. Nonlinear and linear natural frequencies of nanobeams are found, and the results are presented in tables and graphs. When the results are examined, decreases the vibration amplitudes with the increase of magnetic field and the elastic foundation coefficient. Higher frequency values and correction terms were obtained in clamped-clamped support conditions due to the structure's stiffening.

Thermal stress and magnetic effects on nonlinear vibration of nanobeams embedded in nonlinear elastic medium

Nonlinear vibration of nanobeams embedded in the linear and nonlinear elastic materials under magnetic and temperature effects is investigated in this study. Von Karman’s strain–displacement relation is applied to a nonlocal Euler–Bernoulli beam model. Equation of motion is derived using Hamilton’s principle. Galerkin’s method is applied to decompose the nonlinear partial differential equation into a nonlinear ordinary differential equation (NODE). The NODE is solved using He’s method. The nanobeams are embedded in the Winkler, Pasternak, and nonlinear elastic media. The effects of low and high temperatures, nonlocal parameter, magnetic force, amplitude, and linear and nonlinear elastic materials are examined.

Nonlinear vibration control of nano-beam based on capacitive acoustic sensors

The nonlinear vibration control of the Euler–Bernoulli beam is studied based on capacitive micro-mechanical acoustic sensors The graphene film has the characteristics of high sensitivity and high accuracy which can be applied to sense the vibration signal. Capacitive micro-mechanical acoustic sensors can be used to detect the acoustic signal of the vibration of the nano-beam. The nonlinear vibration control equation of nano-beam can be established with the displacement and velocity voltage feedback controller based on capacitive micro-mechanical acoustic sensors. The amplitude-frequency response equation of the primary resonance of nano-beam can be gotten by using the multiple scales method. The relationship between the nonlinear vibration of nano-beam and system parameters is investigated. The influencing factors of how to weak system nonlinearity and enhance system stability are analyzed. The static bifurcation behavior of the system is discussed. The numerical results show that the nonlinearity of vibration can be reduced and the stability of the system can be improved by selecting the appropriate control gains and appropriately reducing the amplitude of DC and AC excitation voltages.

Nonlinear vibration of nanobeams under electrostatic force based on the nonlocal strain gradient theory

The nonlinear vibration of a nanobeam under electrostatic force is investigated through the nonlocal strain gradient theory. Using Galerkin method, the partial differential equation of motion is reduced to an ordinary nonlinear differential one. The equivalent linearization method with a weighted averaging and a variational approach are used independently to establish the frequency–amplitude relationship under closed-forms for comparison purpose. Effects of material and operational parameters on the frequency ratio (the ratio of nonlinear frequency to linear frequency), on the nonlinear frequency, and on the stable configuration of the nanobeam are studied and discussed.

Effects of magnetic field on size sensitivity of nonlinear vibration of embedded nanobeams

ABSTRACTThe influence of magnetic field on size sensitivity of nonlinear vibration of embedded nanobeams is studied based on von Kármán geometric nonlinearity and nonlocal Timoshenko beam theory. Adopting Hamilton's principle, governing equations for nonlinear vibration of nanobeams are derived and then solved by using Differential Quadrature method to obtain nonlinear responses under different boundary conditions. The results reveal that high magnetic flux restrains nonlinear vibration of nanobeams. At higher magnetic flux, the nonlocal effect could be ignored. For soft foundation, nonlinear vibration of embedded nanobeams is independent on its stiffness variation, and the increase of magnetic flux broadens this range.

Non-linear forced vibration analysis of nanobeams subjected to moving concentrated load resting on a viscoelastic foundation considering thermal and surface effects

• Non-linear vibration of nanobeam considering thermal and surface effects is investigated. • The nanobeam resting on a viscoelastic foundation is subjected to moving concentrated load. • The Eringen's nonlocal and the Euler–Bernoulli theories are applied. • The Galerkin and the multiple scales methods are employed to solve the problem. • The influences of the various parameters on the jump phenomenon are studied. Analytical solution for the steady-state response of an Euler–Bernoulli nanobeam subjected to moving concentrated load and resting on a viscoelastic foundation with surface effects consideration in a thermal environment is investigated in this article. At first, based on the Eringen's nonlocal theory, the governing equations of motion are derived using the Hamilton's principle. Then, in order to solve the equation, Galerkin method is applied to discretize the governing nonlinear partial differential equation to a nonlinear ordinary differential equation; solution is obtained employing the perturbation technique (multiple scales method). Results indicate that by increasing of various parameters such as foundation damping, linear stiffness, residual surface stress and the temperature change, the jump phenomenon is postponed and with increasing the amplitude of the moving force and the nonlocal parameter, the jump phenomenon occurs earlier and its frequency and the peak value of amplitude of vibration increases. In addition, it is seen that the non-linear stiffness and the critical velocity of the moving load are important factors in studying nanobeams subjected to moving concentrated load. Presence of the non-linear stiffness of Winkler foundation resulting nanobeam tends to instability and so, the jump phenomenon occurs. But, presence of the linear stiffness will lead to stability of the nanobeam. In the next sections of the paper, frequency responses of the nanobeam made of temperature-dependent material properties under multi-frequency excitations are investigated.

Erratum to: Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory

Erratum to: Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory

Nonlinear vibration of nanobeam with attached mass at the free end via nonlocal elasticity theory

In the present study, nonlinear free and forced vibration of Euler---Bernoulli nanobeam with attached nanoparticle at the free end is investigated based on nonlocal elasticity theory. The effects of the different nonlocal parameters (ź) and mass ratios (ź) as well as effects of fixed-free boundary conditions on the vibrations are determined. To obtain the equation of motion of the system, the Hamilton's principle is employed. The stretching of neutral axis which introduces cubic nonlinearity is included into the equation for deriving nonlinear equation. And also effects of damping and forcing are included into the equations. The approximate solutions of the equations are derived by using the multiple scale method. Fundamental frequencies, frequency shift and mode shapes for the linear problem are estimated for a nonlocal Euler---Bernoulli nanobeam with an attached nanoparticle and graphically represented the frequency shift and mode shapes. Nonlinear frequencies are derived depending on amplitude and phase modulation. Frequency---response curves are drawn for different nonlocal parameters and different modes.

Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory

In this study, nonlinear vibrations of Euler-Bernoulli nanobeams with various supports condition is investigated. The non-linear equations of motion including stretching of the neutral axis are derived. Forcing and damping effects are included in the analysis. Exact solutions for the mode shapes and frequencies are obtained for the linear part of the problem. For the non-linear problem approximate solutions using perturbation technique is applied to the equations of motion. The different of support cases are investigated and the cases analyzed in detail. The method of multiple time scale that is a perturbation technique is applied to the equations of motion. Natural frequencies and mode shapes for the linear problem are found for the nanobeam. Nonlinear frequencies are calculated; amplitude and phase modulation figures are presented for different cases. Frequency-response curves are drawn.