Sharif Digital Repository

This paper aims to explore the dynamic behaviour of a nano-resonator under ac and dc excitation using strain gradient theory. To achieve this goal, the partial differential equation of nano-beam vibration is first converted to an ordinary differential equation by the Galerkin projection method and the lumped model is derived. Lumped parameters of the nano-resonator, such as linear and nonlinear springs and damper coefficients, are compared with those of classical theory and it is demonstrated that beams with smaller thickness display greater deviation from classical parameters. Stable and unstable equilibrium points based on classic and non-classical theories are also compared. The results... 

Different nonlinearities in micro-electro-mechanical resonators lead to various nonlinear behaviors such as chaotic motion which can affect the resonator performance. As a result, it is important to properly identify and analyze the chaotic regions in resonators. In this paper, a novel method is proposed for prediction of the chaos in the micro- and nano-electro-mechanical resonators. Based on the proposed method, first an accurate analytical solution for the dynamics behavior of the nano-resonators is derived using the multiple scales method up to the second order. The results obtained by this analytical solution are validated by comparing them with the numerical ones. Using the analytical... 

In this study, a nonlinear absorber that works with a negative stiffness mechanism is suggested to mitigate vibration, and its effect on the reduction of vibration is investigated. The negative stiffness, which is inherently nonlinear, creates internal resonance; therefore, the vibration energy can be transmitted from low-frequency to high-frequency vibrating modes, causing vibration suppression. The nonlinear absorber is added to the primary nonlinear system, and when the main system is subjected to external resonance due to harmonic excitation, the negative stiffness parameter of absorber is so adjusted that autoparametric resonance occurs and vibration is reduced. First, the mathematical... 

In this paper, the nonlinear dynamic response of an inclined pinned-pinned beam with a constant cross section, finite length subjected to a concentrated vertical force traveling with a constant velocity is investigated. The study is focused on the mode summation method and also on frequency analysis of the governing PDEs equations of motion. Furthermore, the steady-state response is studied by applying the multiple scales method. The nonlinear response of the beam is obtained by solving two coupled nonlinear PDEs governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-pint of the... 

Chaotic vibrations of a bistable resonator comprised of doubly clamped shallow arch under simultaneous harmonic AC and static DC distributed electrostatic actuation are investigated. A single degree of freedom model obtained by application of the Galerkin decomposition method to the Euler-Bernoulli shallow arch equation is used for the studies. The bistable arch possessing an asymmetric double-well potential is vulnerable to homoclinic chaos at certain values of parameters. We have implemented the Melnikov's method to derive a necessary condition for the initiation of chaos in this type of resonators. Moreover, we have used a heuristic chaos prediction criterion, together with an analytical... 

The lateral response of a single degree of freedom structural system containing a rigid circular cylindrical liquid tank under harmonic and earthquake excitations at a 1:2 autoparametric resonance case is considered. The governing nonlinear differential equations of motion for the combined system are solved by means of a multiple scales method considering the first three liquid sloshing modes (1,1), (0,1), and (2,1), under horizontal excitation. The fixed points of the gyroscopic type of governing differential equations are determined and their stability is investigated employing the perturbation method. The obtained results reveal an increase in the stability region for a single-mode... 

In this paper, a continuum–atomistic multi-scale method is presented in modeling the nonlinear behavior of nano-materials under large deformation. In order to identify an appropriate strain energy function for crystalline nano-structures with different percentages of spherical voids, the hyperelastic method is employed for specimen whose behavior is determined based on the molecular dynamics analyses. In the atomistic level, the EAM many-body potential is employed to model the interactions between the atoms of Al RVEs. The atomistic strain energy density curves and surfaces are generated by applying the uniaxial, biaxial and simple shear deformations to the boundaries of RVEs. The material... 

In this paper, the nonlinear oscillation of a pendulum wrapping and unwrapping on two cylindrical bases is studied, and an analytical solution is obtained using the multiple scales method. The equation of motion is derived based on an energy conservation technique. By applying the perturbation method to the differential equation, the nonlinear natural frequency of the system is calculated, along with its time response. Analytical results are compared with numerical findings and good agreement is found. The effect of large amplitude and radius of cylinders on system frequency is evaluated. The results indicate that as the radius of the cylinder increases, the system frequency is increased.... 

In this paper, nonlinear oscillation of a pendulum wrapping and unwrapping around two cylindrical bases is studied and an analytical solution is obtained using multiple scales method. Equations of motion are derived based on energy conservation technique. Applying perturbation method on the equations, nonlinear natural frequency of the system is calculated along with its time response. Analytical results are compared with numerical findings and good agreement is found. Effect of nonlinearity due to large amplitude and radius of cylinders on the system frequency is evaluated. Results indicate that as the radius of cylinder is increased, nonlinear frequency is enhanced. Initial amplitude plays... 

The effect of substrate thickness and its Debye temperature on the bolometric response of the freestanding-membrane type of superconductor transition-edge detectors is investigated. The investigation is based on the calculation of the variation of the specific heat per unit volume and the heat conductivity using the finite-size scaling method for different Debye temperatures and micron size thickness of substrate. We also calculated the heat capacity and time constant for various materials with Debye temperatures in the range of 600-1400 K. The calculated results are compared with previously reported response values obtained theoretically and experimentally for the thermal-based infrared... 

This paper presents the vibration and stability analyses of an unbalanced rotor mounted on high-static-low-dynamic-stiffness supports. The stiffness of the supports is modeled as symmetric of cubic order. Then a second-order multiple scales method is used for studying the primary resonance of the system. The types of singular points are investigated and phase-plane of the system is plotted using analytical and numerical methods. The difference between analytical and numerical solutions is less than 2 percent. © 2017 Elsevier Masson SAS