Occurrence Of Internal Resonance Research Articles

Nonlinear Vibration and Stability Analysis of Thermally Postbuckled Double-Layered Graphene Sheet under 1:1 and 3:1 Internal Resonance

In the present research, vibration behavior is presented for a thermally postbuckled double layered graphene sheet (DLGS). The DLGS is modeled as a nonlocal orthotropic plate and contains small-scale effects. The formulations are based on Kirchhoff’s plate theory and nonlinearity of von Karman type is considered in strain–displacement relations. The thermal effects, van der Waals forces between layers and chirality are also included, and some of the material properties are assumed to be temperature-dependent. A coupled system of equations is derived and a new semi-analytical solution is obtained using multiple time-scale methods. The effects of variation of small-scale parameter on the natural frequencies, deflections and response curve of DLGS are analyzed, and the numerical results are obtained from the nonlocal plate model; also, molecular dynamics (MD) simulations are used to investigate different vibration behaviors of DLGS and calibration of the small-scale coefficient. Numerical results are compared with those of similar researches. Effects of various parameters on the postbuckled vibration of DLGS in thermal environments such as scale parameter, environmental damping, length and thermal load are presented. The stability and occurrence of internal resonance between vibration modes around a stable buckled configuration are investigated.

Nonlinear vibration analysis of a novel moving mass flight vehicle

In view of the control authority and configuration, a novel configuration of moving mass with large mass ratio is proposed and its nonlinear dynamics is investigated. The coupling dynamic equations between angle of attack and deflection of moving mass are established. An analysis of these equations indicates that the moving mass with large mass ratio will result in dynamic equations having nonlinearities and the occurrence of internal resonances in such system. Multiple-scale method is used in the analysis of the primary resonances of the external excitation and internal resonances. The steady-state solutions and the effects of different parameters of moving mass on the frequency response have been investigated. Numerical results show that the proposed system is of hardening spring characteristic when excitation frequency is near to different natural frequencies. The mass ratio and the relative position also lead to the occurrence of a jump phenomenon and multi-valued regions. The reasonable design for parameters of the moving mass system can ensure stability and high performance of flight vehicle.

Internal resonance vibration induced by nonlinearity of primary suspension system in high-speed vehicle system

This paper studies the phenomenon of internal resonance in high-speed vehicle system under high frequency periodic excitations. A numerical model of the vehicle system, taking into consideration the dynamic effects of the primary suspension system and the flexibility of the car-body, is established for the study. An approximate approach incorporating the incremental harmonic balance method with frequency response function is adopted to solve the dynamic responses of the vehicle system in frequency domain. Numerical results show that internal resonance vibration in the vehicle system may occur with certain combinations of design parameters of the vehicle system. The vibration of the car-body and the primary suspension system are significantly amplified with energy transmitted between the natural modes of the car-body and the primary suspension system. Parametric studies on the internal resonance are further explored. Results show that the nonlinearity of the primary suspension spring and the modal damping ratio of the vehicle system play very important roles to the occurrence of internal resonance.

Internal resonance of a flexible rotor supported by a magnetic bearing

Magnetic bearings can support rotating rotors without any contacts. So itispossible torotatea rotor at extremely high rotational speed. On the other hand, they can easily show elastic deformation with nonlinear oscillation, which is complicated and difficult to deal with. This study investigates nonlinear coupling of oscillation modes appearing in such a flexible rotor system with a magnetic bearing, by considering both the nonlinearity of the electromagnetic force and the continuousness of the rotor. First, an essential model of a rotor with an elastic shaft supported by a magnetic bearing was introduced. The numerical results indicate occurrence of internal resonance caused by the nonlinear coupling of the modes, if the ratio of their natural frequencies is 1 to 3 Experiments were also carried out and obtained results showed qualitative accordance to the numerical results.

Effect of an Additional Mass on Nonlinear Resonance of a Beam Levitated Over High-Tc Superconducting Bulks

This paper deals with effect of an additional mass on nonlinear resonance in a high-Tc superconducting magnetic levitation. The concept of an additional mass can be found in studies of various machines. In this research, using an elastic beam levitated above high-Tc superconductors, occurrence of internal resonance between the beam's two modes was investigated with respect to the mass position theoretically and experimentally. As a result, the beam's natural frequencies can change by the additional mass position. Accordingly, the frequency ratio between the 1st mode and the 3rd mode can be nearly 1 to 2 for a certain mass position. In that condition internal resonance between both the modes can occur by nonlinearity of the electromagnetic force. Its mechanism was explained theoretically, and its features were clarified by numerical analysis and confirmed by experiments.

Subharmonic Resonance of a Rotor Supported by a High-Tc Superconductor

This paper investigates subharmonic resonance, one of typical nonlinear phenomena, appearing in a high-Tc superconducting bearing system. In such low-damping systems having noncontact support by magnetic force, complex dynamical behaviors can be caused by nonlinearity of the magnetic force. In this study, the magnetic rotor, supported by a high-Tc superconducting bulk, is bound to a D.C. motor with a universal joint. According to the equation of motion, caused by the quadratic term of the levitation force, subharmonic resonance of the rotor can occur when the rotor rotates, not at its critical speed, but at twice its critical speed. This analytical prediction was confirmed by our numerical and experimental results. Additionally, our study also found occurrence of internal resonance induced by this subharmonic resonance. These findings beyond linear regimes can be important for the design of high-Tc superconducting levitation systems.

Experimental Investigation on the Occurrence of Internal Resonances in a Clamped-Clamped Beam

Experimental Investigation on the Occurrence of Internal Resonances in a Clamped-Clamped Beam

Shielding of wire segments and loops in electric circuits by spherical shells

The susceptibility of an electric circuit to electromagnetic radiation incident on it is analyzed by the application of Lorentz's reciprocity relation. An equivalent Thevenin or Norton representation of the circuit serves to determine the induced signals quantitatively. The effect of a (multilayered) spherical shield on the performance of elementary parts of the circuit, namely, a short wire segment and a loop placed at the center of the shield, is investigated. The corresponding shielding performance is expressed as the reduction of the induced source strength in the equivalent networks. Numerical results are presented in a frequency range that includes the occurrence of internal resonances in the shielding structure. >