Cauchy problem for a substantially loaded hyperbolic equation

В работе проводится исследование задачи Коши для существенно нагруженного уравнения колебания одномерной струны. Приводятся примеры характеристических многообразий, для которых задача Коши поставлена корректно, а также нехарактеристических многообразий, для которых задача Коши поставлено некорректно. In this work, we study the Cauchy problem for a substantially loaded vibration equation of a one-dimensional string. Examples are given of characteristic manifolds for which the Cauchy problem is posed correctly, as well as non-characteristic manifolds for which the Cauchy problem is posed incorrectly.

Modeling and analytical methods for a mounting system with double stage isolation

A calculation method for obtaining the displacements and rigid body modes of a Powertrain Mounting System (PMS) with double stage isolation is proposed in this paper. Firstly, the PMS with double stage isolation is modeled as a 12 Degree of Freedoms (DOFs) model, which includes six DOFs for the powertrain and the subframe respectively. The mounts are simplified as a three-dimensional spring along each axis of its Local Mount Coordinate System (LMCS), which takes the non-linear relation of the force versus the displacement of each spring into account. Secondly, the quasi-static equilibrium equation and the free vibration equation as well as the forced vibration equation of the proposed model are derived and the solutions of equations are presented. Then, the calculation and solution methods are validated by the simulation results. The differences of rigid body modes and displacements of the powertrain between single and double stage isolation are estimated, which demonstrates that the proposed model is more accurate, especially when powertrain mounts are stiff. Also, the effect of locations for powertrain mounts on car body is investigated, which shows that is beneficial for motion control of powertrain.

Investigation on the Nonlinear Vibration Characteristics of Current-Carrying Crescent Iced Conductors under Aerodynamic Forces, Ampere’s Forces, and Forced Excitation Conditions

Aiming at the problem of nonlinear vibration of current-carrying iced conductors, the aerodynamic forces are introduced into the previous vibration equation of current-carrying conductors that only considered Ampere’s forces. At the same time, on this basis, a forced excitation load is further introduced to study the influence of dynamic wind on the nonlinear vibration characteristics of current-carrying iced conductors, and a new current-carrying iced conductors system under the combined action of Ampere’s forces, forced excitation, and aerodynamic forces has been established, and the improved theoretical modeling of current-carrying iced transmission lines made the model more in line with practical engineering. Firstly, the model of current-carrying iced conductors was established, and then the vibration equation of the model was derived. And the vibration equation was transformed into a finite dimensional ordinary differential equation by using the Galerkin method. The amplitude-frequency response functions of the nonlinear forced primary resonances and super-harmonic and subharmonic resonances of the system are derived by using the multiscale method. Through numerical calculation, the influence of current-carrying, spacing, wind velocity, tension, and excitation amplitude on the response amplitude when the primary resonance of the system appears is analyzed, and the difference between the two working conditions (considering the aerodynamic forces and without considering aerodynamic forces) is compared. The influence of the variation of current-carrying i on the response amplitude of super-harmonic and subharmonic resonances and the stability of the steady-state solution of forced primary resonance was analyzed. The results show that the response amplitude and the nonlinearilty of system under the action of aerodynamic forces are smaller and weaker than without the action of aerodynamic forces; the variation of line parameters has a certain influence on the response amplitude of conductor and the nonlinearity of system; the response amplitudes of the primary resonance, super-harmonic resonance, and subharmonic resonance increase with the increase in the excitation amplitudes, and the resonance peak is offset towards the negative value of the tuning parameter σ, showing the characteristics of soft spring, and the response amplitudes are accompanied by complex nonlinear dynamic behaviors such as the multivalue and jump phenomenon. The change of current-carrying i has an obvious effect on the nonlinearity of the system. The nonlinear and response amplitudes of the system are also enhanced with the increase in wind velocity. The stability of the system is judged when the primary resonance occurs, and it is found that the response amplitude shows synchronization and the out-of-step phenomenon with the change of tuning parameters. The research results obtained in this paper would help to further improve the theoretical modeling about current-carrying iced lines, and the research of line parameters can give a certain reference value to practical engineering, and it will have a positive effect on the safe operation of high-voltage transmission lines.

Identification of Rotor Crack Faults by Vibration Analysis

According to the vibration equation of the cracked rotor, the main vibration characteristics of the cracked rotor are summarized. On this basis, combined with the field diagnosis experience, a practical method of identifying the cracked rotor through vibration analysis is proposed. Furthermore, the proposed method is illustrated by three cases of rotor crack fault identification in the operation of steam turbine and boiler primary air fan. Successful diagnosis avoids the occurrence of potential major accidents.

A Modified Incremental Harmonic Balance Method for Periodic Forced Oscillations of a Dielectric Elastomer Membrane Undergoing In-Plane Deformation

Dielectric elastomers (DEs) are widely used in soft transducers with mechanical or electrical loads. DE devices are mainly used for applications under dynamic loads, such as, ocean wave generators, loudspeakers, oscillators, and artificial muscles. It is still a challenge to analytically solve the vibration equation of a DE transducer. For example, for a DE membrane undergoing stretching deformation that is studied in this paper, its vibration equation is highly nonlinear with high-order and fractional-order polynomials. Numerical integration (NI) methods or traditional harmonic balance (HB) methods were used in previous works, but the two methods have low efficiency for strong and complex nonlinearities, and it is difficult to improve the accuracy of the solution. In this work, a free-energy model is used to study the dynamic characteristics of a DE membrane undergoing in-plane deformation, which undergoes a combined load excited by mechanical compression and electric fields. To improve the calculation efficiency and accuracy, we employ a modified incremental harmonic balance (IHB) method based on the fast Fourier transform to solve the periodically-excited nonlinear dynamic equation of the DE membrane. Finally, results of the example verify that the modified IHB method is fast and accurate, and has a very good performance in solving a problem with high nonlinearities.

Dynamic Analysis of the Rod-Fastened Rotor Considering the Characteristics of Circumferential Tie Rods

The research on the dynamic performance of the rod-fastened rotor (RFR) has always been a hotspot. However, the structural complexity of RFR has brought significant challenges to the dynamic study of the RFR. The tie rods provide preload for the rotor shaft segment, while the coordinate deformation of the tie rods will occur during the process of vibration. In addition, the tie rods and the rotor shaft segments are structurally connected in parallel. These factors all will influence the dynamic performance of the RFR. In this paper, for a RFR system, the vibration equation of the RFR considering all factors of the tie rods is deduced in detail. The influence of various factors on the dynamic performance of the rotor is investigated. Results show that the preload directly affects the dynamic performance of the RFR system. When the preload is small, the tie rod has a larger influence on the natural frequencies of the rotor. However, when the preload force reaches a certain value, the influence of the tie rod on the natural frequencies of the rotor is almost negligible. The research results provide a theoretical reference for the understanding of and further research on RFR.

Linear Barycentric Rational Collocation Method for Beam Force Vibration Equation

The linear barycentric rational collocation method for beam force vibration equation is considered. The discrete beam force vibration equation is changed into the matrix forms. With the help of convergence rate of barycentric rational interpolation, both the convergence rates of space and time can be obtained at the same time. At last, some numerical examples are given to validate our theorem.