Periodic Response and Chaos in Nonlinear Systems with Parametric Excitation and Time Delay

In this paper, the periodic motions of a nonlinear system with quadratic,cubic, and parametrically excited stiffness terms and with time-delayterms are obtained by the incremental harmonic balance (IHB) method. Theelements of the Jacobian matrix and residue vector arising in the IHBformulation are derived in closed form. A mechanism model representingthe one-mode oscillation of beams and plates is considered as anexample. A path-following algorithm with an arc-length parametriccontinuation procedure is used to obtain the response diagrams. Thesystem also exhibits chaotic motion through a cascade of period-doublingbifurcations, which is characterized by phase planes, Poincaré sectionsand Lyapunov exponents. The interpolated cell mapping (ICM) procedure isused to obtain the initial condition map corresponding to multiplesteady-state solutions.     

双稳态压电悬臂梁发电性能分析

利用增量谐波平衡法(IHB)对双稳态压电发电系统的发电性能进行了研究.首先通过与龙格-库塔法(R-K)数值计算的结果相对比,证明IHB法解的有效性;其次利用IHB法分别计算了磁化强度不同时双稳态压电发电系统的电压幅频响应曲线及不同的负载电阻下的发电功率,得出双稳态压电发电系统的电压幅频响应存在解的跳跃现象,并且当磁场强度增大时,电压幅频曲线向右偏移,大幅运动的响应频带变宽,最大幅值变大.另外,分析了系统电阻匹配问题,只有选择合适的电阻值时,发电功率才能达到最大;最后与线性压电发电系统相比,得到双稳态压电发电系统在低频宽带下能产生较高的发电功率.     

Synthesis and cytotoxicity of two novel alcohols based on a benzo[c]phenanthrene moiety

Synthetically, 1-(benzo[c]phenanthren-2-yl)ethanol and 1-(benzo[c]phenanthren-2-yl)-3-phenylpropane-1,3-diol were successfully obtained from 2-acetylbenzo[c]phenanthrene and methyl benzo[c]phenanthrene-2-carboxylate, respectively, and fully characterized. The desired compounds were purified by silica gel column chromatography, and their structures were characterized by melting points, ¹H NMR, ¹³C NMR, and mass spectroscopy. Next, the in vitro cytotoxicity of the new polyaromatic alcohols was evaluated against two human carcinoma cell lines (Hep-2 and Caco-2) using the 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) assay method. Consequently, the 1,3-diol derivative displayed the highest cytotoxicity against both cell lines (IC₅₀ = 0.7 and 0.6 μg/mL). This allowed us to infer that the effect of intramolecular hydrogen bond seems to be important for the cytotoxic activity.     

NONLINEAR DYNAMIC INSTABILITY OF DOUBLE-WALLED CARBON NANOTUBES UNDER PERIODIC EXCITATION

A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Taking the geometric nonlinearity of structure deformation, the effects of van der Waals forces as well as the non- coaxial curvature of each nested tube into account, the nonlinear parametric vibration governing equations are derived. Numerical results indicate that the double-walled nanotube （DWNT） can be considered as a single column when the van der Waals forces are sufficiently strong. The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes.     

Non-linear dynamic model of a fluid-conveying pipe undergoing overall motions

In this study, the investigation of the three-dimensional nonlinear dynamics of a fluid-conveying pipe undergoing overall motions is carried out. Considering the effect of the internal and external fluids, and using a non-Cartesian variable along with two Cartesian variables to describe the elastic deformation, the nonlinear differential equations are derived based on Kane’s equation in combination with the Ritz method. An alternative approach to the existing methods utilizing Newtonian balance equations or Hamilton’s principle is thus provided. The equations of motion are linearized in the neighborhood of the equilibrium position to implement the multimode linear stability analysis. In addition, the time histories for the displacements are obtained with the help of the Incremental Harmonic Balance (IHB) method. The validity of the new modelling is substantiated by comparing the model and results with those proposed by Païdoussis (1998).     

Non-linear vibration of bimaterial magneto-elastic cantilever beam with thermal loading

Formulas and numerical results are studied for the transient vibration and dynamic instability of a bimaterial magneto-elastic cantilever beam which is subjected to alternating magnetic field and thermal loading. Materials are assumed isotropic, and the physical properties are assumed to have unique values in each layer. The governing equation of motion is derived by the extended Hamilton's principle, in which the damping factor, the electromagnetic force, the electromagnetic torque, and the thermal load are considered. The solution of thermal effect is obtained by superposing certain fundamental linear elastic stress states which are compatible with the Euler–Bernoulli beam theory. The axial stresses results are found to be in good agreement with some known numerical solutions. Using Galerkin's method, the equation of motion is reduced to a time-dependent Mathieu equation. The numerical results of the regions of dynamic instability are determined by the incremental harmonic balance (IHB) method, and the transient vibratory behaviors are presented by the fourth-order Runge–Kutta method. The results show that the responses of the transient vibration and dynamic instability of the system are influenced by the magnetic field, the thickness ratio, the excitation frequency, but not by the temperature increase in this study.     

Stability analysis of the active control system with time delay using IHB method

In this paper, the incremental harmonic balance method is employed to solve the periodic solution that a vibration active control system with double time delays generates, and the stability analysis of which is achieved by the Poincare theorem. The system stability regions can be obtained in view of time delay and feedback gain, the variation of which is also studied. It turns out that along with the increase of time delay, the active control system is not always from stable to unstable, and the system can be from stable to unstable state, whereas the system can be from unstable to stable state. The extent that the two times delays impact on the system stability region is mainly related to the relative magnitude of the two feedback gains. The system can maintain the stable state under the condition of the well-matched feedback gains. The results can provide evidence to design the control strategy of time-delayed feedback.     

Molecular Tailoring Approach for the Estimation of Intramolecular Hydrogen Bond Energy

Hydrogen bonds (HBs) play a crucial role in many physicochemical and biological processes. Theoretical methods can reliably estimate the intermolecular HB energies. However, the methods for the quantification of intramolecular HB (IHB) energy available in the literature are mostly empirical or indirect and limited only to evaluating the energy of a single HB. During the past decade, the authors have developed a direct procedure for the IHB energy estimation based on the molecular tailoring approach (MTA), a fragmentation method. This MTA-based method can yield a reliable estimate of individual IHB energy in a system containing multiple H-bonds. After explaining and illustrating the methodology of MTA, we present its use for the IHB energy estimation in molecules and clusters. We also discuss the use of this method by other researchers as a standard, state-of-the-art method for estimating IHB energy as well as those of other noncovalent interactions.