Vol. 3, No. 3 (2019): Regular Issue

In this paper, the size-dependent effect on the free vibration analysis of cylindrical piezoelectric nano-shell with arbitrary boundary conditions is studied. The cylindrical piezoelectric nano-shell is modeled based on Gurtin-Murdoch surface elasticity theory and the linear Von-Karman- Donnell’s strain-displacement. Also, the assumed mode method is used for changing the partial differential equations into ordinary differential equations. A variety of new vibration results including frequencies and mode shapes for piezoelectric cylindrical nano-shell with non-classical restraints as well as different material parameters are presented, which may serve as benchmark solution for future researches. The convergence, accuracy and reliability of the current formulation are validated by comparisons with existing experimental and numerical results published in the literature, with excellent agreements achieved.

In this paper, periodic motions in a periodically forced, damped double pendulum are analytically predicted through a discrete implicit mapping method. The implicit mapping is developed from discretization of the corresponding differential equation. From the mapping structures, period-1 to period-4 motions are obtained and the corresponding stability and bifurcation analysis of the periodic motions are completed through eigenvalue analysis. Using the finite Fourier series, nonlinear frequency-amplitude characteristics of period-1 to period-4 motions are presented. Numerical simulations of period motions in the double pendulum is completed, and the initial conditions are obtained from the analytical predictions. The harmonic amplitude spectrums are also presented for showing harmonic term effects on periodic motions.

The study of dynamical systems chaotic behavior and their routes to chaos was in particular attention at recent years. These phenomena study in non-smooth dynamical system is of the special scientists’ interest. We apply the Continuous Wavelet Transform (hereinafter - CWT) to investigate the intermittent route to chaos, boundary crisis, and transitional regimes under quasi-periodic route to chaos in strongly nonlinear non-smooth discontinuous 2-DOF vibroimpact system. We show that CWT application is very useful to observe the intermittency, chaos and transitional regimes. It allows one to detect and to determine these phenomena with great confidence, reliability, and clearness.

We demonstrate that the tail dependence should always be taken into account as a proxy for systematic risk of loss for investments. We provide the clear statistical evidence of that the structure of investment portfolios on a regulated market should be adjusted to the price of gold. Our finding suggests that the active bartering of oil for goods would prevent collapsing the national market facing the international sanctions.

Existing fault locating algorithms for T-splice transmission lines are hugely susceptible to traveling wave velocity. To address this issue, this paper presents a new fault locating algorithm for T-splice transmission lines based on the initial voltage backward traveling wave. In this algorithm, the three-terminal busbar initial voltage backward traveling waves are collected and S-transform is implemented to analyze the ratio of voltage amplitude and construct discriminant of the faulted transmission line. Once the faulted branch is detected, three-terminal line is converted into two-terminal line. The fault range locating algorithm can be developed by using line parameters and the time initial traveling wave used to reach the three-terminal busbar. The algorithm making it less susceptible to swing amid the uncertainty of traveling wave velocity and overcomes the shortcomings of the unreliability of traditional method for detecting the faulted line near T node. Simulation results demonstrate high accuracy of the algorithm, which is less susceptible to the changes in fault types, transitional resistances, initial fault angles and other factors.

This paper is concerned with a review of the size effect involved in the similar experimental models. The review covers in many fields, including size effect in microscopic system structure such as the study of the micro-beam mode, civil structure and mechanical structure such as the study of mechanical properties, the application of dynamic similarity model design in large structures. This is followed by the influencing factors of size effect and methods of predicting fatigue strength and fatigue life of large structures. Analysis of formulas for predicting the stress and strain, stress field near notched specimens used in large structures are established. Finally, the formulas for predicting the size factor and fatigue life of large structures about size effect are summarized and prospected.

In this paper, a global analysis of equilibrium stability in 1-dimensional nonlinear dynamical systems is presented. The classification of dynamical systems is given first, and infinite-equilibrium systems are defined. The 1-dimensional dynamical systems with a single equilibrium are discussed. The 1-dimensional dynamical systems with two and three equilibriums are discussed. Simple and higher-order equilibriums in 1-dimensional dynamical systems are analyzed, and a higherorder equilibrium is an equilibrium with higher-order singularity. The flows of equilibriums in 1-dimensional systems in phase space are illustrated for a better understanding of the global stability of equilibriums in 1-dimensional dynamical systems.

In the underlying work, a general theorem for the derivation of the normal form of N-dimensional systems reduced to its center manifold is proposed and proved. In the present addendum, some observations regarding the conditions of the theorem are added. The corrections and the additions not only don’t affect the value of the best part of the published article but also enhance the value of the original manuscript.