The Noether symmetry and the conserved quantity for a Hamiltonian system on time scales are proposed and studied in this paper. The Hamilton principle on time scales is established, and corresponding Hamilton canonical equations are deduced. Based upon the invariance of the Hamilton action on time scales under the infinitesimal transformations of a group, the Noether theorem for the Hamiltonian system on time scales is established. The proof of the theorem is composed of two steps. First, we prove the Noether theorem under the infinitesimal transformations of a special one-parameter group without varying the time. Second using the technique of time-re-parameterization, we obtain the Noether theorem in its general form. The Noether-type conserved quantities for Hamiltonian system in both the classical and the discrete cases are given. At the end of the paper, two examples are given to illustrate the application of the theorem.

For axially moving beams with opening cracks, by meeans of the continuous equivalent stiffness model, the crack effect was introduced into the governing equations of their transversal vibration. Using the transfer matrix method, characteristic equations were derived to obtain the vibration frequencies. The numerical solutions of the first two frequencies of the beams were obtained while the crack and axially moving parameters change continuously. The effects of the crack and axially moving parameters on the vibration frequencies were investigated. The results showed that crack depth and axial moving parameters impose coupling effect on the first two frequencies rather than influence them independently. Deeper crack leads to faster frequency attenuation caused by axial velocity, while faster axial moving makes the frequency attenuation more significant caused by the cracks. Compared with the second frequency, such effects are more significant for the first frequency.

The shale oil gas extraction is just beginning in China. Many of fundamental theories and key scientific (mechanical) problems should be clarified and addressed. In this paper, the whole process of shale oil gas extraction was naturally divided into four interrelated sections and discussed in detail: the mechanical characteristics of engineering geology and prediction theory of shale for finding shale oil gas; multiplicity coupling safety and quality well drilling theory for exposing to shale oil gas; dynamic random crack control mechanism for the shale layers and a novel concept hydraulic fracturing theory for gas release; multiscale permeability characteristic and production theory for the shale oil gas transfer. In order to achieve the goal of effective and sustainable extraction, a novel research concept of compatibility between the flow capacity in shale and the gas supply from matrixes was proposed to avoid the “no gas supply” phenomena. Solving these key fundamental scientific (mechanical) problems could lay a reliable foundation for the efficient extraction of shale oil gas, which is both theoretically and practically significant.

The time reversal imaging technology has the merits of accurate positioning and simple operation, in this paper it had been applied to the detection of damage of concrete structures. The transfer matrix of ultrasonic transmission was constructed by extracting transmitted signals from transducer arrays and scattered signals from damages, and then it underwent singular value decomposition and the singular vectors containing information about the damage were obtained. The damages of concrete structure were imaged by MUSIC (multiple signal classification) algorithm based on the data from simulations and experiments respectively, a precise positioning of damage was obtained, and a comparison with the result from migration imaging was made. This work explored the feasibility of employing the time reversal imaging technology to detect the internal damage of concrete structures in real situation. It also provided a theoretical reference for nondestructive testing engineers to analyze the internal defects of concrete structures qualitatively or quantitatively.

In this paper, the analytical solution of a bending anisotropic rectangular thin plate with four free edges on the transversely isotropic elastic half-space was derived. The governing equation of bending plate on the elastic foundation was combined with the deformation compatibility equation of the plate and foundation. The latter was based on static integral transform solution of the displacement on the transversely isotropic elastic half-space loaded with arbitrary vertical load. According to symmetrical decomposition, the analytical solution was obtained through triangular series method. The analytical expressions of the foundation reaction force, deflection and the internal force of the plate were derived. The proposed analytical solution overcomes the numerical limitations, and avoids the assumption of the Winkler foundation model or double parameter foundation model. The achieved internal force and plate foundation pressure are more reasonable in practical engineering. The results are consistent with the solution in open literatures, which proves the feasibility of the proposed method.

Paper jam is one of the common fault phenomena in paper-feeding mechanism including printers and copiers. It also commonly exists in all kinds of the transmission systems. Force and motion states need to be clarified to solve the problem. Paper-feeding mechanism was adopted to establish the computational model of paper in the roller. The governing equation of paper control was also derived. Theoretical deduction shows that the material and size of the mechanism have influences over paper jam. Meanwhile, simulation model of paper-feeding mechanism was built in dynamic analysis software RecurDyn. Running state of mechanism was studied and effects of multiple factors on paper jam were also analyzed. Effect laws of friction coefficient, wheel speed, paper thickness and modulus effect on the motion were obtained. The numerical simulation was validated by comparing with experimental results of torque. The results show that, paper motion is mainly influenced by material and size of the mechanism during the roller paper-holding stage; when the paper moves out of rollers, it is substantially influenced by friction and contact force. Paper jam is prone to occur in the mechanism, with the decrease of roller speed, as well as the increase of friction coefficient, the modulus and thickness of the paper. Conclusions drawn in the paper potentially provides guidance for the solution of paper jam fault.

In order to study the shear lag phenomenon in RC core tube and RC core tube with mixed concealed bracing, a parametric study using nonlinear finite element analysis was carried out. The influences of the corner columns, coupling beams, reinforcement distribution and concealed bracing on shear lag effect of RC core tube were discussed. The degree of the shear lag effect in RC core tube and RC core tube with mixed concealed bracing was compared. The results indicate that compared with RC core tube, the load-bearing capacity and deformation capacity of RC core tube with mixed concealed bracing have been improved, and its shear lag effect has been greatly reduced.

The secondary atomization plays a key role in increasing both evaporation and mixing rates in a variety of engineering applications. The phenomenon was studied by numerical simulation based on SIMPLE scheme. The VOF method, coupled with the Level-Set method, was used to capture the boundary; the adaptive mesh strategy was taken to balance the demands for raising accuracy of calculation and for reducing computational expenditures. In the case of low Oh number, when Oh < 0.1, four typical regimes of droplet breakup are observed in the simulation; and the comparatively more complicated the second and the third modes had undergone detailed analysis and comparison. The condition for the occurance of these modes and the pertinent features were obtained. Finally, comparison between these results and those of past experiments were made; in most part of significant aspects the two have very good agreement.

Fretting damage is a common phenomenon in engineering. It can cause fastening components loose, reduce fatigue life and enhance corrosion. Fretting experiments are generally time-consuming and difficult to conduct direct observation of damages. Computer simulation of fretting is becoming more and more popular in recent years. In this article, we shall give a review on some methods relevant for simulation and analysis of fretting wear and fretting fatigue life. For fretting wear simulation, Archard model is realized in finite element calculation together with suitable multilayer nodes update method. To estimate fretting fatigue life, multi-axial fatigue criteria are often used. Especially the so called Smith-Watson-Topper parameter can be easily implemented in simulation of fatigue crack initiation and life estimations. However, coupled calculation of fretting wear and fretting fatigue is still very time consuming, in particularly in three dimensions, although both experiments and calculations have shown clearly that fretting wear can have rather strong influence on the fatigue crack initiation and life estimation. To demonstrate this, a two dimensional example is presented. The results indicate that fatigue life estimation without considering the effect on fretting wear could be several magnitudes smaller than the life with fretting wear.

In this paper the optimal nonholonomic motion planning of the free-floating space robot system with two arms is solved using adaptive dynamic programming. Based on the principle of the translational and rotational momentum conservations in the multi-body dynamics theorem, the nonholonomic motion equations of the bi-arm space robot system are established, which are then transferred into the state equations of the optimal control for the system. In this way, the nonholonomic motion planning of the robot system is translated into the solution of a canonical nonlinear control problem. Based on the network of adaptive dynamic programming, the performance index function can be approximated within the neural network, and the state variables can be solved using Runge-Kutta integration algorithm. In addition, we provide an explicit expression of the utility function which is suitable for this kind of problem. The objective of the optimal control of nonholonomic motion planning is achieved that the investigated bi-arm space robot no longer move once it reaches the desired location. The effectiveness of optimal control of nonholonomic motion planning for free-floating space robot system using ADP is verified by the numerical simulation experiments.

Firstly, a fractional gene and a fractional increment are put forward and the definitions and properties of fractional derivative and integral with fractional gene are given. Secondly, the exchanging relationship between the isochronous variation and fractional derivative with the fractional gene is proved. Thirdly, the fractional Hamilton principles and fractional differential equations with fractional gene for holonomic dynamical systems are presented. Further, the fractional circulatory integrals of the systems are obtained and the fractional Routh’s equations with fractional gene are derived. Finally, two examples are given. This research indicates that the fractional differential equations can become the conventional differential equations with fractional gene, and the general methods for solving the conventional differential equations are also applicable for solving the fractional differential equations.

The cyclic integral and Routh method of reduction for the dynamic system based on exponential Lagrangians and power law Lagrangians were studied. Firstly, the cyclic coordinate was defined, and the form of cyclic integral were obtained by using cyclic coordinates and Lagrange equations of the system with non-standard Lagrangians. Then, the Routh method of reduction was extended, the Routh equations for the dynamic system with non-standard Lagrangians were established. Two examples were given to illustrate the application of the results.

Single angle members have been used for over a century and a strength reduction method is recommended by Chinese code for design of single angle compression member. Researches show that the method of Chinese code is questionable, especially when applied to unequal leg angle connected by short leg. In this study, a test of 16 specimens was carried out, and with 15 existing data points by former researchers collected, the total number of effective test data reaches 31; and a numerical model by the finite element method was built for single angle compression member to investigate the effects of parameters, such as initial eccentricity, residual stress, initial bending as well as the width of gusset plate, on the bearing capacity; in the end, a design formula for evaluating the bearing capacity of single angle compression member was recommended. The formula fits test data well in contrast with methods of other codes.