This study applies the numerical inversion of Laplace transform methods to study the piezoelectric dynamic fracture problem, recalculating Chen and Karihaloo's [1] analysis on the transient response of a impermeable crack subjected to anti-plane mechanical and in-plane electric impacts. Three numerical methods were adopted for calculating the dynamic stress intensity factor: Durbin method, Zhao method 1, and Zhao method 2. The results obtained were more accurate than the results in Chen and Karihaloo's [1] study. Through the calculation, this study presents a better range of parameters for the above three methods, and compares the advantages and disadvantages of each method in detail.

In this study the Maximum Likelihood Estimator is utilized to identify the characteristics of failure of class-H insulation by considering accelerated life test data under censored situations from Nelson. The hazard rate function is considered in terms of the reliability, h(R), so-called AE model. The AE model is used to model the failures which are expressed as the serial connection between three modes, namely the turn, phase, and ground. This is the so-called competing failure. The main concern in the present investigation relates to the characteristic of changes in cumulative damage with temperature. The characteristic of the damage process basically change, with less capability of cumulation. The failure tends to be unpredictable in a constant hazard rate situation in much higher temperature environments. The parameters of the model are related to the temperature and follow the Arrhenius law. The numerical results indicate that the AE model is well fitted to the data and gives more information to identify the failure modes with fewer parameters. This is better than the using Weibull distribution with both parameters varied with temperature. According to the predicted lifetime, the turn needs to be rearranged primarily, followed by the phase. The ground mode only has influence on the failure at much higher temperatures.

The Lie symmetry and Hojman conserved quantity of Lagrange equations for a weakly nonholonomic system and its first-degree approximate holonomic system are studied. The differential equations of motion for the system are established. Under the special infinitesimal transformations of group in which the time is invariable, the definition of the Lie symmetry for the weakly nonholonomic system and its first-degree approximate holonomic system are given, and the exact and approximate Hojman conserved quantities deduced directly from the Lie symmetry are obtained. Finally, an example is given to study the exact and approximate Hojman conserved quantity for the system.

Concentration of a diffusing substance in a medium was derived in various cases of uni-dimensional diffusion, including in a semi-infinite medium and a plate-shaped medium. Multi-dimensional diffusion involves boundary conditions in each coordinate direction. The algorithm dealing with uni-dimensional case becomes very complicated in multi-dimensional cases. This study proposes an algorithm, which is called the complementary method, that combines complementary functions of the normalized solution in uni-dimensional diffusion case by multiplication to solve those in various multi-dimensional diffusion cases with dramatically simplified mathematics. Besides, the complementary method is used to solve various kinds of boundary conditions for multi-dimensional diffusion.

The objective of this study is to develop a framework using nonlinear autoregressive model process with exogenous inputs (NARX) neural networks (NNs) to identify the dynamic hysteresis of high load capacity suspension systems. Here, a vertical excitation test is used to simulate various terrains at an oscillation frequency range from 0.1Hz to 10Hz by using NARX NNs. The model results are in good agreement with suspension component oscillation responses that manifest as variations in model order selection as the excitation frequency approaches 7Hz. Furthermore, mapping the models into generalized frequency response functions (GFRFs), elucidates any unanticipated couplings between surroundings and mechanical hysteresis within the suspension. The proposed approach's systematic design procedure is advantageous because it provides a cost-efficient method that achieves precise identification of online data.

In this paper, stress distribution of micro cantilever beams in the presence of a dielectric-layer is studied using an analytic method. The Modified Adomian Decomposition Method (MADM) is applied to obtain a semi-analytical solution for a distributed parameter model of the micro cantilever beam. The important parameters for designing and manufacturing micro-actuators such as shear force, bending moment and stress distribution along the cantilevers are computed for different values of the dielectric-layer parameter. The results of MADM are compared with the numerical results, and they found in good agreement. It is found that increase of the dielectric-layer parameter increases the dimensionless pull-in voltage, tip deflection, internal stress and bending moment of the micro cantilever actuators at the onset of pull-in instability.

Although the numerical properties of a step-by-step integration method can be evaluated based on the currently available techniques, there is still lack of a technique for evaluating its capability to capture dynamic loading. In this work, the amplitude error caused by the step discretization error is identified and the correlation between the relative amplitude error and relative step discretization error is analytically established. As a result, it is thoroughly confirmed that the asymptotic constant of the discretization error amplification factor for the displacement response to a cosine loading can be considered as an indicator of the capability to capture dynamic loading for a general step-by-step integration method.

The Lie group transformation method is applied for solving the problem of mixed convection flow with mass transfer over a permeable stretching surface with Soret and Dufour effects. The application of Lie group method reduces the number of independent variables by one and consequently the system of governing partial differential equations reduces to a system of ordinary differential equations with appropriate boundary conditions. Further, the reduced non-linear ordinary differential equations are solved numerically by using the shooting method. The effects of various parameters governing the flow and heat transfer are shown through graphs and discussed. Our aim is to detect new similarity variables which transform our system of partial differential equations to a system of ordinary differential equations. In this work a special attention is given to investigate the effect of the Soret and Dufour numbers on the velocity, temperature and concentration fields above the sheet.

This study adopted the distinct element method (DEM) to explore the key influencing factors on the variations of lateral earth pressure, including packing type, interior friction angle, particle stiffness and particle size. The reference parameters for the DEM model were retrieved from direct shear tests of a rod assembly. Based on the reference parameters, the evolution of lateral earth pressure is further simulated, and a parametric study was conducted. The results showed that: (1) the analysis model could effectively capture the variation of lateral earth pressure under both active and passive conditions, and the simulated failure patterns were consistent with those from the sandbox tests; (2) the greater interior friction angle ϕinterior decreased the active coefficient Ka and increased the passive coefficient Kp; (3) increasing particle stiffness decreased the active coefficient Ka and increased the passive coefficient Kp; (4) larger particle sizes led to a larger active coefficient Ka and a smaller passive coefficient Kp; and (5) when the particle assembly was arranged in order, its lateral pressure was much larger than that of the randomly packed assembly.

The influences of acoustic excitation on the velocity field and mixing characteristic of a jet in cross-flow were investigated in a wind tunnel. The acoustic excitation waves at resonance Strouhal number were generated by a loudspeaker. The time-averaged velocity field and streamlines of the excited elevated transverse jet in the symmetry plane were measured by a high-speed particle image velocimetry. The visual penetration height and spread width were obtained by using an image processing technique. The dispersion characteristics were obtained from the tracer-gas concentration measurement. The results showed that the streamline pattern of the non-excited transverse jet was significantly modified by the acoustic excitation—the bent streamlines evolved from the jet exit escalated and the vortex rings in the jet and tube wakes and the recirculation bubble in the jet wake disappeared. The time-averaged velocity distributions revealed that the excited transverse jet produces large momentum in the up-shooting direction so that the velocity trajectories were located at levels higher than those of the non-excited one. The mixing characteristics, which include the visual penetration height, spread width, and dispersion, were drastically improved by the acoustic excitation due to the changes in the flow structures. The excited transverse jet characterized at larger jet-to-crossflow momentum flux ratios presented larger improvement in the mixing characteristics than at lower jet-to-crossflow momentum flux ratios.

The nonlinear characteristics of a simply-supported three-layer circular piezoelectric plate-like power harvester near resonance are examined in the paper, where the energy-scavenging structure consists of two properly poled piezoceramic layers separated by a central metallic layer. The structure is subjected to a uniform harmonic pressure on the upper surface. Nonlinear effects of large deflection near resonance to induce the incidental in-plane extension are considered. Results on output powers are presented, which exhibit multi-valuedness and jump phenomena.

The effects of boundary slip on the stability of finite miscible/immiscible liquid-liquid stratified microchannel flow were investigated. In this approach, the boundary slip was considered by Navier slip assumption and the finite-miscible liquid-liquid interface was modeled by double film model. The stability of the flow was studied by the small disturbance theory. The results indicated that the effects of boundary slip on the instability of finite miscible stratified microchannel flow with different viscosity ratio, interface location and the property of interface (i.e. thickness and viscosity distribution of mixed layer) are distinct and complex. The effect intensity of upper and lower boundary slip on flow stability is determined by viscosity ratio, interface structure (different Ns) and film thickness. When the interface changes from the channel center to the wall, the critical Re number is enhanced by boundary slip and especially markedly near the critical line and after across the critical line it suddenly decreases to a small value (even to 424). The flow stability always increased by boundary slip.