This study investigates the nonlinear steady-state responses of longitudinally traveling functionally graded material (FGM) plates immersed in liquid for the first time. The liquid is assumed to be ...ideal, and therefore it is inviscid, incompressible and irrotational. The velocity potential and Bernoulli’s equation are utilized to describe the dynamic liquid pressure. The large amplitude motion of the FGM plate is considered so that the present model includes both geometry and material nonlinearities. Based on the Newton’s second law, the equation of out-of-plane motion of the plate is obtained. The Galerkin method is used to discretize the partial differential equation of motion and then the method of harmonic balance is used to analytically solve a set of ordinary differential equations. Also, the numerical solutions are carried out by utilizing an adaptive step-size fourth-order Runge-Kutta technique. The analytical and numerical results agree with each other quite well. Furthermore, the stability of steady-state solutions is performed for the analytical results. The frequency characteristics, time- and frequency-domain response characteristics of the plate are fully discussed. The nonlinear frequency-response relationships show strong hardening-type behavior of the system. Additionally, the influences of different parameters on the nonlinear dynamical responses of the system are shown.
In this research work, we constructed the solitary wave solutions of generalized Kadomtsev–Petviashvili modified equal width (KP-MEW) equation with the help of new technique which is modification ...form of extended auxiliary equation mapping method. The generalized KP-MEW equation is the nonlinear PDEs which described the propagation of long-wave with dissipation and dispersion in nonlinear media. As a result, families of solitary wave solutions are obtained in different form of solitons, bright–dark solitons and traveling wave solutions. The physical structure of these new solutions is shown graphically in two and three dimensions with the aid of computer software Mathematica. These obtained new solutions show the power and effectiveness of this new method. We can also solve other nonlinear system of PDEs which are involved in mathematical physics and many other branches of physical sciences with the help of this new method.
This article presents a mission allocation and path-planning solution for the pesticide spraying mission of dense trees in hilly terrains using cooperative multicopters. The problem is formulated as ...a single-depot single-end multiple traveling salesman problem (mTSP). Three different algorithms, namely classical mTSP algorithm, Grouping-TSP combined algorithm, and Grouping-TSP decoupled algorithm, are developed to solve the proposed mTSP. Simulation results indicate that the classical mTSP algorithm provides an evenly distributed task allocation while the Grouping-TSP combined algorithm delivers the optimal solution. In addition, the Grouping-TSP decoupled algorithm minimizes computational complexity. Both Grouping-TSP algorithms integrate a subregions segmentation process to guarantee collision avoidance between the multicopters.
•Propose an efficient analysis method for dynamic stability.•Introduce a FE method for simulating time-dependent properties of concrete.•Conduct a case study of an existing large-span CFST arch ...bridge.•Investigate the effect of creep and shrinkage on seismic behaviour of CFST bridges.•The post-seismic performance of an existing bridge is evaluated.
Creep and shrinkage of the confined concrete changes the dynamic performance of concrete-filled steel tubular (CFST) arch bridges over time. However, less attention is paid to the seismic behaviour of CFST arches considering such long-term effects. The effects of long-term behaviour on the dynamic strength of CFST arch bridges are analysed and discussed in detail in this paper. A novel dynamic stability analysis method for structures subjected to any arbitrary excitations is proposed and validated. The time-dependent properties of concrete have been numerically implemented and also the difference in concrete pouring time at different arch positions is considered. An existing large-span CFST arch bridge is analysed as a case study adopting the proposed method. Moreover, the long-term performance evolution of CFST sections are discussed. It is found that the creep-induced stress within CFST sections has a great influence on the dynamic stability of arch bridges. The critical peak ground acceleration (PGA) at the 1000th day of the service life is suggested as the reference value for the limit state under earthquake excitations. The influence of travelling wave effect and concrete pouring sequence are also investigated. Finally, the post-seismic performance of the whole bridge is evaluated.
•Fast LP-free exact method for small instances.•Effective LP-free heuristic method for medium/large instances.•New benchmark instances.
The use of drones in urban logistics is gaining more and more ...interest. In this paper we consider the flying sidekick traveling salesman problem, where some customers require a delivery and they can be served either by a truck or by a drone. The aim is minimizing the total time required to service all the customers.
We present a branch and bound algorithm especially designed to efficiently target small instances up to 15 customers and a heuristic algorithm, using the branch and bound as a subroutine, to attack larger instances. Extensive experimental results suggest the effectiveness of the exact solver for small instances and shows that the heuristic is able to provide state-of-the-art results for medium/large instances.
We consider the Schrödinger equation with a logarithmic nonlinearty and non-trivial boundary conditions at infinity. We prove that the Cauchy problem is globally well posed in the energy space, which ...turns out to correspond to the energy space for the standard Gross-Pitaevskii equation with a cubic nonlinearity, in small dimensions. We then characterize the solitary and traveling waves in the one dimensional case.
In large-scale interconnected power grids, the frequency dynamic response exhibits temporal-spatial distribution characteristics, of which the internal mechanism is not clear. In this paper, we use a ...statistical-model-based method to analyze the propagation characteristic of frequency dynamic behavior. The frequency data collected from the wide area measurement system are decomposed into standing and traveling wave components with complex empirical orthogonal function, while the information reflecting the spatial-temporal features of frequency dynamics is also obtained in the process. An index is defined to gauge the travelling wave and standing wave components, and the distribution of propagation speed in the entire grid is estimated by the bicubic interpolation method. Finally, the proposed method is applied in a standard test system as well as a real power system to validate its effectiveness. This work explores the mechanism of frequency dynamic in large-scale power grids from a novel view point.
Genetic algorithm (GA) is an artificial intelligence search method that uses the process of evolution and natural selection theory and is under the umbrella of evolutionary computing algorithm. It is ...an efficient tool for solving optimization problems. Integration among (GA) parameters is vital for successful (GA) search. Such parameters include mutation and crossover rates in addition to population that are important issues in (GA). However, each operator of GA has a special and different influence. The impact of these factors is influenced by their probabilities; it is difficult to predefine specific ratios for each parameter, particularly, mutation and crossover operators. This paper reviews various methods for choosing mutation and crossover ratios in GAs. Next, we define new deterministic control approaches for crossover and mutation rates, namely Dynamic Decreasing of high mutation ratio/dynamic increasing of low crossover ratio (DHM/ILC), and Dynamic Increasing of Low Mutation/Dynamic Decreasing of High Crossover (ILM/DHC). The dynamic nature of the proposed methods allows the ratios of both crossover and mutation operators to be changed linearly during the search progress, where (DHM/ILC) starts with 100% ratio for mutations, and 0% for crossovers. Both mutation and crossover ratios start to decrease and increase, respectively. By the end of the search process, the ratios will be 0% for mutations and 100% for crossovers. (ILM/DHC) worked the same but the other way around. The proposed approach was compared with two parameters tuning methods (predefined), namely fifty-fifty crossover/mutation ratios, and the most common approach that uses static ratios such as (0.03) mutation rates and (0.9) crossover rates. The experiments were conducted on ten Traveling Salesman Problems (TSP). The experiments showed the effectiveness of the proposed (DHM/ILC) when dealing with small population size, while the proposed (ILM/DHC) was found to be more effective when using large population size. In fact, both proposed dynamic methods outperformed the predefined methods compared in most cases tested.
Uncontrolled beams and plates often perform poorly as sound radiating structures because of their resonant modes, creating a frequency response with sharp peaks and nulls as well as rapid changes in ...acoustic directionality. An active control technique known as Traveling Wave Control (TWC) has been previously demonstrated to perform well at forcing beams and plates to vibrate without modes, as though they were infinitely large, producing an improved acoustic response. This paper is specifically concerned with evaluating the interaction of piezoelectric actuators with simulated TWC systems and comparing the vibratory and acoustic responses as well as the derived filters to those of ideal point source actuators. Simulations demonstrate that piezoelectric actuators act in a very similar manner to point source actuators on simulated beams and plates, and that the bandwidth of control is proportional to the inverse distance between secondary actuators and edges. An experiment demonstrates that the TWC system implemented on a beam with both moving-coil and piezoelectric actuators is able to mitigate the modal response considerably.
•TWC filters for piezoelectric actuators on beams are similar to those for point source actuators.•Control bandwidth for TWC systems on beams is proportional to secondary actuator placement.•Control bandwidth for TWC systems on plates is proportional to the number of TWC module pairs.•Experiments achieve similar results with both point-source and piezoelectric actuators.
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