Search results for: Zhaoyun Ding

Authors: Changqiao Wu, Guoqing Ding, Xin Chen

Abstract:

In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.

Keywords: Dynamic system modeling, neural network, normal equation, second order gradient descent.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 781

Authors: Biao Wang, Tao Li, Qi-wen Sun, Wei-yong Ying, Ding-ye Fang

Abstract:

Methanol-to-olefins (MTO) coupled with transformation of coal or natural gas to methanol gives an interesting and promising way to produce ethylene and propylene. To investigate solid concentration in gas-solid fluidized bed for methanol-to-olefins process catalyzed by SAPO-34, a cold model experiment system is established in this paper. The system comprises a gas distributor in a 300mm internal diameter and 5000mm height acrylic column, the fiber optic probe system and series of cyclones. The experiments are carried out at ambient conditions and under different superficial gas velocity ranging from 0.3930m/s to 0.7860m/s and different initial bed height ranging from 600mm to 1200mm. The effects of radial distance, axial distance, superficial gas velocity, initial bed height on solid concentration in the bed are discussed. The effects of distributor shape and porosity on solid concentration are also discussed. The time-averaged solid concentration profiles under different conditions are obtained.

Keywords: Branched pipe distributor, distributor porosity, gas-solid fluidized bed, solid concentration.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2275

Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

Abstract:

The problem of N cracks interaction in an isotropic elastic solid is decomposed into a subproblem of a homogeneous solid without crack and N subproblems with each having a single crack subjected to unknown tractions on the two crack faces. The unknown tractions, namely pseudo tractions on each crack are expanded into polynomials with unknown coefficients, which have to be determined by the consistency condition, i.e. by the equivalence of the original multiple cracks interaction problem and the superposition of the N+1 subproblems. In this paper, Kachanov-s approach of average tractions is extended into the method of moments to approximately impose the consistence condition. Hence Kachanov-s method can be viewed as the zero-order method of moments. Numerical results of the stress intensity factors are presented for interactions of two collinear cracks, three collinear cracks, two parallel cracks, and three parallel cracks. As the order of moment increases, the accuracy of the method of moments improves.

Keywords: Crack interaction, stress intensity factor, multiplecracks, method of moments.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1582

Authors: Hong Ding, Fatiha Benslimane, Isra Marei, Chris R. Triggle

Abstract:

Hyperglycaemia is a key factor that contributes to the development of diabetes-related microvascular disease and a major risk factor for endothelial dysfunction. In the current study, we have explored glucose-induced abnormal intracellular calcium (Ca2+ i) homeostasis in mouse microvessel endothelial cells (MMECs) in high glucose (HG) (40mmol/L) versus control (low glucose, LG) (11 mmol/L). We demonstrated that the exposure of MMECs to HG for 3 days did not change basal Ca2+ i, however, there was a significant increase of acetylcholine-induced Ca2+ entry. Western blots illustrated that exposure to HG also increased STIM1 (Stromal Interaction Molecule 1), but not Orai1 (the pore forming subunit), protein expression levels. Although the link between HG-induced changes in STIM1 expression, enhanced Ca2+ entry and endothelial dysfunction requires further study, the current data are suggestive that targeting these pathways may reduce the impact of HG on endothelial function.

Keywords: store-operated calcium entry, hyperglycaemia, STIM1, endothelial dysfunction

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1709

Authors: Ding Jue, Li Jiahua, Lei Zhidi, Weng Peifen, Li Xiaowei

Abstract:

With the rapid development of national modern industry, people begin to pay attention to environmental pollution and harm caused by industrial dust. Based on above, a numerical study on the dedusting technology of industrial environment was conducted. The dynamic models of multicomponent particles collision and coagulation, breakage and deposition are developed, and the interaction of water droplet and aerosol particle in 2-Dimension flow field was researched by Eulerian-Lagrangian method and Multi-Monte Carlo method. The effects of the droplet scale, movement speed of droplet and the flow field structure on scavenging efficiency were analyzed. The results show that under the certain condition, 30μm of droplet has the best scavenging efficiency. At the initial speed 1m/s of droplets, droplets and aerosol particles have more time to interact, so it has a better scavenging efficiency for the particle.

Keywords: Water droplet, aerosol particle, collision and coagulation, multi-Monte Carlo method.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 878

Authors: Bo Wan, Xiu Wen, Lingling An, Xiaoling Ding

Abstract:

The paper describes a Chinese shadow play animation system based on Kinect. Users, without any professional training, can personally manipulate the shadow characters to finish a shadow play performance by their body actions and get a shadow play video through giving the record command to our system if they want. In our system, Kinect is responsible for capturing human movement and voice commands data. Gesture recognition module is used to control the change of the shadow play scenes. After packaging the data from Kinect and the recognition result from gesture recognition module, VRPN transmits them to the server-side. At last, the server-side uses the information to control the motion of shadow characters and video recording. This system not only achieves human-computer interaction, but also realizes the interaction between people. It brings an entertaining experience to users and easy to operate for all ages. Even more important is that the application background of Chinese shadow play embodies the protection of the art of shadow play animation.

Keywords: Gesture recognition, Kinect, shadow play animation, VRPN.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2703

Authors: Biao Wang, Tao Li, Qi-Wen Sun, Wei-Yong Ying, Ding-Ye Fang

Abstract:

Methanol-to-olefins coupled with transformation of coal or natural gas to methanol gives an interesting and promising way to produce ethylene and propylene. To investigate solid concentration in gas-solid fluidized bed for methanol-to-olefins process catalyzed by SAPO-34, a cold model experiment system is established in this paper. The system comprises a gas distributor in a 300mm internal diameter and 5000mm height acrylic column, the fiber optic probe system and series of cyclones. The experiments are carried out at ambient conditions and under different superficial gas velocity ranging from 0.3930m/s to 0.7860m/s and different initial bed height ranging from 600mm to 1200mm. The effects of radial distance, axial distance, superficial gas velocity, initial bed height on solid concentration in the bed are discussed. The effects of distributor shape and porosity on solid concentration are also discussed. The time-averaged solid concentration profiles under different conditions are obtained.

Keywords: Branched pipe distributor, distributor porosity, gas-solid fluidized bed, solid concentration.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1460

Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

Abstract:

Nanomaterials have attracted considerable attention during the last two decades, due to their unusual electrical, mechanical and other physical properties as compared with their bulky counterparts. The mechanical properties of nanostructured materials show strong size dependency, which has been explained within the framework of continuum mechanics by including the effects of surface stress. The size-dependent deformations of two-dimensional nanosized structures with surface effects are investigated in the paper by the finite element method. Truss element is used to evaluate the contribution of surface stress to the total potential energy and the Gurtin and Murdoch surface stress model is implemented with ANSYS through its user programmable features. The proposed approach is used to investigate size-dependent stress concentration around a nanosized circular hole and the size-dependent effective moduli of nanoporous materials. Numerical results are compared with available analytical results to validate the proposed modeling approach.

Keywords: Nanomaterials, finite element method, sizedependency, surface stress

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2780

Authors: Wenzhe Li, Xiaoyu Ying, Grace Ding

Abstract:

Architecture plane form is an important consideration in the design of green buildings due to its significant impact on energy performance. The most effective method to consider energy performance in the early design stages is parametric modelling. This paper presents a methodology to program plane forms using MATLAB language, generating 16 kinds of plane forms by changing four designed parameters. DesignBuilder (an energy consumption simulation software) was proposed to simulate the energy consumption of the generated planes. A regression mathematical model was established to study the relationship between the plane forms and their energy consumption. The main finding of the study suggested that there was a cubic function relationship between the depth-ratio of U-shaped buildings and energy consumption, and there is also a cubic function relationship between the width-ratio and energy consumption. In the design, the depth-ratio of U-shaped buildings should not be less than 2.5, and the width-ratio should not be less than 2.

Keywords: Graphic parameterization, green building design, mathematical model, U-shaped buildings.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 856

Authors: Mingtao Ding, Zheng Tian, Haixia Xu

Abstract:

The batch nature limits the standard kernel principal component analysis (KPCA) methods in numerous applications, especially for dynamic or large-scale data. In this paper, an efficient adaptive approach is presented for online extraction of the kernel principal components (KPC). The contribution of this paper may be divided into two parts. First, kernel covariance matrix is correctly updated to adapt to the changing characteristics of data. Second, KPC are recursively formulated to overcome the batch nature of standard KPCA.This formulation is derived from the recursive eigen-decomposition of kernel covariance matrix and indicates the KPC variation caused by the new data. The proposed method not only alleviates sub-optimality of the KPCA method for non-stationary data, but also maintains constant update speed and memory usage as the data-size increases. Experiments for simulation data and real applications demonstrate that our approach yields improvements in terms of both computational speed and approximation accuracy.

Keywords: adaptive method, kernel principal component analysis, online extraction, recursive algorithm

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1551

Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

Abstract:

When the characteristic length of an elastic solid is down to the nanometer level, its deformation behavior becomes size dependent. Surface energy /surface stress have recently been applied to explain such dependency. In this paper, the effect of strain-independent surface stress on the deformation of an isotropic elastic solid containing a nanosized elliptical hole is studied by the finite element method. Two loading cases are considered, in the first case, hoop stress along the rim of the elliptical hole induced by pure surface stress is studied, in the second case, hoop stress around the elliptical opening under combined remote tension and surface stress is investigated. It has been shown that positive surface stress induces compressive hoop stress along the hole, and negative surface stress has opposite effect, maximum hoop stress occurs near the major semi-axes of the ellipse. Under combined loading of remote tension and surface stress, stress concentration around the hole can be either intensified or weakened depending on the sign of the surface stress.

Keywords: Surface stress, finite element method, stress concentration, nanosized elliptical hole

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2074

Authors: Nan Ding, Motoki Shino, Nobuyasu Tomokuni, Genki Murata

Abstract:

The wheelchair is the major means of transport for physically disabled people. However, it cannot overcome architectural barriers such as curbs and stairs. In this paper, the authors proposed a method to avoid falling down of a wheeled inverted pendulum type robotic wheelchair for climbing stairs. The problem of this system is that the feedback gain of the wheels cannot be set high due to modeling errors and gear backlash, which results in the movement of wheels. Therefore, the wheels slide down the stairs or collide with the side of the stairs, and finally the wheelchair falls down. To avoid falling down, the authors proposed a slider control strategy based on skyhook model in order to decrease the movement of wheels, and a rotary link control strategy based on the staircase dimensions in order to avoid collision or slide down. The effectiveness of the proposed fall avoidance control strategy was validated by ODE simulations and the prototype wheelchair.

Keywords: EPW, fall avoidance control, skyhook, wheeled inverted pendulum.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1198

Authors: Qiuhua Miao, Peng Huang, Yifei Ding

Abstract:

Particles with different properties tend to be unevenly distributed along an axial direction of the rotating drum, which is usually ignored. Therefore, it is important to study the relationship between axial segregation characteristics and particle crushing efficiency in longer drums. In this paper, a relative area total energy (RRTE) index is proposed, which aims to evaluate the overall crushing energy distribution characteristics. Based on numerical simulation verification, the proposed RRTE index can reflect the overall grinding effect more comprehensively, clearly representing crushing energy distribution in different drum areas. Furthermore, the proposed method is applied to the relation between axial segregation and crushing energy in drums. Compared with the radial section, the collision loss energy of the axial section can better reflect the overall crushing effect in long drums. The axial segregation characteristics directly affect the total energy distribution between medium and abrasive, reducing overall crushing efficiency. Therefore, the axial segregation characteristics should be avoided as much as possible in the crushing of the long rotary drum.

Keywords: Relative regional total energy, crushing energy, axial segregation characteristics, rotary drum.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 378

Authors: Maazuza Z. Othman, Liqiang Ding, Yi Jiao

Abstract:

A local wastewater treatment plant (WWTP) experiencing poor nitrification tracked down high level of surfactants in the plant-s influent and effluent. The aims of this project were to assess the potential inhibitory effect of surfactants on activated sludge processes. The effect of the presence of TergitolNP-9, TrigetolNP-7, Trigetol15-S-9, dodecylbenzene sulphonate (SDBS) and sodium dodecyl sulfate (SDS) on activated sludge oxygen uptake rate (OUR) and nitrification were assessed. The average concentration of non-ionic and anionic surfactants in the influent to the local WWTP were 7 and 8.7 mg/L, respectively. Removal of 67% to 90% of the non-ionic and 93-99% of the anionic surfactants tested were measured. All surfactants tested showed inhibitory effects both on OUR and nitrification. SDS incurred the lowest inhibition whereas SDBS and NP-9 caused severe inhibition to OUR and Nitrification. Activated sludge flocs sizes slightly decreased after 3 hours contact with the surfactant present in the test. The results obtained indicated that high concentrations of surfactants are likely to have an adverse effect on the performance of WWTPs utilizing activated sludge processes.

Keywords: surfactants, activated sludge oxygen uptake rate (OUR), nitrification, anionic surfactants, non-ionic surfactants

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 3501

Authors: Shoujia Fang, Guoqing Ding, Xin Chen

Abstract:

The quality of press-fit assembly is closely related to reliability and safety of product. The paper proposed a keypoint detection method based on convolutional neural network to improve the accuracy of keypoint detection in press-fit curve. It would provide an auxiliary basis for judging quality of press-fit assembly. The press-fit curve is a curve of press-fit force and displacement. Both force data and distance data are time-series data. Therefore, one-dimensional convolutional neural network is used to process the press-fit curve. After the obtained press-fit data is filtered, the multi-layer one-dimensional convolutional neural network is used to perform the automatic learning of press-fit curve features, and then sent to the multi-layer perceptron to finally output keypoint of the curve. We used the data of press-fit assembly equipment in the actual production process to train CNN model, and we used different data from the same equipment to evaluate the performance of detection. Compared with the existing research result, the performance of detection was significantly improved. This method can provide a reliable basis for the judgment of press-fit quality.

Keywords: Keypoint detection, curve feature, convolutional neural network, press-fit assembly.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 941

Authors: Hong-fang Ma, Hai-tao Zhang, Wei-yong Ying, Ding-ye Fang

Abstract:

Radial flow reactor was focused for large scale methanol synthesis and in which the heat transfer type was cross-flow. The effects of operating conditions including the reactor inlet air temperature, the heating pipe temperature and the air flow rate on the cross-flow heat transfer was investigated and the results showed that the temperature profile of the area in front of the heating pipe was slightly affected by all the operating conditions. The main area whose temperature profile was influenced was the area behind the heating pipe. The heat transfer direction according to the air flow directions. In order to provide the basis for radial flow reactor design calculation, the dimensionless number group method was used for data fitting of the bed effective thermal conductivity and the wall heat transfer coefficient which was calculated by the mathematical model with the product of Reynolds number and Prandtl number. The comparison of experimental data and calculated value showed that the calculated value fit the experimental data very well and the formulas could be used for reactor designing calculation.

Keywords: Cross-flow, Heat transfer, Fixed bed, Mathematical model

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1874

Authors: Shan Ding, Lijia Zhang, Hongming Xu

Abstract:

this paper presents a novel scheme which is capable of reducing the error rate and improves the transmission performance in the asynchronous cooperative MIMO systems. A case study of image transmission is applied to prove the efficient of scheme. The linear dispersion structure is employed to accommodate the cooperative wireless communication network in the dynamic topology of structure, as well as to achieve higher throughput than conventional space–time codes based on orthogonal designs. The LDPC encoder without girth-4 and the STBC encoder with guard intervals are respectively introduced. The experiment results show that the combined coder of LDPC-STBC with guard intervals can be the good error correcting coders and BER performance in the asynchronous cooperative communication. In the case study of image transmission, the results show that in the transmission process, the image quality which is obtained by applied combined scheme is much better than it which is not applied the scheme in the asynchronous cooperative MIMO systems.

Keywords: Cooperative MIMO, image transmission, lineardispersion codes, Low-Density Parity-Check (LDPC)

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1933

Authors: Zhang Tianci, Ding Meng, Zuo Hongfu, Zeng Lina, Sun Zejun

Abstract:

Automation of airport operations can greatly improve ground movement efficiency. In this paper, we study the speed profile design problem for advanced airport ground movement control and guidance. The problem is constrained by the surface four-dimensional trajectory generated in taxi planning. A decomposed approach of two stages is presented to solve this problem efficiently. In the first stage, speeds are allocated at control points, which ensure smooth speed profiles can be found later. In the second stage, detailed speed profiles of each taxi interval are generated according to the allocated control point speeds with the objective of minimizing the overall fuel consumption. We present a swarm intelligence based algorithm for the first-stage problem and a discrete variable driven enumeration method for the second-stage problem, since it only has a small set of discrete variables. Experimental results demonstrate the presented methodology performs well on real world speed profile design problems.

Keywords: Airport ground movement, fuel consumption, particle swarm optimization, smoothness, speed profile design.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1941

Authors: Wenguang Ding, Yang Wu, Xia Wang, Yayu Gao

Abstract:

Biogas, a clean renewable energy, is attracting a growing concern of researchers and professionals in many fields. Based on the natural and climatic conditions in semi-arid regions of northwestern China, the present study introduces a specifically-designed family-size biogas plant (with a digester of 10m3) with manure and urine of animals and humanity as raw materials. The biogas plant is applicable to areas with altitudes of more than 2000 meters in northwestern China. In addition to the installation cost, a little operational expenditure, structure, characteristics, benefits of this small-scale biogas plant, this article introduces a wide range of specific popularization methods such as training, financial support, guided tour to the biogas plant, community-based group study and delivery of operational manuals. The feasibility of the biogas plant is explored on the basis of the availability of the raw materials. Simple operations contained in the current work increase the possibility of the wide use of this small-scale biogas plant in similar regions of the world.

Keywords: biogas, family-size biogas plant, northwestern China, popularization

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2772

Authors: Zheng Zhang, Xin Chen, Guoqing Ding

Abstract:

Electronic apex locators (EAL) has been widely used clinically for measuring root canal working length with high accuracy, which is crucial for successful endodontic treatment. In order to maintain high accuracy in different measurement environments, this study presented a system for root canal length measurement based on multifrequency impedance method. This measuring system can generate a sweep current with frequencies from 100 Hz to 1 MHz through a direct digital synthesizer. Multiple impedance ratios with different combinations of frequencies were obtained and transmitted by an analog-to-digital converter and several of them with representatives will be selected after data process. The system analyzed the functional relationship between these impedance ratios and the distance between the file and the apex with statistics by measuring plenty of teeth. The position of the apical foramen can be determined by the statistical model using these impedance ratios. The experimental results revealed that the accuracy of the system based on multifrequency impedance ratios method to determine the position of the apical foramen was higher than the dual-frequency impedance ratio method. Besides that, for more complex measurement environments, the performance of the system was more stable.

Keywords: Root canal length, apex locator, multifrequency impedance, sweep frequency.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 744

Authors: Haiping Ding, Rongchu Zhu, Zhenxia Song

Abstract:

Local irregular topography has a great impact on earthquake ground motion. For scarp topography, using numerical simulation method, the influence extent and scope of the scarp terrain on scarp's upside and downside ground motion are discussed in case of different vertical incident SV waves. The results show that: (1) The amplification factor of scarp's upside region is greater than that of the free surface, while the amplification factor of scarp's downside part is less than that of the free surface; (2) When the slope angle increases, for x component, amplification factors of the scarp upside also increase, while the downside part decrease with it. For z component, both of the upside and downside amplification factors will increase; (3) When the slope angle changes, the influence scope of scarp's downside part is almost unchanged, but for the upside part, it slightly becomes greater with the increase of slope angle; (4) Due to the existence of the scarp, the z component ground motion appears at the surface. Its amplification factor increases for larger slope angle, and the peaks of the surface responses are related with incident waves. However, the input wave has little effects on the x component amplification factors.

Keywords: Scarp topography, ground motion, amplification factor, vertical incident wave.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 800

Authors: Qing Zhang, Jiachen Nie, Yujia Wen, Guanyuan Kou, Peng Yu, Kun Xia, Qin Yang, Li Ding

Abstract:

Background: A facility layout problem (FLP) is an NP-complete (non-deterministic polynomial) problem, for which is hard to obtain an exact optimal solution. FLP has been widely studied in various limited spaces and workflows. For example, cafeterias with many types of equipment for troops cause chaotic processes when dining. Objective: This article tried to optimize the layout of a troops’ cafeteria and to improve the overall efficiency of the dining process. Methods: First, the original cafeteria layout design scheme was analyzed from an ergonomic perspective and two new design schemes were generated. Next, three facility layout models were designed, and further simulation was applied to compare the total time and density of troops between each scheme. Last, an experiment of the dining process with video observation and analysis verified the simulation results. Results: In a simulation, the dining time under the second new layout is shortened by 2.25% and 1.89% (p<0.0001, p=0.0001) compared with the other two layouts, while troops-flow density and interference both greatly reduced in the two new layouts. In the experiment, process completing time and the number of interferences reduced as well, which verified corresponding simulation results. Conclusion: Our two new layout schemes are tested to be optimal by a series of simulation and space experiments. In future research, similar approaches could be applied when taking layout-design algorithm calculation into consideration.

Keywords: Troops’ cafeteria, layout optimization, dining efficiency, AnyLogic simulation, field experiment

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 508

Authors: Xiaobai Li, Li Li, Yujin Hu, Weiming Deng, Zhe Ding

Abstract:

A size-dependent Euler–Bernoulli beam model, which accounts for nonlocal stress field, strain gradient field and higher order inertia force field, is derived based on the nonlocal strain gradient theory considering velocity gradient effect. The governing equations and boundary conditions are derived both in dimensional and dimensionless form by employed the Hamilton principle. The analytical solutions based on different continuum theories are compared. The effect of higher order inertia terms is extremely significant in high frequency range. It is found that there exists an asymptotic frequency for the proposed beam model, while for the nonlocal strain gradient theory the solutions diverge. The effect of strain gradient field in thickness direction is significant in low frequencies domain and it cannot be neglected when the material strain length scale parameter is considerable with beam thickness. The influence of each of three size effect parameters on the natural frequencies are investigated. The natural frequencies increase with the increasing material strain gradient length scale parameter or decreasing velocity gradient length scale parameter and nonlocal parameter.

Keywords: Euler-Bernoulli Beams, free vibration, higher order inertia, nonlocal strain gradient theory, velocity gradient.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1005