Search results for: nonlinear incremental dynamic analysis

Authors: Prakash Persad, Kelvin Loutan, Trichelle Seepersad

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The Finite Element Method is commonly used in the analysis of flexible manipulators to predict elastic displacements and develop joint control schemes for reducing positioning error. In order to preserve simplicity, regular geometries, ideal joints and connections are assumed. This paper presents the dynamic FE analysis of a 4- degrees of freedom open chain manipulator, intended for striking a curved 3D surface percussion musical instrument. This was done utilizing the new MultiBody Dynamics Module in COMSOL, capable of modeling the elastic behavior of a body undergoing rigid body type motion.

Keywords: dynamic modeling, entertainment robots, finite element method, flexible robot manipulators, multibody dynamics, musical robots

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Authors: Mahesh K. Chudasama, Harit K. Raval

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3-roller conical bending process is widely used in the industries for manufacturing of conical sections and shells. It involves static as well dynamic bending stages. Analytical models for prediction of bending force during static as well as dynamic bending stage are available in the literature. In this paper, bending forces required for static bending stage and dynamic bending stages have been compared using the analytical models. It is concluded that force required for dynamic bending is very less as compared to the bending force required during the static bending stage.

Keywords: analytical modeling, cone frustum, dynamic bending, static bending

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In this study, a vibrational differential equation governing on swinging single-degree-of-freedom pendulum in a viscous fluid has been investigated. The damping process is characterized according to two different regimes: at first, damping in stationary viscous fluid, in the second, damping in flowing viscous fluid with constant velocity. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equation with a simple and innovative approach. Comparisons are made between new method and Numerical Method (rkf45). The results show that this method is very effective and simple and can be applied for other nonlinear problems.

Keywords: oscillating systems, angular frequency and damping ratio, pendulum at fluid, locus of maximum

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Authors: Paweł Żur, Alicja Żur, Andrzej Baier

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Modal analysis is a crucial tool in the field of engineering for understanding the dynamic behavior of structures. In this study, numerical modal analysis was conducted on a multi-material 3D-printed composite bushing, which comprised a polylactic acid (PLA) outer shell and a thermoplastic polyurethane (TPU) flexible filling. The objective was to investigate the modal characteristics of the bushing and assess its potential for practical applications. The analysis involved the development of a finite element model of the bushing, which was subsequently subjected to modal analysis techniques. Natural frequencies, mode shapes, and damping ratios were determined to identify the dominant vibration modes and their corresponding responses. The numerical modal analysis provided valuable insights into the dynamic behavior of the bushing, enabling a comprehensive understanding of its structural integrity and performance. Furthermore, the study expanded its scope by investigating the entire shaft mounting of a small electric car, incorporating the 3D-printed composite bushing. The shaft mounting system was subjected to numerical modal analysis to evaluate its dynamic characteristics and potential vibrational issues. The results of the modal analysis highlighted the effectiveness of the 3D-printed composite bushing in minimizing vibrations and optimizing the performance of the shaft mounting system. The findings contribute to the broader field of composite material applications in automotive engineering and provide valuable insights for the design and optimization of similar components.

Keywords: 3D printing, composite bushing, modal analysis, multi-material

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Authors: Yanling Li, Linying Ji, Zita Oravecz, Timothy R. Brick, Michael D. Hunter, Sy-Miin Chow

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Assessing several individuals intensively over time yields intensive longitudinal data (ILD). Even though ILD provide rich information, they also bring other data analytic challenges. One of these is the increased occurrence of missingness with increased study length, possibly under non-ignorable missingness scenarios. Multiple imputation (MI) handles missing data by creating several imputed data sets, and pooling the estimation results across imputed data sets to yield final estimates for inferential purposes. In this article, we introduce dynr.mi(), a function in the R package, Dynamic Modeling in R (dynr). The package dynr provides a suite of fast and accessible functions for estimating and visualizing the results from fitting linear and nonlinear dynamic systems models in discrete as well as continuous time. By integrating the estimation functions in dynr and the MI procedures available from the R package, Multivariate Imputation by Chained Equations (MICE), the dynr.mi() routine is designed to handle possibly non-ignorable missingness in the dependent variables and/or covariates in a user-specified dynamic systems model via MI, with convergence diagnostic check. We utilized dynr.mi() to examine, in the context of a vector autoregressive model, the relationships among individuals’ ambulatory physiological measures, and self-report affect valence and arousal. The results from MI were compared to those from listwise deletion of entries with missingness in the covariates. When we determined the number of iterations based on the convergence diagnostics available from dynr.mi(), differences in the statistical significance of the covariate parameters were observed between the listwise deletion and MI approaches. These results underscore the importance of considering diagnostic information in the implementation of MI procedures.

Keywords: dynamic modeling, missing data, mobility, multiple imputation

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Authors: E. Dehghan, R. Dehghan

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Generally, the slender structural walls have flexural behavior. Since behavior of bending members can be explained by moment–curvature relation, therefore, an analytical model is proposed based on moment–curvature relation for slender structural walls. The moment–curvature relationships of RC sections are constructed through section analysis. Governing equations describing the bond-slip behavior in walls are derived and applied to moment–curvature relations. For the purpose of removing the imprecision in analytical results, the plastic hinge length is included in the finite element modeling. Finally, correlation studies between analytical and experimental results are conducted with the objective to establish the validity of the proposed algorithms. The results show that bond-slip effect is more significant in walls subjected to larger axial compression load. Moreover, preferable results are obtained when ultimate strain of concrete is assumed conservatively.

Keywords: nonlinear analysis, slender structural walls, moment-curvature relation, bond-slip, plastic hinge length

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Authors: Susmita Panda, Arnab Banerjee, Ajinkya Baxy, Bappaditya Manna

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The design of short to medium-span high-speed bridges in critical locations is an essential aspect of vehicle-bridge interaction. Due to dynamic interaction between moving load and bridge, mathematical models or finite element modeling computations become time-consuming. Thus, to reduce the computational effort, a universal approximator using an artificial neural network (ANN) has been used to evaluate the dynamic response of the bridge. The data set generation and training of surrogate models have been conducted over the results obtained from mathematical modeling. Further, the robustness of the surrogate model has been investigated, which showed an error percentage of less than 10% with conventional methods. Additionally, the dependency of the dynamic response of the bridge on various load and bridge parameters has been highlighted through a parametric study.

Keywords: artificial neural network, mode superposition method, moving load analysis, surrogate models

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Authors: Nesrine Gaaliche

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This study provides a finite element dynamic model for analyzing rolling bearing system vibration response. The vibration responses of polypropylene bearings with and without defects are studied using FE analysis and compared to experimental data. The viscoelastic behavior of thermoplastic is investigated in this work to evaluate the influence of material flexibility and damping viscosity. The vibrations are detected using 3D dynamic analysis. Peak vibrations are more noticeable in an inner ring defect than in an outer ring defect, according to test data. The performance of thermoplastic bearings is compared to that of metal parts using vibration signals. Both the test and numerical results show that Polypropylene bearings exhibit less vibration than steel counterparts. Unlike bearings made from metal, polypropylene bearings absorb vibrations and handle shaft misalignments. Following validation of the overall vibration spectrum data, Von Mises stresses inside the rings are assessed under high loads. Stress is significantly high under the balls, according to the simulation findings. For the test cases, the computational findings correspond closely to the experimental results.

Keywords: viscoelastic, FE analysis, polypropylene, bearings

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Authors: Jawid Ahmad Baktash, Mursal Dawodi, Tomokazu Nagata

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With the rapid growth of Cloud Computing, Formal Methods became a good choice for the refinement of message specification and verification for Dynamic Routing in Cloud Computing. Cloud-based Dynamic Routing is becoming increasingly popular. We propose feedback in Formal Methods for Dynamic Routing and Cloud Computing; the model and topologies show how to send messages from index zero to all others formally. The responsibility of proper verification becomes crucial with Dynamic Routing in the cloud. Formal Methods can play an essential role in the routing and development of Networks, and the testing of distributed systems. Event-B is a formal technique that consists of describing the problem rigorously and introduces solutions or details in the refinement steps. Event-B is a variant of B, designed for developing distributed systems and message passing of the dynamic routing. In Event-B and formal methods, the events consist of guarded actions occurring spontaneously rather than being invoked.

Keywords: cloud, dynamic routing, formal method, Pro-B, event-B

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Authors: Siti Khadijah Che Osmi, Syed Mohd Ahmad

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This paper presents a methodology to develop fragility curves for shallow tunnels so as to describe a relationship between seismic hazard and tunnel vulnerability. Emphasis is given to the influence of surrounding soil material properties because the dynamic behaviour of the tunnel mostly depends on it. Four ground properties of soils ranging from stiff to soft soils are selected. A 3D nonlinear time history analysis is used to evaluate the seismic response of the tunnel when subjected to five real earthquake ground intensities. The derived curves show the future probabilistic performance of the tunnels based on the predicted level of damage states corresponding to the peak ground acceleration. A comparison of the obtained results with the previous literature is provided to validate the reliability of the proposed fragility curves. Results show the significant role of soil properties and input motions in evaluating the seismic performance and response of shallow tunnels.

Keywords: fragility analysis, seismic performance, tunnel lining, vulnerability

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Authors: P. Deepak Kumar, Aishwarya Alok, P. R. Maiti

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Liquid storage tanks have become widespread during the recent decades due to their extensive usage. Analysis of liquid containing tanks is known to be complex due to hydrodynamic force exerted on tank which makes the analysis a complex one. The objective of this research is to carry out analysis of liquid domain along with structural interaction for various geometries of circular tanks considering seismic effects. An attempt has been made to determine hydrodynamic pressure distribution on the tank wall considering impulsive and convective components of liquid mass. To get a better picture, a comparative study of Draft IS 1893 Part 2, ACI 350.3 and Eurocode 8 for Circular Shaped Tank has been performed. Further, the differences in the magnitude of shear and moment at base as obtained from static (IS 3370 IV) and dynamic (Draft IS 1892 Part 2) analysis of ground supported circular tank highlight the need for us to mature from the old code to a newer code, which is more accurate and reliable.

Keywords: liquid filled containers, circular tanks, IS 1893 (part 2), seismic analysis, sloshing

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Authors: A. Mudau, T. R. Stacey, R. A. Govender

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This paper reports for the first time the findings on the dynamic compressive strength data of Bushveld Complex brittle rock materials. These rocks were subjected to both quasi-static and impact loading tests to help understand their behaviour both under quasi-static and dynamic loading conditions. Unlike quasi-static tests, characterization of dynamic behaviour of materials is challenging, in particularly brittle rock materials. The split Hopkinson pressure bar (SHPB) results reported for anorthosite and norite showed relatively low values for dynamic compressive strength compared to the quasi-static uniaxial compressive strength data. It was noticed that the dynamic stress conditions were not fully attained during testing, as well as constant strain rate.

Keywords: Bushveld Complex, dynamic comperession, rock brittleness, stress equilibrium

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Authors: Hesamoddin Abdollahpour, Roghayeh Abdollahpour, Elham Rahgozar

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This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task.

Keywords: large amplitude, free vibrations, analytical solution, Danell Equation, diagram of phase plane

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Authors: Edamana Vasudevan Krishnan

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This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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Authors: K. Vigneshwaran, Manoj Pandey

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In this paper, breathing crack is considered for the non linear dynamic analysis. The stiffness of the cracked beam is found out by using influence coefficients. The influence coefficients are calculated by using Castigliano’s theorem and strain energy release rate (SERR). The equation of motion of the beam was derived by using Hamilton’s principle. The stiffness and natural frequencies for the cracked beam has been calculated using XFEM and Eigen approach. It is seen that due to presence of cracks, the stiffness and natural frequency changes. The mode shapes and the FRF for the uncracked and breathing cracked cantilever beam also obtained and compared.

Keywords: breathing crack, XFEM, mode shape, FRF, non linear analysis

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Authors: M. S. Ahmed, F. A. Mohammad

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This paper focuses on the dynamic behavior of reinforced concrete (RC) slabs. Therefore, the theoretical modal analysis was performed using two different types of boundary conditions. Modal analysis method is the most important dynamic analyses. The analysis would be modal case when there is no external force on the structure. By using this method in this paper, the effects of freely and simply supported boundary conditions on the frequencies and mode shapes of RC square slabs are studied. ANSYS software was employed to derive the finite element model to determine the natural frequencies and mode shapes of the slabs. Then, the obtained results through numerical analysis (finite element analysis) would be compared with an exact solution. The main goal of the research study is to predict how the boundary conditions change the behavior of the slab structures prior to performing experimental modal analysis. Based on the results, it is concluded that simply support boundary condition has obvious influence to increase the natural frequencies and change the shape of mode when it is compared with freely supported boundary condition of slabs. This means that such support conditions have direct influence on the dynamic behavior of the slabs. Thus, it is suggested to use free-free boundary condition in experimental modal analysis to precisely reflect the properties of the structure. By using free-free boundary conditions, the influence of poorly defined supports is interrupted.

Keywords: natural frequencies, mode shapes, modal analysis, ANSYS software, RC slabs

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Authors: Seyed Abolhasan Naeini, Saeideh Mohammadi

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Rapid urban development leads to the construction of urban tunnels for transport. Passage of tunnels under the surface structures and utilities prompted the changes in the site conditions and hence alteration of the dynamic response of surface structures. Therefore, in this study, the effect of the interaction of tunnel-superstructure on the site response is investigated numerically. For this purpose, Fast Lagrangian Analysis of Continua (FLAC 2D) is used, and stratification and properties of soil layers are selected based on the line No 7 of Tehran subway. The superstructure is modeled both as an equivalent surcharge and the actual structure, and the results are compared. A comparison of the results shows that consideration of structure geometry is necessary for dynamic analysis and it leads to the changes in displacements and accelerations. Consequently, the geometry of the superstructure should be modeled completely instead of the application of an equivalent load. The effect of tunnel diameter and depth on the settlement of superstructures is also studied. Results show that when the tunnel depth and diameter grow, the settlements increase considerably.

Keywords: tunnel, FLAC2D, settlement, dynamic analysis

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Authors: Felipa De Mello-Sampayo

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Background: The aim of this study is to undertake, from a patient perspective, an economic analysis of presurgical teledermatology, comparing it with a conventional referral system. Store-and-forward teledermatology allows surgical planning, saving both time and number of visits involving travel, thereby reducing patients’ out-of-pocket expenses, i.e., costs that patients incur when traveling to and from health providers for treatment, visits’ fees, and the opportunity cost of time spent in visits. Method: Patients’ out-of-pocket expenses-effectiveness of presurgical teledermatology were analyzed in the setting of a public hospital during two years. The mean delay in surgery was used to measure effectiveness. The teledermatology network covering the area served by the Hospital Garcia da Horta (HGO), Portugal, linked the primary care centers of 24 health districts with the hospital’s dermatology department. The patients’ opportunity cost of visits, travel costs, and visits’ fee of each presurgical modality (teledermatology and conventional referral), the cost ratio between the most and least expensive alternative, and the incremental cost-effectiveness ratio were calculated from initial primary care visit until surgical intervention. Two groups of patients: those with squamous cell carcinoma and those with basal cell carcinoma were distinguished in order to compare the effectiveness according to the dermatoses. Results: From a patient perspective, the conventional system was 2.15 times more expensive than presurgical teledermatology. Teledermatology had an incremental out-of-pocket expenses-effectiveness ratio of €1.22 per patient and per day of delay avoided. This saving was greater in patients with squamous cell carcinoma than in patients with basal cell carcinoma. Conclusion: From a patient economic perspective, teledermatology used for presurgical planning and preparation is the dominant strategy in terms of out-of-pocket expenses-effectiveness than the conventional referral system, especially for patients with severe dermatoses.

Keywords: economic analysis, out-of-pocket expenses, opportunity cost, teledermatology, waiting time

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Authors: Blaise Fyama, Elie Museng, Grace Mukoma

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In this article we present a java implementation of video telephony using the SIP protocol (Session Initiation Protocol). After a functional analysis of the SIP protocol, we relied on the work of Italian researchers of University of Parma-Italy to acquire adequate libraries for the development of our own communication tool. In order to optimize the code and improve the prototype, we used, in an incremental approach, test techniques based on a static analysis based on the evaluation of the complexity of the software with the application of metrics and the number cyclomatic of Mccabe. The objective is to promote the emergence of local start-ups producing IP video in a well understood local context. We have arrived at the creation of a video telephony tool whose code is optimized.

Keywords: static analysis, coding complexity metric mccabe, Sip, uml

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Authors: Morteza Raminnia

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In this study, dynamic analysis of functionally graded nano-composite pipe reinforced by single-walled carbon nano-tubes (SWCNTs) with simply supported boundary condition subjected to moving mechanical loads is investigated. The material properties of functionally graded carbon nano tube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction and are estimated through a micro-mechanical model. In this paper polymeric matrix considered as isotropic material and for the CNTRC, uniform distribution (UD) and three types of FG distribution patterns of SWCNT reinforcements are considered. The system equation of motion is derived by using Hamilton's principle under the assumptions of first order shear deformation theory (FSDT).The thin piezoelectric layers embedded on inner and outer surfaces of FG-CNTRC layer are acted as distributed sensor and actuator to control dynamic characteristics of the FG-CNTRC laminated pipe. The modal analysis technique and Newmark's integration method are used to calculate the displacement and dynamic stress of the pipe subjected to moving loads. The effects of various material distribution and velocity of moving loads on dynamic behavior of the pipe is presented. This present approach is validated by comparing the numerical results with the published numerical results in literature. The results show that the above-mentioned effects play very important role on dynamic behavior of the pipe .This present work shows that some meaningful results that which are interest to scientific and engineering community in the field of FGM nano-structures.

Keywords: nano-composite, functionally garded material, moving load, active control, PZT layers

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Lucie Novakova, Petr Homola, Vaclav Kafka

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Asymmetric incremental sheet forming (AISF) could significantly reduce costs incurred by the fabrication of complex industrial components with a minimal environmental impact. The AISF experiments were carried out on commercially pure titanium (Ti-Gr2), Timetal (15-3-3-3) alloy, and Ti-6Al-4V (Ti-Gr5) alloy. A special testing geometry was used to characterize the titanium alloys properties from the point of view of the forming zone and titanium structure effect. The structure and properties of the materials were assessed by means of metallographic analyses and microhardness measurements.The highest differences in the parameters assessed as a function of the sampling zone were observed in the case of alpha-phase Ti-Gr2at the expense of the most substantial sheet thinning occurrence. A springback causes a smaller stored deformation in Timetal (β alloy) resulting in less pronounced microstructure refinement and microhardness increase. Ti-6Al-4V alloy exhibited early failure due to its poor formability at ambient temperature.

Keywords: incremental forming, metallography, hardness, titanium alloys

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Authors: M. Najafi, F. Rahimi Dehgolan

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In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: non-linear vibration, stability, axially moving beam, bifurcation, multiple scales method

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Authors: Evgeniia V. Mekhonoshina, Vladimir Ya. Modorskii, Vasilii Yu. Petrov

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At present, vibrations of rotors of gas transmittal unit evade sustainable forecasting. This paper describes elastic oscillation modes in resilient supports and rotor impellers modeled during computational experiments with regard to interference in the system of gas-dynamic flow and compressor rotor. Verification of aeroelastic approach was done on model problem of interaction between supersonic jet in shock tube with deformed plate. ANSYS 15.0 engineering analysis system was used as a modeling tool of numerical simulation in this paper. Finite volume method for gas dynamics and finite elements method for assessment of the strain stress state (SSS) components were used as research methods. Rotation speed and material’s elasticity modulus varied during calculations, and SSS components and gas-dynamic parameters in the dynamic system of gas-dynamic flow and compressor rotor were evaluated. The analysis of time dependence demonstrated that gas-dynamic parameters near the rotor blades oscillate at 200 Hz, and SSS parameters at the upper blade edge oscillate four times higher, i.e. with blade frequency. It has been detected that vibration amplitudes correction in the test points at magnetic bearings by aeroelasticity may correspond up to 50%, and about -π/4 for phases.

Keywords: Centrifugal compressor, aeroelasticity, interdisciplinary calculation, oscillation phase displacement, vibration, nonstationarity

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Authors: Jiangbo Pu, Hanhui Xu, Yazhou Wang, Hongyan Cui, Yong Hu

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Spinal cord injury (SCI) brings great negative influence to the patients and society. Neurological loss in human after SCI is a major challenge in clinical. Instead, neural regeneration could have been seen in animals after SCI, and such regeneration could be retarded by blocking neural plasticity pathways, showing the importance of neural plasticity in functional recovery. Here we used sample entropy as an indicator of nonlinear dynamical in the brain to quantify plasticity changes in spontaneous EEG recordings of rats before and after SCI. The results showed that the entropy values were increased after the injury during the recovery in one week. The increasing tendency of sample entropy values is consistent with that of behavioral evaluation scores. It is indicated the potential application of sample entropy analysis for the evaluation of neural plasticity in spinal cord injury rat model.

Keywords: spinal cord injury (SCI), sample entropy, nonlinear, complex system, firing pattern, EEG, spontaneous activity, Basso Beattie Bresnahan (BBB) score

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Authors: Baoshan Huang, Fanbiao Bao, Bing Li, Lianghua Zeng, Yi Zheng

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Parameter control strategy based on statistical characteristics can analyze the choice of the transmission ratio of an automobile transmission. According to the difference of the transmission gear, the number and spacing of the gear can be determined. Transmission ratio distribution of transmission needs to satisfy certain distribution law. According to the statistic characteristics of driving parameters, the shift control strategy of the vehicle is analyzed. CVT shift schedule adjustment algorithm based on statistical characteristic parameters can be seen from the above analysis, if according to the certain algorithm to adjust the size of, can adjust the target point are in the best efficiency curve and dynamic curve between the location, to alter the vehicle characteristics. Based on the dynamic characteristics and the practical application of the vehicle, this paper presents the setting scheme of the transmission ratio.

Keywords: vehicle dynamics, transmission ratio, transmission parameters, statistical characteristics

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Authors: Xuezhang Hou

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In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: C. J. W. Habets, D. J. Peters, J. G. de Gijt, A. V. Metrikine, S. N. Jonkman

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Conventional seismic designs of quay walls in ports are mostly based on pseudo-static analysis. A more advanced alternative is the Performance-Based Design (PBD) method, which evaluates permanent deformations and amounts of (repairable) damage under seismic loading. The aim of this study is to investigate the suitability of this method for anchored sheet pile quay walls that were not purposely designed for seismic loads. A research methodology is developed in which pseudo-static, permanent-displacement and finite element analysis are employed, calibrated with an experimental reference case that considers a typical anchored sheet pile wall. A reduction factor that accounts for deformation behaviour is determined for pseudo-static analysis. A model to apply traditional permanent displacement analysis on anchored sheet pile walls is proposed. Dynamic analysis is successfully carried out. From the research it is concluded that PBD evaluation can effectively be used for seismic analysis and design of this type of structure.

Keywords: anchored sheet pile quay wall, simplified dynamic analysis, performance-based design, pseudo-static analysis

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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