Investigation On The Interaction Analysis Of Beam-Nonlinear Isolator With Low And High Stiffness Support

This paper presents the study of the interaction between a beam and a nonlinear isolator for low and high supporting stiffness. The system consists of an elastic beam- like structure and a geometrically nonlinear isolation system in which a horizontal degree provides a physical approach for realising the required horizontal force. The generalised dynamic equations of the system are derived and the modal summation method is used to analyse the beam. The dynamic interaction mechanism between the nonlinear isolation system and the elastic structure is revealed. The beam- nonlinear isolator design for low stiffness support and high stiffness support is discussed. It is found that the beam provides additional mass, stiffness and force to the nonlinear vibration isolator and the requirement to perform ground vibration test whereby the rigid mode of the beam must be less than one third of the first elastic natural frequency of the free-free beam has been satisfied. The condition to achieve high stiffness support has also been satisfied. Nonlinear dynamical behaviour of the beam-nonlinear isolator indicates that period doubling bifurcation occurs when the excitation force is 1 and excitation frequency is 0.5Hz. Poincare’ maps reveals that the system form closed loops and no chaotic behaviour is observed. Perfomance analysis in terms of force transmissibility of the nonlinear isolator shows that the nonlinear isolator performs better than a linear isolator and also performs better than a hardening HSLDS mount

A geometry optimization framework for photonic crystal design

AbstractThe performance of photonic crystal devices can depend strongly on their geometry. Alas, their fundamental physics offers relatively little by way of pointers in terms of optimum shapes, so numerical design search techniques must be used in an attempt to determine high performance layouts. We discuss strategies for solving this type of optimization problem, the main challenge of which is the conflict between the enormous size of the space of potentially useful designs and the relatively high computational cost of evaluating the performance of putative shapes. The optimization technique proposed here operates over increasing levels of fidelity, both in terms of the resolution of its non-parametric shape definition and in terms of the resolution of the numerical analysis of the performance of putative designs. This is a generic method, potentially applicable to any type of electromagnetic device shape design problem. We also consider a methodology for assessing the robustness of the optima generated through this process, investigating the impact of manufacturing errors on their performance. As an illustration, we apply this technology to the design of a two-dimensional photonic crystal structure; the result features a large complete band gap structure and a topology that is different from previously published designs

Low Reynolds Number Effect on Energy Extraction Performance of Semi-Passive Flapping Foil

In this paper, 2-D numerical solution scheme is used to study the performance of semi-passive flapping foil flow energy harvester at Reynolds numbers ranging from 5000 to 50,000. The energy harvester comprises of NACA0015 airfoil which is supported on a translational spring and damper. An external sinosoidal pitch excitation is provided to the airfoil. Energy is extracted from the flow induced vibration of airfoil in translational mode. Movement of airfoil is accommodated in fluid domain by using a hybrid meshfree-Cartesian fluid grid. A body conformal meshfree nodal cloud forms the near field domain, encompassing the airfoil. During the simulation, the solid boundary causes the motion of the meshfree nodal cloud, without necessitating re-meshing. In the far field, the static Cartesian grid encloses and partly overlaps the meshfree nodal cloud. A coupled mesh based and meshfree solution scheme is utilized to solve laminar flow, viscous, incompressible equations, in Arbitrary-Lagrangian-Eulerian (ALE) formulation, over a hybrid grid. Spatial discretization of flow equations is carried out using radial basis function in finite difference mode (RBF-FD) over meshfree nodes and conventional finite differencing over Cartesian grid. Stabilized flow momentum equations are used to avoid spurious fluctuations at high Reynolds numbers. A closely coupled, partitioned, sub iteration method is used for fluid structure interaction. The study is focused to analyse the behaviour of flow energy harvesters at various Reynolds numbers. Effects of changing the translational spring stiffness and pitch activation frequency are also investigated. Instantaneous flow structures around the airfoil have been compared at different Reynolds numbers and pitch amplitudes. It is found that net power extracted by the system increases at high Reynolds numbers. Moreover, re-attachment of leading edge separation vortex plays an important role in ther overall system performance

Shape adaptive RBF-FD implicit scheme for incompressible viscous Navier-Strokes equations

Meshless methods for solving fluid flow problems have become a promising alternative to mesh-based methods. In this paper, a meshless method based on radial basis functions in a finite difference mode (RBF-FD) has been developed for the incompressible Navier-Stokes (N-S) equations in primitive variable form. Pressure-velocity decoupling has been achieved using a fractional step method whereas time splitting has been done using both explicit and implicit schemes. The RBF-FD implicit scheme shows better accuracy and stability, and is able to accurately capture higher gradients of field variables even at coarser grids; unlike the RBF-FD explicit scheme where loss of accuracy was especially prominent at places with larger gradients. To overcome the ill-conditioning and accuracy problems arising from the use of non-uniform and random node distribution, a novel concept of adaptive shape parameter (ASP) for RBF functions is introduced. The use of ASP allows much finer nodal distribution at regions of interest enabling accurate capturing of gradients and leading to better results. The performance of the implicit RBF-FD scheme with the ASP strategy is validated against a variety of benchmark problems, including lid driven cavity flow problems, and steady and unsteady laminar flow around circular cylinder at various Reynolds, and is found to be in good agreement with the existing results<br/

An ALE based hybrid meshfree local RBF-cartesian FD scheme for incompressible flow around moving boundaries

A solution scheme is presented to simulate incompressible viscous flow around moving boundaries using hybrid meshfree-Cartesian grid. The presented solution approach avoids intensive re-meshing and enhances computational efficiency by combining the advantages of both meshfree and mesh-based methods for flow around moving objects. The scheme employs a body conformal meshfree nodal cloud around the solid object which convects with the moving solid boundary. On the outer side, meshfree nodal cloud is surrounded and partially overlapped by a stationary Cartesian grid. Navier Strokes equations in Arbitrary-Lagrangian-Eulerian (ALE) formulations are solved over moving nodal cloud using meshfree local Radial Basis Functions in finite difference Mode (RBF-FD). Eulerian form of flow equations are solved over static Cartesian grid using conventional finite difference scheme. Meshfree nodes can efficiently adapt to the moving boundary without necessitating re-meshing. Use of finite difference method over Cartesian grid allows faster computing and improves computational efficiency. Variation in computation time has been studied with corresponding change in size of meshfree and Cartesian grids. Significant reduction in computation time is achieved by reducing the size of meshfree cloud. The solution scheme is validated by simulating two dimensional flows around vibrating cylindrical objects. For this purpose, forced as well as vortex induced cylindrical vibration cases are investigated and solutions are compared with computational and experimental results available in literature

Some modifications of MPS method for incompressible free surface flow

As a Lagrangian mesh-free method, the Moving Particle Semi-implicit (MPS)[1] method is very suitable for simulating violent flows, such as breaking waves on free surface. However, despite its wide range of applicability, the original MPS algorithm suffers from some inherent difficulties in obtaining an accurate fluid pressure in both spatial and time domain. Different modifications to improve the method have been proposed [2-5] in the literature. In this paper, the authors developed a particle position shifting and collision handling technique which could effectively suppress the pressure fluctuation. In addition, a new version of “cell-link” neighbour particle searching strategy, which reduces about 7/9 (~78%) of the searching area compared with traditional “cell-link” algorithm, is proposed.The developed MPS method with the proposed modifications has been tested on two free surface flow problems: 2D dam break and liquid sloshing. The numerical results obtained are found to be in good agreement with the available numerical and experimental results. With the proposed modifications, the stability and accuracy of the pressure field are improved in spatial and time domains

Explicit and implicit meshless methods for linear advection-diffusion type of partial differential equations

Simple, mesh/grid free, explicit and implicit numerical schemes for the solution of linear advection-diffusion problems is developed and validated herein. Unlike the mesh or grid-based methods, these schemes use well distributed quasi-random points and approximate the solution using global radial basis functions. The schemes can be seen as generalized finite differences with random points instead of a regular grid system. This allows the computation of problems with complex-shaped boundaries in higher dimensions with no need for complex mesh/grid structure and with no extra implementation difficulties

Numerical methods for some time-dependent partial differential equations

SIGLEAvailable from British Library Document Supply Centre- DSC:DX79752 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equations

An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations, with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm

Coupled MPS-modal superposition method for 2D nonlinear fluid-structure interaction problems with free surface

In this paper, a coupled MPS-modal superposition method is developed for 2D nonlinear fluid-structure interaction problems. In this method, the rigid-body and relatively small elastic deformation are coupled together, which considers the mutual effect between them. The elastic deformation of the structure is represented by a mode superposition formulation, which is more efficient compared with FEM, regardless of the size of the structure. For 2D cases, if the first three modes are chosen to represent the flexible deformation of the structure, it only results in a 6×6 matrix equation to be solved. For the fluid motion, the modified Moving Particle Semi-implicit (MPS) method, which significantly reduces the fluctuation of pressure calculation of the original MPS method, is used.Two nonlinear problems, i.e. breaking-water-dam impacting a floating beam and flexible wedge slamming into the water are simulated to demonstrate the performance of the developed method. The numerical simulations show that this coupling model is capable of providing stable results that are generally in good agreement with the available experimental data. For the highly nonlinear case with very large rigid motions, the mutual effect between elastic deformation and rigid motions could accumulate to a relatively remarkable level shown by the curves of trajectories or acceleration history of the body mass centre. This also indicates the importance of mutual effect to analyse highly nonlinear FSI problems with large rigid-body motions and relatively small flexible deformation.KeywordsMoving particle semi-implicit (MPS) method; Fluid structure interaction (FSI); Modal superposition; Free surface flow; Floating beam; Flexible wedge droppin