Wave Problems for Repetitive Structures and Symplectic Mathematics

1992 ◽  
Vol 206 (6) ◽  
pp. 371-379 ◽  
Author(s):  
W X Zhong ◽  
F W Williams
Keyword(s):  
Wave Scattering ◽  
Power Flow ◽  
Turbine Blades ◽  
Expansion Method ◽  
Space Structures ◽  
Scattering Problems ◽  
Symplectic Matrix ◽  
Conservation Result ◽  
Wave Problems ◽  
Chain Type

Based on the analogy between structural mechanics and optimal control theory, the eigensolutions of a symplectic matrix, the adjoint symplectic ortho-normalization relation and the eigenvector expansion method are introduced into the wave propagation theory for sub-structural chain-type structures, such as space structures, composite material and turbine blades. The positive and reverse algebraic Riccati equations are derived, for which the solution matrices are closely related to the power flow along the sub-structural chain. The power flow orthogonality relation for various eigenvectors is proved, and the energy conservation result is also proved for wave scattering problems.

Geometrically exact, intrinsic mixed variational formulation for smart, slender multilink composite structures

2021 ◽  
pp. 1045389X2110322
Author(s):  
P M G Bashir Asdaque ◽  
Sitikantha Roy
Keyword(s):  
Composite Structures ◽  
Turbine Blades ◽  
Space Structures ◽  
Wind Turbine Blades ◽  
Weak Formulation ◽  
Helicopter Blades ◽  
Static Mechanical ◽  
Computational Platform ◽  
Swept Wings ◽  
Variational Statement

Flexible links are often part of massive aerospace structures like helicopter or wind turbine blades, satellite bae, airplane wings, and space stations. In the present work, a mixed variational statement based on intrinsic variables is derived for multilinked smart slender structures. Equations involved in the derivation do not involve approximations of kinematical variables to describe the deformation of the reference line or the rotation of the deformed cross-section of the slender links resulting in a geometrically exact formulation. Finite element equations are derived from weak formulation, which can analyze large geometrically non-linear problems. The weakest possible variational statement provides greater flexibility in the choice of shape functions, therefore reducing the associated numerical complexities. The present work focuses on developing a single integrated computational platform which can study multibody, multilink, lightweight composite, structural system built with both embedded actuations, sensing, as well as passive links. Validation of static mechanical and electrical outputs from 3D FE simulation and literature proves the efficacy of the computational platform. Dynamic results will be communicated in future correspondence. The computational platform developed here can be applied for monitoring and active control applications of flexible smart multilink structures like swept wings, multi-bae space structures, and helicopter blades.

The Calculation of Photovoltaic System Generation Access Capacity in Distribution Network Based on Probabilistic Power Flow and the PSO Optimization

2012 ◽  
Vol 529 ◽  
pp. 371-375
Author(s):  
Lu Yao Ma ◽  
Shu Jun Yao ◽  
Yan Wang ◽  
Jing Yang ◽  
Long Hui Liu
Keyword(s):  
Distributed Generation ◽  
Power Flow ◽  
Optimization Problem ◽  
Flow Model ◽  
Expansion Method ◽  
Pso Algorithm ◽  
Photovoltaic System ◽  
System Generation ◽  
Probabilistic Power Flow ◽  
The Cost

With the distributed generation such as photovoltaic power system (PVS) is largely introduced into power grid, some significant problems such as system instability problem increase seriously. In order to make full use of PVS and make sure the voltage exceeding probability is limited within a certain range to ensure the power quality, as well as consider the cost of access device, the suitable PVS access node and capacity is important. Based on this problem, this paper establishes the probabilistic power flow model of PVS by introducing the combined Cumulants and the Gram-Charlier expansion method. Also, to solve the nonlinear combinatorial optimization problem, this paper uses PSO algorithm. Finally to get the suitable PVS access node and capacity, also calculate the solution of voltage exceeding probability.

Parallel Volume Integral Equation Method for Two-Dimensional Elastodynamic Analysis

2019 ◽  
Vol 16 (06) ◽  
pp. 1840025
Author(s):  
Jungki Lee ◽  
Hogwan Jeong
Keyword(s):  
Integral Equation ◽  
Wave Scattering ◽  
Integral Equation Method ◽  
Equation Method ◽  
Two Dimensional ◽  
Volume Integral ◽  
Scattering Problems ◽  
Volume Integral Equation ◽  
Parallel Volume ◽  
Volume Integral Equation Method

The parallel volume integral equation method (PVIEM) is applied for the analysis of two-dimensional elastic wave scattering problems in an unbounded isotropic solid containing various types of multiple multilayered anisotropic inclusions. It should be noted that the volume integral equation method (VIEM) does not require the use of the Green’s function for the anisotropic inclusion — only the Green’s function for the unbounded isotropic matrix is needed. A detailed analysis of the SH wave scattering problem is presented for various types of multiple multilayered orthotropic inclusions. Numerical results are presented for the elastic fields at the interfaces for square and hexagonal packing arrays of various types of multilayered orthotropic inclusions in a broad frequency range of practical interest. Standard parallel programming was used to speed up computation in the VIEM. The PVIEM enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), multilayer’s shapes and geometry, isotropy/anisotropy, and softness/hardness of various types of multiple multilayered anisotropic inclusions on displacements and stresses at the interfaces of the inclusions and far-field scattering patterns. Also, powerful capabilities of the PVIEM for the analysis of general two-dimensional multiple scattering problems are investigated.

WATER WAVE SCATTERING BY A VERTICAL POROUS BARRIER WITH TWO GAPS

2019 ◽  
Vol 61 (1) ◽  
pp. 47-63 ◽  
Author(s):  
M. SIVANESAN ◽  
S. R. MANAM
Keyword(s):  
Water Wave ◽  
Wave Scattering ◽  
Original Problem ◽  
Analytical Procedure ◽  
Explicit Solutions ◽  
Scattering Problems ◽  
Geometrical Structures ◽  
Water Wave Scattering ◽  
Weakly Singular ◽  
Porous Barrier

Explicit solutions are rarely available for water wave scattering problems. An analytical procedure is presented here to solve the boundary value problem associated with wave scattering by a complete vertical porous barrier with two gaps in it. The original problem is decomposed into four problems involving vertical solid barriers. The decomposed problems are solved analytically by using a weakly singular integral equation. Explicit expressions are obtained for the scattering amplitudes and numerical results are presented. The results obtained can be used as a benchmark for other wave scattering problems involving complex geometrical structures.

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