Forward and backward continuation for neutral functional differential equations

Basic theory of existence, uniqueness, and continuation for neutral functional differential equation

Attracting Manifolds for Evolutionary Equations

Attracting Manifolds for Evolutionary Equation

Coupled Oscillators on a Circle

We consider a continuum of diffusively coupled oscillators on a circle. When each oscillator is of Lienard type, very little is known about the corresponding hyperbolic POE. When each oscillator is represented by a lossless transmission line, we obtain a partial neutral delay differential equation and give the beginnings of a qualitative theory for the dynamics. In particular, we discuss the properties of the solution map, the existence of the global attractor, behavior near an equilibrium point including the Hopf bifurcation, and some elementary properties near a periodic orbit

Meshless methods for shear-deformable beams and plates based on mixed weak forms

Thin structural theories such as the shear-deformable Timoshenko beam and Reissner-Mindlin plate theories have seen wide use throughout engineering practice to simulate the response of structures with planar dimensions far larger than their thickness dimension. Meshless methods have been applied to construct numerical methods to solve the shear deformable theories. Similarly to the finite element method, meshless methods must be carefully designed to overcome the well-known shear-locking problem. Many successful treatments of shear-locking in the finite element literature are constructed through the application of a mixed weak form. In the mixed weak form the shear stresses are treated as an independent variational quantity in addition to the usual displacement variables. We introduce a novel hybrid meshless-finite element formulation for the Timoshenko beam problem that converges to the stable first-order/zero-order finite element method in the local limit when using maximum entropy meshless basis functions. The resulting formulation is free from the effects shear-locking. We then consider the Reissner-Mindlin plate problem. The shear stresses can be identified as a vector field belonging to the Sobelov space with square integrable rotation, suggesting the use of rotated Raviart-Thomas-Nedelec elements of lowest-order for discretising the shear stress field. This novel formulation is again free from the effects of shear-locking. Finally we consider the construction of a generalised displacement method where the shear stresses are eliminated prior to the solution of the final linear system of equations. We implement an existing technique in the literature for the Stokes problem called the nodal volume averaging technique. To ensure stability we split the shear energy between a part calculated using the displacement variables and the mixed variables resulting in a stabilised weak form. The method then satisfies the stability conditions resulting in a formulation that is free from the effects of shear-locking.Open Acces

Limits of Semigroups Depending on Parameters

nuloIt is reasonable to compare dissipative semigroups with a global attractor by restricting the flows to the attractor. However, if the rate of approach to the attractor is not uniform with respect to parameters, then the transient behavior near the attractor will give more information. We introduce a concept which takes into account this transient behavior. The concept also is useful when the limit system is conservative. We give the general theory with applications to parabolic and hyperbolic PDE on thin domains as well as situations where the limit problem is conservative

Active Vibration Control of a Doubly Curved Composite Shell Stiffened by Beams Bonded with Discrete Macro Fibre Composite Sensor/Actuator Pairs

Doubly curved stiffened shells are essential parts of many large-scale engineering structures, such as aerospace, automotive and marine structures. Optimization of active vibration reduction has not been properly investigated for this important group of structures. This study develops a placement methodology for such structures under motion base and external force excitations to optimize the locations of discrete piezoelectric sensor/actuator pairs and feedback gain using genetic algorithms for active vibration control. In this study, fitness and objective functions are proposed based on the maximization of sensor output voltage to optimize the locations of discrete sensors collected with actuators to attenuate several vibrations modes. The optimal control feedback gain is determined then based on the minimization of the linear quadratic index. A doubly curved composite shell stiffened by beams and bonded with discrete piezoelectric sensor/actuator pairs is modeled in this paper by first-order shear deformation theory using finite element method and Hamilton’s principle. The proposed methodology is implemented first to investigate a cantilever composite shell to optimize four sensor/actuator pairs to attenuate the first six modes of vibration. The placement methodology is applied next to study a complex stiffened composite shell to optimize four sensor/actuator pairs to test the methodology effectiveness. The results of optimal sensor/actuator distribution are validated by convergence study in genetic algorithm program, ANSYS package and vibration reduction using optimal linear quadratic control scheme