On the Application of Beam on Elastic Foundation Theory to the Analysis of Stiffened Plate Strips

The main objective of this thesis is to show that plate strips subjected to transverse line loads can be analysed by using the beam on elastic foundation (BEF) approach. It is shown that the elastic behaviour of both the centre line section of a semi infinite plate supported along two edges, and the free edge of a cantilever plate strip can be accurately predicted by calculations based on the two parameter BEF theory. The transverse bending stiffness of the plate strip forms the foundation. The foundation modulus is shown, mathematically and physically, to be the zero order term of the fourth order differential equation governing the behaviour of BEF, whereas the torsion rigidity of the plate acts like pre tension in the second order term. Direct equivalence is obtained for harmonic line loading by comparing the differential equations of Levy's method (a simply supported plate) with the BEF method. By equating the second and zero order terms of the semi infinite BEF model for each harmonic component, two parameters are obtained for a simply supported plate of width B: the characteristic length, 1/ λ, and the normalized sum, n, being the effect of axial loading and stiffening resulting from the torsion stiffness, nlin. This procedure gives the following result for the first mode when a uniaxial stress field was assumed (ν = 0): 1/λ = √2B/π and nlin = 1. For constant line loading, which is the superimposition of harmonic components, slightly differing foundation parameters are obtained when the maximum deflection and bending moment values of the theoretical plate, with v = 0, and BEF analysis solutions are equated: 1 /λ= 1.47B/π and nlin. = 0.59 for a simply supported plate; and 1/λ = 0.99B/π and nlin = 0.25 for a fixed plate. The BEF parameters of the plate strip with a free edge are determined based solely on finite element analysis (FEA) results: 1/λ = 1.29B/π and nlin. = 0.65, where B is the double width of the cantilever plate strip. The stress biaxial, v > 0, is shown not to affect the values of the BEF parameters significantly the result of the geometric nonlinearity caused by in plane, axial and biaxial loading is studied theoretically by comparing the differential equations of Levy's method with the BEF approach. The BEF model is generalised to take into account the elastic rotation stiffness of the longitudinal edges. Finally, formulae are presented that take into account the effect of Poisson's ratio, and geometric non linearity, on bending behaviour resulting from axial and transverse inplane loading. It is also shown that the BEF parameters of the semi infinite model are valid for linear elastic analysis of a plate strip of finite length. The BEF model was verified by applying it to the analysis of bending stresses caused by misalignments in a laboratory test panel. In summary, it can be concluded that the advantages of the BEF theory are that it is a simple tool, and that it is accurate enough for specific stress analysis of semi infinite and finite plate bending problems.

Analysis and Control of Excitation, Field Weakening and Stability in Direct Torque Controlled Electrically Excited Synchronous Motor Drives

Direct torque control (DTC) is a new control method for rotating field electrical machines. DTC controls directly the motor stator flux linkage with the stator voltage, and no stator current controllers are used. With the DTC method very good torque dynamics can be achieved. Until now, DTC has been applied to asynchronous motor drives. The purpose of this work is to analyse the applicability of DTC to electrically excited synchronous motor drives. Compared with asynchronous motor drives, electrically excited synchronous motor drives require an additional control for the rotor field current. The field current control is called excitation control in this study. The dependence of the static and dynamic performance of DTC synchronous motor drives on the excitation control has been analysed and a straightforward excitation control method has been developed and tested. In the field weakening range the stator flux linkage modulus must be reduced in order to keep the electro motive force of the synchronous motor smaller than the stator voltage and in order to maintain a sufficient voltage reserve. The dynamic performance of the DTC synchronous motor drive depends on the stator flux linkage modulus. Another important factor for the dynamic performance in the field weakening range is the excitation control. The field weakening analysis considers both dependencies. A modified excitation control method, which maximises the dynamic performance in the field weakening range, has been developed. In synchronous motor drives the load angle must be kept in a stabile working area in order to avoid loss of synchronism. The traditional vector control methods allow to adjust the load angle of the synchronous motor directly by the stator current control. In the DTC synchronous motor drive the load angle is not a directly controllable variable, but it is formed freely according to the motor’s electromagnetic state and load. The load angle can be limited indirectly by limiting the torque reference. This method is however parameter sensitive and requires a safety margin between the theoretical torque maximum and the actual torque limit. The DTC modulation principle allows however a direct load angle adjustment without any current control. In this work a direct load angle control method has been developed. The method keeps the drive stabile and allows the maximal utilisation of the drive without a safety margin in the torque limitation.