The Kantorovich-Vlasov method was used, in this study, for the flexural analysis of rectangular Kirchhoff plates with opposite edges (x = 0, and x = a) simply supported and the other opposite edges (y = 0, and y = b) clamped (CSCS plates). The plate was subjected to a linear distribution of load over the entire plate domain. Vlasov method was used in finding the coordinate function in the x-direction, and Kantorovich method was used to consider the displacement function for the plate. The total potential energy functional, and the corresponding Euler-Lagrange differential equations were then obtained for the plate problem. This was solved subject to the boundary conditions in the y direction to obtain the displacement function which minimized the total potential energy functional. Bending moment distributions were obtained using the bending moment-displacement equations. The solutions obtained for deflection and bending moment distributions were found to be rapidly convergent single series. Deflections and bending moment computed at the center of the plate were also rapidly convergent series. The solutions obtained for deflections and bending moments (M xx and M yy) were exactly identical with solutions presented by Timoshenko and Woinowsky-Krieger who used the method of superposition.

Abstract-Electrical energy is indispensable in people's lives for the sake of survival and for life on the work. Society is now very dependent on electric energy because without the existence of electrical energy the community activity will be stalled.The loads used in electric energy operations vary widely. Electrical energy operations are severely disrupted due to unbalanced load and nonlinear loads. Unbalanced load and nonlinear loads used for the operation of electrical energy can be disturbing because they produce non-pure sinusoidal waves. THD_i (harmonics) caused by the unbalance of load and nonlinear load have an impact on electric energy losses and heat on the transformer. THD_i (harmonics) is caused by unbalance of load and nonlinear load Between Phases RN equal to 7.87%, at SN equal to 3.22%, and at TN 2,41%. After the Passive Filter design is installed THD_i between Phases becomes smaller that is at RN becomes 1.82%, SN becomes 0.82%, and in TN becomes 0.57%.THD_i (harmonics) between phases can be decreased by 76% after Passive Filter is installed. Desain Passive filters are very effective at reducing THD_i (harmonics) in buildings such as laboratories that use the load of imbalances and nonlinear loads for lab.For your paper to be published in the conference proceedings, you must use this document as both an instruction set and as a template into which you can type your own text. If your paper does not conform to the required format, you will be asked to fix it. Keyword : Passive Filter Design, THD_i (Harmonics), Lighting, Convenience.I. INTRODUCTION The use of electrical appliances is increasingly a top priority and causes more expensive electrical energy. Electrical equipment used in power systems can affect the distribution of electrical energy. Distribution of electrical energy is affected by the unbalanced load and non-linear loads used by consumers. Unbalanced loads and nonlinear loads cause current and voltage THD_i (harmonics) and they affect electrical energy conditions. The distortion of the current wave and the voltage generated from the imbalance and non-linear load will be formed waves.The form of current and voltage supplied by an electric power system generator that ideal for the consumer is a pure sinusoid wave. THD_i (harmonics) is generated by the unbalance of load and the nonlinear load forms an impure wave and causes heat to the distribution transformer. Total Harmonic Distortion (THD) depends largely on the unbalance load andof non-linear load ⦋3⦌ . Equipment that uses semiconductor components can be categorized non linear load. The waves generated by the nonlinear load affect the original wave so that the original wave becomes defective and not a sinusoidal wave anymore. Defective waves will cause a decrease in performance on the equipment and will even be damaged. These defective waves can also cause a decrease in fundamental voltage and RMS current on each channel. Defective waves will affect the distribution of electrical energy and cause the phase of the neutral current to ...

Abstract-In this work, the mathematical theory of elasticity has been used to formulate and derive from fundamental principles, the first order shear deformation theory originally presented by Mindlin using variational calculus. A relaxation of the Kirchhoff's normality hypothesis was used to account for the effect of the transverse shear strains in the behaviour of the plate. This made the resulting theory appropriate for use for moderately thick plates. A simultaneous use of the strain-displacement relations for small-deformation elasticity, stress-strain laws and the stress differential equations of equilibrium was used to obtain the differential equations of static flexure for Mindlin plates in terms of three unknown generalised displacements. The equations were found to be coupled in the unknown displacements; but reducible to the Kirchhoff plate equations when the removed Kirchhoff normality hypothesis was introduced. This showed the Kirchhoff plate theory to be a specialization of the Mindlin plate theory. The theory of elasticity foundations of the Mindlin and Kirchhoff plate theories are thus highlighted.