Analytical solution of problem of shielding low-frequency magnetic field by thin-walled cylindrical screen in presence of cylinder by G. Ch. Shushkevich

“…It is shown that the solution of formulated boundary value problem is reduced to the solution of linear algebraic equations system for coefficients included in the representation of secondary fields. …”
Get full text

Variationally Improved Bézier Surfaces with Shifted Knots by Daud Ahmad, Kanwal Hassan, M. Khalid Mahmood, Javaid Ali, Ilyas Khan, M. Fayz-Al-Asad

“…Instead of variational minimization of usual area functional, the quasi-minimal Bézier surface with shifted knots is obtained as the solution of variational minimization of Dirichlet functional that turns up as the sum of two integrals and the vanishing condition gives us the system of linear algebraic constraints on the control points. The coefficients of these control points bear symmetry for the pair of summation indices as well as for the pair of free indices. …”
Get full text

Free Vibration Analysis of Laminated Composite Double-Plate Structure System with Elastic Constraints Based on Improved Fourier Series Method by Ying Zhang, Dongyan Shi, Dongze He, Dong Shao

“…After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. …”
Get full text

Phase-lag mixed integral equation of a generalized symmetric potential kernel and its physical meanings in (3+1) dimensions by Azhar Rashad Jan

“…The degenerate method is employed to deduce the linear algebraic system (LAS). In addition, our endeavor yielded novel and distinct instances. …”
Get full text

FEATURES OF ELECTROMECHANICAL ACOUSTIC ENERGY CONVERSION BY CYLINDRICAL PIEZOCERAMIC TRANSDUCERS WITH INTERNAL SCREENS IN COMPOSITION OF FLAT SYSTEMS by A. G. Leiko, I. V. Kandrachuk, A. O. Sviatnenko

“…The physical fields arising from the emission of sound by such a system are determined by the joint solution of the system of differential equations: the wave equation; equations of motion of thin piezoceramic shells with circular polarization in displacements; the equations of forced electrostatics for piezoceramics at given boundary conditions, the conditions of conjugation of fields at the boundaries of the division of domains and electric conditions.The solution of the problem is reduced to the solution of an infinite system of linear algebraic equations with respect to unknown coefficients of field expansions.An analysis of the results of numerical calculations, performed on the basis of the obtained analytical relations, called to establish a number of features in the electromechanical acoustic transformation of energy by emitters in the composition of flat systems. …”
Get full text

PHYSICAL FIELDS OF CIRCULAR CYLINDRICAL PIEZOCERAMIC RECEIVER IN PRESENCE OF A FLAT ACOUSTIC SOFT SCREEN by A. V. Derepa, A. G. Leiko, O. N. Pozdniakova

“…The physical fields of the system under consideration were determined by following solutions: the wave equation; equations of motion of thin piezoceramic cylindrical shells in displacements; equations of stimulated electrostatics for piezoceramics for given boundary conditions, conditions for coupling fields at interfaces and electrical conditions.A general conclusion was made concerning solving of an infinite system of linear algebraic equations with respect to the unknown coefficients of the expansion of the fields. …”
Get full text

Accelerated Modeling of Transients in Electromagnetic Devices Based on Magnetoelectric Substitution Circuits by Sergii Tykhovod, Ihor Orlovskyi

“…This helps to transform integro-differential state equations into linear algebraic equations for the representations of the solution functions. …”
Get full text

First Basic Problem of Elasticity Theory for a Composite Layer with Two Thick-Walled Tubes by Oleksandr Yu. Denshchykov, Valentyn P. Pelykh, Yaroslav V. Hrebeniuk, Vitalii Yu. Miroshnikov

“…Satisfying the boundary conditions and conjugation conditions between the layer and the tubes, an infinite system of integro-algebraic equations is formed, which is reduced to linear algebraic equations of the second kind, and the reduction method is applied. …”