Alexei S. Nikiforov
Krylov Shipbuilding Res. Inst., 196158, Moskovskoe shosse, 44, St. Petersburg, Russia
Energy methods (for example, statistical energy analysis) are used for a calculation of various engineering structures (ships, aircraft, cars, etc.) for a long time. Methods by Westphal and by Maidanik and Lyon proposed by them in 1950--1960 led to make calculations by a numerical solution of algebraical equations systems. Recently the method of equivalent plates was proposed to determine a distribution of vibration energy on a surface of structure elements by using differential equations similar to heat conductivity ones. Sometimes solutions of these equations can be received in analytical form. Equations of energy balance are formulated in a general form. Coupling coefficients in Westphal's and Maidanik--Lyon's forms are solved for diffusive fields of bending waves. Limitations for the use of these coefficients are discussed in reference to a frequency range and difference of thickness of jointed plates. Examples of the use of Westphal's and Maidanik--Lyon's methods are shown. Some examples of an analytical solution of equations for equivalent plates method are shown for various boundary conditions. Solutions received by Westphal's and equivalent plates methods are compared.