### ASA 127th Meeting M.I.T. 1994 June 6-10

## 4pSAa12. Evolution of energy methods for calculation of engineering
structures vibration.

**Alexei S. Nikiforov
**

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*Krylov Shipbuilding Res. Inst., 196158, Moskovskoe shosse, 44, St.
Petersburg, Russia
*

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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.