Forced vibrations of two welded plates: A prototype for assessment of the extent of applicability of SEA concepts

Abstract

Statistical Energy Analysis (SEA) has as a fundamental tenet that the power flow between two vibrating components of a system is a weighted difference of the energies of the two components, where the coefficients are intrinsic properties of the system, independent of the excitation. A prototype that may give new insight into when and to what extent such a tenet is satisfied for strongly coupled continuous systems is explored here. Two rectangular plates, welded together at right angles along a common edge and simply supported at all other edges are caused to vibrate by random forces applied on one of the plates. The displacement field of each plate is expanded in modal eigenfunctions of the uncoupled plates following a procedure analogous to that previously used for strongly coupled beams by Davies and Wahab [J. Sound Vib. 77, 311–321 (1981)]. The formally exact solution for plate energy spectral density and power flow spectral density is given and is approximated by replacing modal sums by integrals. At higher frequencies and with averages over sufficiently wide frequency bands, the theory yields approximate results consistent with SEA concepts. [Work supported by Whirlpool Corporation.] S77_4 S77 S77 4 Forced vibrations of two welded plates: A prototype for assessment of the extent of applicability of SEA concepts Emilios K. Dimitriadis Allan D. Pierce School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332 Statistical Energy Analysis (SEA) has as a fundamental tenet that the power flow between two vibrating components of a system is a weighted difference of the energies of the two components, where the coefficients are intrinsic properties of the system, independent of the excitation. A prototype that may give new insight into when and to what extent such a tenet is satisfied for strongly coupled continuous systems is explored here. Two rectangular plates, welded together at right angles along a common edge and simply supported at all other edges are caused to vibrate by random forces applied on one of the plates. The displacement field of each plate is expanded in modal eigenfunctions of the uncoupled plates following a procedure analogous to that previously used for strongly coupled beams by Davies and Wahab [J. Sound Vib. 77, 311–321 (1981)]. The formally exact solution for plate energy spectral density and power flow spectral density is given and is approximated by replacing modal sums by integrals. At higher frequencies and with averages over sufficiently wide frequency bands, the theory yields approximate results consistent with SEA concepts. [Work supported by Whirlpool Corporation.]