TY - JOUR
T1 - Approximate elliptical integral solution for the large amplitude free vibration of a rectangular single mode plate backed by a multi-acoustic mode cavity
AU - Hui, C.K.
AU - Lee, Y.Y.
AU - Reddy, J.N.
PY - 2011/9
Y1 - 2011/9
N2 - The nonlinear structuralacoustic problem considered in this study is the large amplitude free vibration of a rectangular elastic plate backed by a cavity. Very few classical solutions for this nonlinear structuralacoustic problem have been developed, although there are many for nonlinear plate or linear structuralacoustic problems. Thus, the main contributions of this study paper include (1) a concise multi-acoustic single structural modal formulation that is derived from two coupled partial differential equations representing the nonlinear structural free vibration and the acoustic pressure induced and (2) the approximate elliptical integral solution that is obtained by solving one residual equation only, and well agrees with that obtained from a harmonic balance finite element analysis. It is found that the natural frequency convergences with the increase in the numbers of acoustic modes and harmonic terms, and the effects of vibration amplitude, air cavity depth, and aspect ratio on the nonlinear natural frequency are also examined.
AB - The nonlinear structuralacoustic problem considered in this study is the large amplitude free vibration of a rectangular elastic plate backed by a cavity. Very few classical solutions for this nonlinear structuralacoustic problem have been developed, although there are many for nonlinear plate or linear structuralacoustic problems. Thus, the main contributions of this study paper include (1) a concise multi-acoustic single structural modal formulation that is derived from two coupled partial differential equations representing the nonlinear structural free vibration and the acoustic pressure induced and (2) the approximate elliptical integral solution that is obtained by solving one residual equation only, and well agrees with that obtained from a harmonic balance finite element analysis. It is found that the natural frequency convergences with the increase in the numbers of acoustic modes and harmonic terms, and the effects of vibration amplitude, air cavity depth, and aspect ratio on the nonlinear natural frequency are also examined.
KW - Elliptical integral
KW - Large amplitude vibration
KW - Structuralacoustic interaction
UR - http://www.scopus.com/inward/record.url?scp=79959327417&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-79959327417&origin=recordpage
U2 - 10.1016/j.tws.2011.03.002
DO - 10.1016/j.tws.2011.03.002
M3 - 21_Publication in refereed journal
VL - 49
SP - 1191
EP - 1194
JO - Thin-Walled Structures
JF - Thin-Walled Structures
SN - 0263-8231
IS - 9
ER -