Random energy flow analysis of coupled beam structures and its correlation with SEA

Abstract

Energy flow analysis (EFA) method is a vibration simulation tool developed for structures under single-frequency excitation. The work described in this paper aims to extend the application of EFA to situations where structures are subject to random broadband excitations. The proposed energy formulation for beam structures under random excitations, which is based on conventional EFA, is referred to as random EFA. Due to the new capability of random EFA, a comprehensive relationship between random EFA and the widely used statistical energy analysis (SEA) method in modeling energy response as well as power flow is established. Both random EFA and SEA are utilized to model the vibration behavior of a complex planar frame structure on which random broadband forces are applied. Good correlation between energy as well as power flow solutions is demonstrated between the two methods for beam members in close proximity to the external excitations, which validates the random EFA development.

Experimental measurement of energy density of a vibrating beam

“…It states a relationship between dissipated power, energy density stored in the control volume, and the simple relationship between space and time-averaged energy density and intensity. For a transversely vibrating beam, on which a concentrated force is applied, the EFEA equation gives the energy distribution on the beam is (You et al., 2011) where 〈e〉 is the far field, locally space and time averaged energy density, c g is the group velocity of flexural waves, η is the structural loss factor, Pin is the time averaged power input, and δ(x-x0)is the Dirac delta function.…”

“…Cho (1993) formulated a system of equations of EFEA and calculated power transmission factors for coupled structures. You et al. (2011) extended the application of EFA to the random vibrations of beams.…”

Validity Investigation of Random Energy Flow Analysis for Beam Structures

“…where E is an energy variable associated with position as well as frequency, which represents the time and locally space averaged energy density spectrum [25], ω is the radian frequency of the excitation, c g is the group velocity of bending waves, η is the structural loss factor, δ(x) is the Dirac delta function defining the location of the driving force, Π in is the real part of the cross spectrum between the random force and velocity response at the driving point, which is defined as the power input spectrum of the random excitation. The time averaged energy density of waves with different frequencies are incoherent and can be superimposed, and this accounts for the validity of applying the energy conductivity equation of EFA with respect to the differential spectral component of relative spectrum quantities, as expressed in Eq.…”

“…The average energy density and intensity of a beam under stationary random excitation can be obtained from the integration of the approximate energy density spectrum solved from Eq. 2, which are respectively given by [25] e(x) = 1 2π…”

“…The energy flow characteristics of beams and plates under random excitations were once investigated using EFA [8,9], where the energy response characteristics of the structures in one frequency band in the relatively low frequency range were mainly focused on. The application of EFA for beam structures under random excitation is systematically proposed by You et al [25], which is referred to as random energy flow analysis. In random EFA, the average energy density is not solved directly from the energy conductivity equation of EFA but indirectly obtained from the spectral integration of an energy spectrum variable, and a detailed relationship between random EFA and SEA is established with respect to both energy and power flow variables for coupled beam structures.…”