L. Ji

The statistical energy analysis of coupled sets of oscillators

The paper concerns the statistical energy analysis (SEA) of two conservatively coupled oscillators, sets of oscillators and continuous subsystems under broadband excitation. The oscillator properties are assumed to be random and ensemble averages found. Account is taken of the correlation between the coupling parameters and the oscillator energies. For coupled sets of oscillators or continuous subsystems, it is assumed that the coupling power between a pair of oscillators is proportional to the difference of either their actual energies or their ‘blocked’ energies, and expressions for the ensemble averages and coupling loss factors (CLFs) are found. Various observations are made, some of which differ from those that are commonly assumed within SEA. The coupling power and CLF are governed by two parameters: the ‘strength of connection’ and the ‘strength of coupling’. The CLF is proportional to damping at low damping and independent of damping in the high damping, weak coupling limit. Equipartition of energy does not occur as damping tends to zero, except for the case of two oscillators that have identical natural frequencies. While attention is focused on spring-coupled oscillators, similar results hold for more general forms of conservative coupling. The examples of two spring-coupled rods and two spring-coupled plates are considered. Conventional SEA and the coupled oscillator results are in good agreement for weak coupling but diverge for strong coupling. For strong coupling and weak connection, the coupled oscillator results agree well with an exact wave analysis and Monte Carlo simulations.

A power mode approach to estimating vibrational power transmitted by multiple sources

A power mode method for the estimation of the power transmitted to a flexible receiver by an array of point force excitations is described. The vibrational power transmitted by N discrete point forces is regarded as the power transmitted by N independent power modes following eigendecomposition of the mobility matrix of the receiving structure. Approximate expressions for the upper and lower bounds and the mean value of the transmitted power are then developed in terms of these power modes. The approach is extended to more general cases, including that where both force and moment excitations are applied to the structure and where there are velocity source excitations. Numerical examples are presented.

Estimation of power transmission to a flexible receiver from a stiff source using a power mode approach

A power mode approach to estimating the vibrational power transmitted to a receiver structure by multiple sources is reviewed. This approach is then extended to estimating the power transmitted to a flexible receiver from a stiff source through discrete couplings. There may be both translational and rotational coupling degrees of freedoms, and/or force and moment excitations. Approximations are developed for the upper and lower bounds and the frequency average of the transmitted power. These depend only on the point mobilities of the source and receiver, and thus require much less data than an exact description. The approximations are most accurate when the mobility or stiffness mismatch of the coupled system is large enough, e.g., the source has, on average, low mobility compared to that of the receiver. Numerical examples are presented concerning a multi-point coupled beam/plate model.