Some effects of tyre tread and road surface on road noise

A complex dynamic system can often be modeled in terms of coupled basic dynamic systems. A basic dynamic system is a system whose response can be specified in terms of a scalar quantity. A general formalism, dealing with the response of a complex dynamic system, is developed. The formalism spans several previous formalisms and encompasses new material that has not been previously considered, e.g., direct couplings between the ribs on a panel. The format is chosen so that it provides for consideration of elements of the statistical energy analysis (SEA). Thus, for example, the expression for the frequency spectral power flow between two basic dynamic systems is derived and cast in a modal form. In particular, various conditions and approximations under which cross modal terms vanish in the expression are specified and interpreted. Modal densities are defined and used to obtain further reductions in the expression for the power flow between two multimodal basic dynamic systems.