INTEGRAL-EQUATION FORMULATION FOR TRANSIENT STRUCTURAL SYNTHESIS

An exact formulation for time domain structural synthesis is developed. Volterra integral equations are derived from the convolution integral which address substructure coupling and structural modification. The theory is cart in physical coordinates and, therefore, no transformation or mode truncation is required to achieve model reduction, As a minimum, only those coordinates directly involved in the synthesis need be retained, although synthesized transient response can be found for all coordinates, if so desired. The formulation makes use of transient response data and impulse response functions at the retained physical coordinates. Modified or coupled transient response is directly calculated; no synthesized system model is assembled. The formulation exactly synthesizes system damping, regardless of the uncoupled system damping models used, The numerical solution of the integral equations involves the solution of a lower triangular linear system only; no matrix factorization or eigensolution is required. Simple yet representative numerical examples are included.