Study on the exactness of alternative indirect force estimation methods, power dissipation calculation by power or energy flow, and transfer path analysis for structure-borne sound

In our presentation, it is first clarified that the matrix inverse method which gives interfacial forces using X/F-type frequency response functions among parallel interfacial points is an exact method derived from Newton’s equation of motion. The alternative method using F/X-type frequency response functions with blocked boundaries is next explained as another exact method, though implementation of the blocked boundary may be difficult for real-life systems. Next, as an application of interfacial force, it is shown that the real part of power flow and the imaginary part of energy flow correspond to mechanical power dissipation. When all the power or energy flows into a system are counted, it gives the exact power dissipation of the system. As another application, the exactness of transfer path analysis for structure-borne sound is examined with brief discussion of velocity potential. Computational demonstrations and validations are given for the derived formulas, using a simple finite element model. All ...