PRESSURE-BASED AND POTENTIAL-BASED DIFFERENTIAL QUADRATURE PROCEDURES FOR FREE VIBRATION OF CIRCULAR PLATES IN CONTACT WITH FLUID

Abstract

THE DIFFERENTIAL QUADRATURE METHOD (DQM) HAS BEEN SO FAR APPLIED TO A WIDE VARIETY OF FLUID AND/OR STRUCTURAL PROBLEMS. THE RESULTS OF MANY RESEARCHERS REVEAL THAT THE DQM IS COMPUTATIONALLY EFFICIENT AND IS APPLICABLE TO A LARGE CLASS OF BOUNDARY VALUE PROBLEMS. HOWEVER, THERE IS LITTLE INFORMATION ABOUT ITS APPLICATIONS TO FLUID-STRUCTURE INTERACTION PROBLEMS. THEREFORE, THE PURPOSE OF THIS PAPER IS TO PROVIDE SOME INFORMATION IN THIS AREA AND TO DEVELOP PROCEDURES BASED ON THE DQM FOR THE NUMERICAL SOLUTION OF FLUID-STRUCTURE INTERACTION PROBLEMS. FIRST, THE GOVERNING PARTIAL DIFFERENTIAL EQUATIONS OF MOTION OF THE STRUCTURE AND FLUID ARE DISCRETIZED SEPARATELY USING THE DQM. THEN, BY APPLYING THE BOUNDARY CONDITION AT FLUID-STRUCTURE INTERFACE, THE GOVERNING EIGENVALUE EQUATIONS OF THE COUPLED SYSTEM ARE OBTAINED WHICH CAN THEN BE SOLVED FOR THE EIGENVALUES OF THE SYSTEM. THE APPLICABILITY OF THE PROPOSED PROCEDURES IS SHOWN HEREIN THROUGH THE FREE VIBRATION ANALYSIS OF THIN CIRCULAR PLATES IN CONTACT WITH A CYLINDRICAL FLUID-FILLED CAVITY. ISSUES RELATED TO THE IMPLEMENTATION OF THE REGULARITY CONDITIONS AT THE CENTER OF THE CIRCULAR PLATE AND THE CENTRAL LINE OF THE CYLINDRICAL CAVITY ARE ADDRESSED. TWO NEW REGULARITY CONDITIONS ARE PROPOSED FOR THE CIRCULAR CYLINDRICAL FLUID DOMAIN. THE ACCURACY AND EFFICIENCY OF THE PROPOSED PROCEDURES ARE DEMONSTRATED BY COMPARING THE OBTAINED RESULTS WITH THOSE AVAILABLE IN THE LITERATURE. IT IS SHOWN THAT HIGHLY ACCURATE CONVERGED RESULTS CAN BE OBTAINED BY THE PROPOSED PROCEDURES USING A SMALL NUMBER OF GRID POINTS. THREE NEW DIMENSIONLESS PARAMETERS AND VARIABLES ARE ALSO INTRODUCED FOR THE FREE VIBRATION OF THE COUPLED SYSTEM. THE INFLUENCES OF THESE PARAMETERS ON DYNAMIC BEHAVIOR OF THE SYSTEM ARE STUDIED.