Finite Element Programs for Structural Vibrations

1 The Finite Element Method.- 1.1 The Finite Element Method.- 1.2 Derivation of the Elemental Stiffness Matrix of a Rod.- 1.3 Derivation of the Elemental Mass Matrix for a Rod.- 1.4 System Stiffness and Mass Matrices.- 1.5 Elemental Stiffness and Mass Matrices in Global Coordinates.- 1.6 Elemental [k] and [m] for a Beam.- 2 Problem Solving in Structural Vibrations.- 2.1 Plane Pin-jointed Trusses.- 2.2 Continuous Beams.- 2.3 Pin-jointed Space trusses.- 3 The Modular Approach in Finite Element Programming.- 3.1 Flow Diagram.- 3.2 The Modular Approach in Programming.- 4 Vibrations of Plane Pin-jointed Trusses.- 4.1 Description of Program.- 4.2 Data.- 4.3 Vibration Problems Involving Plane Pin-jointed Trusses.- 5 Vibrations of Continuous Beams.- 5.1 Description of Program.- 5.2 Data.- 5.3 Continuous Beams Problems.- 6 Vibrations of Rigid-jointed Plane Frames.- 6.1 Description of Program.- 6.2 Data.- 6.3 Rigid-jointed Plane Frame Problems.- 7 Vibrations of Space Trusses.- 7.1 Description of Program.- 7.2 Data.- 7.3 Pin-jointed Space Truss Problems.- 8 Vibrations of Rigid-jointed Space Frames.- 8.1 Description of Program.- 8.2 Data.- 8.3 Rigid-jointed Space Frame Problems.- 9 Vibration of Grillages.- 9.1 Description of Program.- 9.2 Data.- 9.3 Grillage Problems.- Appendix 1 Computer Program for the Vibration of Plane Pin-jointed Trusses.- Appendix 2 Computer Program for the Vibration of Continuous Beams.- Appendix 3 Computer Program for the Vibration of Rigid-jointed Plane Frames.- Appendix 4 Computer Program for the Vibration of Pin-jointed Space Trusses.- Appendix 5 Computer Program for the Vibration of Rigid-jointed Space Frames.- Appendix 6 Computer Program for the Vibration of Cross-stiffened Grids.- References.