Probabilistic and Convex Modelling of Acoustically Excited Structures

Preface. 1. Free Vibration of Single-Span Beams. 1.1. Basic equations and method of solution. 1.2. Boundary conditions. 1.3. Determination of natural frequencies and mode shapes. 2. Free Vibration of Multi-Span Periodic Beams. 2.1. Introduction. 2.2. Two-span beams. 2.3. Multi-span beams on rigid supports. 2.4. Multi-span beams with additional rotational spring at each support. 2.5. Orthogonality conditions. 3. Free Vibration of Rectangular Plates. 3.1. Single-span plates with classical boundary conditions. 3.2. Single-span plates with mixed classical and elastic supports. 3.3. Multi-span plates on rigid supports. 4. Bolotin's Method of Dynamic Edge Effect and Its Generalization. 4.1. Free vibration of uniform beams. 4.2. Free vibration of uniform isotropic plates. 4.3. Generalization of Bolotin's dynamic edge-effect method. 4.4. Some numerical results for orthotropic plates. 4.5. Free vibration of all-round edge-stiffened plates. 4.6. Free vibration of multi-span stiffened plates. 5. Random Vibration of Structures. 5.1. Correlation and spectral analysis. 5.2. Random vibration of linear discrete systems. 5.3. Random vibration of linear continuous structures. 6. Response of Beam-Like Structures to Near-Field Acoustic Environment. 6.1. Preliminary considerations. 6.2. Acoustic environment prediction. 6.3. Response of beam-type structures to launch site acoustic field. 6.4. Numerical examples. 6.5. Wave-number response of multi-span beams. 6.6. Effects of boundary conditions. 6.7. Simplified acoustic loading model. 6.8. Cross-spectral density of the response for multi-span beams. 7. Random Vibration Analysis by Finite Element Method. 7.1. Introduction. 7.2. A. Benchmark example. 7.3. Vibration analysis of beams by the finite element method. 7.4. Assembly of global matrices. 7.5. Deterministic element load vectors. 7.6. Element correlation matrix. 7.7. Global correlation matrix. 7.8. Random vibration analysis. 7.9. Calculation of element and global correlation matrices for the benchmark problem. 8. A Combined Probabilistic and Convex-Theoretic Approach. 8.1. Single-degree-of-freedom system. 8.2. Uncertain parameters belonging to a convex set. 8.3. Uniform beam under acoustic excitation - a single-term approximation. 8.4. Convex modeling of measured data. References. Appendices. Index.