Probabilistic and Convex Modelling of Acoustically Excited Structures: Volume 39(Volume 39 Studies in Applied Mechanics)

This book summarises the analytical techniques for predicting the response of linear structures to noise excitations generated by large propulsion power plants. Emphasis is placed on beams and plates of both single-span and multi-span configurations, common in engineering structural systems. Since the natural frequencies and the associated normal modes play a central role in the random vibration analysis of a continuous dynamical system, rather detailed discussions are devoted to their determination. Material covered in the first chapter provides a useful reference for the subsequent discussion of multi-span structures. Also included in this volume is a hybrid probabilistic and convex-uncertainty modeling approach in which the upper and lower bounds of the cross-spectral densities of the acoustic excitation are obtained on the basis of measured data. The random vibration of a structure is treated, for the first time, as an "anti-optimization" problem of finding the least favourable value of the mean-square response.

Table of Contents:
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.