Mechanical Vibration Analysis and ComputationFocusing on applications rather than rigorous proofs, this volume is suitable for upper-level undergraduates and graduate students concerned with vibration problems. In addition, it serves as a practical handbook for performing vibration calculations. An introductory chapter on fundamental concepts is succeeded by explorations of frequency response of linear systems and general response properties, matrix analysis, natural frequencies and mode shapes, singular and defective matrices, and numerical methods for modal analysis. Additional topics include response functions and their applications, discrete response calculations, systems with symmetric matrices, continuous systems, and parametric and nonlinear effects. The text is supplemented by extensive appendices and answers to selected problems. This volume functions as a companion to the author's introductory volume on random vibrations (see below). Each text can be read separately; and together, they cover the entire field of mechanical vibrations analysis. Book jacket. |
Contents
Frequency response of linear systems | 17 |
General response properties | 56 |
Matrix analysis | 97 |
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Common terms and phrases
algorithm amplitude applied approximation assumed beam bogie C₁ calculation Chapter coefficients column complex constant coordinates corresponding damping ratio dB/decade defined deflection degrees of freedom diag diagonal diagonal matrix eigenvalues eigenvalues and eigenvectors eigenvector matrix elements equations of motion example force Fourier transform frequency-response function given gives graph H(io H(iw Hence Hessenberg Hessenberg matrix imaginary independent eigenvectors infinite input integral inverse iteration iw)² Jordan matrix k₁ magnitude mass Mathieu equation method modal mode shapes multiplying natural frequency nonlinear normal mode function obtained oscillation output parameter partial fractions pendulum plotted Problem QR algorithm rad/s Rayleigh's resonance response function result shaft shown in Fig solution stiffness sub-diagonal sub-matrix substituting symmetric symmetric matrix system in Fig torque torsional undamped values velocity w₁ wheels wheelset y₁ y₁(t zero ίω λ₁ λε λι