Elements of Vibration Analysis

A₁ amplitude arbitrary associated autocorrelation function boundary conditions C₁ C₂ calculate characteristic equation coefficients conclude Consider the system constant continuous systems coordinates corresponding curve damping denoted differential equation discrete systems displacement eigenfunctions eigenvalue problem eigenvectors elements equations of motion equilibrium point ergodic Example excitation FIGURE Fourier transform fundamental frequency Hence inertia initial conditions Inserting Eqs integral Introducing Eqs k₁ k₂ kinetic energy Laplace transform Let us consider linear systems m₁ mass mean square value method Moreover natural frequencies natural modes notation obtain orthogonality parameter pendulum phase angle phase plane plot positive definite potential energy probability density function random process Rayleigh's quotient represents respectively rigid-body shaft shown in Fig simply solution of Eq spring symmetric system of Fig system of Problem t₁ theorem torsional trajectories u₁ undamped variable velocity versus vibration virtual displacements w₁ write x₁