Analytical Methods in Vibrations

admissible functions amplitude associated assume B₁ boundary conditions comparison functions complex constant continuous system coordinates corresponding damping dD(P defined denote derive discrete systems displacement domain eigenfunctions eigenvalue problem eigenvector elements energy expression equations of motion excitation finite force Fourier transform free vibration frequency equation Hankel transform harmonic Hence inertia influence coefficients initial conditions integral iteration k₁ k₂ kinetic energy Laplace transform Let us consider linear transformation m₁ mass matrix form mean square membrane method modal analysis natural frequencies natural modes normal modes obtain the response ordinary differential equations orthogonal positive definite potential energy random process Rayleigh-Ritz method Rayleigh's quotient represents satisfy Section self-adjoint shown in Figure solution solve stiffness symmetric theorem transverse trial vector uncoupled undamped system uniform variable velocity w₁ wave write zero ΕΙ Әх дх