Index
A
Aerodynamic forces, 1
Alternative formulation, 30–31
Amplitude-phase representation, 15–17
Approximations of modal frequencies, 72–75
Arbitrary forcing functions, 20–25
B
Beating phenomenon, 27–28
C
Classical modes of vibration, 98, 99
Continuous systems
flexural beams, 116–123
shear beams, 124–130
Coulomb damping model, 49–51
D
Damped oscillators, 9
Damped systems
coupled equations, 78
equations of motion, 78–79
free vibration, 79, 83–84
initial conditions, q(t), 80
modal coordinates, 78
modal damping ratio, 79
modal shapes, 70–72, 78
solution uniqueness, 82–83
system displacement x(t), 80–82
Damping estimation, 17
Design response spectrum, 91–92
Displacement vector representations, 76–77
Duhamel integral, 22
Dynamic amplification factor (DAF), 31–32,
108
E
Earthquake engineering
design response spectrum, 91–92
seismic ground acceleration, 89–91
Eigenvalue problem
linear algebraic equations, 55–56
non symmetric matrices, 63–65
symmetric matrices, 59–63
Eigenvalues, 99–102
Eigenvectors, 99–102
Equations of motion, 9, 79
F
Finite difference (FD), 39–42
Flexural beams
equations of motion, 116–117
forced vibration, 122–123
free vibration, 123
modal shapes and frequencies,
117–121
physical system, 116–117
Forced vibration, 9, 69, 102–103, 122–123,
128–129
Fourier series (FS) method, 42–44
Fourier series representation, 107
Free vibration, 103–106, 123, 129–130
Frequency domain, 9
© The Editor(s) (if applicable) and The Author(s), under exclusive license
to Springer Nature Switzerland AG 2021
M. D. Grigoriu, Linear Dynamical Systems,
https://doi.org/10.1007/978-3-030-64552-6
151