Skip to content
All courses
0542-4220

Theory of vibrations

Also listed as: תורת התנודות

From one degree of freedom to continuous systems, with modal analysis in the middle. It is the course that turns "the machine shakes" into a number you can design against.

Semester
Semester A
Weekly hours
4h
Counts as
Core: solids
Interest areas
Structures and computational mechanics · Miniaturised systems and materials · Aeronautics and space

Comes after

  • Rigid body dynamics
  • Mechanics of solids 1

Opens up

What it covers

Single degree of freedom

  • Free vibration: undamped, under-, critically and over-damped, logarithmic decrement
  • Harmonic excitation, resonance, magnification factor, phase
  • Rotating unbalance, base excitation, transmissibility, vibration isolation
  • Duhamel's integral for arbitrary and transient forcing

Multiple degrees of freedom

  • Equations of motion by Newton and by Lagrange, mass and stiffness matrices
  • The eigenvalue problem, natural frequencies, mode shapes, orthogonality
  • Modal analysis and the vibration absorber
  • Numerical methods: Rayleigh, Dunkerley, Holzer, matrix iteration

Continuous systems

  • Strings, axial bars, torsional shafts, Euler–Bernoulli beams
  • Boundary conditions and their effect on the spectrum
  • Damping models, instrumentation and measurement
  • Introduction to nonlinear and random vibration

Results worth carrying out

  • Single degree of freedom

    mx¨+cx˙+kx=F(t),ωn=km,ζ=c2kmm\ddot{x} + c\dot{x} + kx = F(t), \qquad \omega_n = \sqrt{\frac{k}{m}}, \qquad \zeta = \frac{c}{2\sqrt{km}}

  • Eigenvalue problem

    [M]{x¨}+[K]{x}=0  ⇒  det⁡ ⁣([K]−ω2[M])=0[M]\{\ddot{x}\} + [K]\{x\} = 0 \;\Rightarrow\; \det\!\left([K] - \omega^2[M]\right) = 0

  • Euler–Bernoulli beam

    EI ∂4w∂x4+ρA ∂2w∂t2=0EI\,\frac{\partial^4 w}{\partial x^4} + \rho A\,\frac{\partial^2 w}{\partial t^2} = 0

Figures worth knowing

  • Magnification and transmissibility against frequency ratio
  • Mode-shape diagrams
  • Campbell diagram
  • Beam mode shapes

Quick answers

When is Theory of vibrations taught?

Theory of vibrations (0542-4220) is taught in Semester A (fall), 4 weekly hours. It counts toward “Core: solids” in the Tel Aviv University Mechanical Engineering elective requirements.

What do I need before 0542-4220?

Before Theory of vibrations you need: Rigid body dynamics, Mechanics of solids 1.

What software is used in Theory of vibrations?

Theory of vibrations is normally taught with MATLAB, Simulink, ANSYS Mechanical (modal).

Which jobs does Theory of vibrations prepare you for?

Theory of vibrations is part of the preparation for these roles: MEMS and sensor engineer, Aerospace structures engineer.

Which interest areas include Theory of vibrations?

Theory of vibrations sits in these interest areas: Structures and computational mechanics, Miniaturised systems and materials, Aeronautics and space.

Related courses

We also write the summaries.

This map tells you what a course contains. The summaries, the tutoring and the people who already took it are the part you get by joining.

Join CARNOTAll courses

The topic outlines are not official syllabi. The university publishes a catalogue blurb per course, not lecture-by-lecture material, so each outline describes what a course of that name, at those hours, with those prerequisites teaches at engineering schools generally, cross-checked against the standard textbook for the subject. Treat it as an informed map, not as a transcript of the lectures.