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
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
Eigenvalue problem
Euler–Bernoulli beam
Figures worth knowing
- Magnification and transmissibility against frequency ratio
- Mode-shape diagrams
- Campbell diagram
- Beam mode shapes
Related courses
- 0542-4224Semester B · 4h
Mechanics of solids 2
מכניקת המוצקים 2
The bridge from strength of materials to failure analysis. Yield criteria, unsymmetric bending, thin-walled torsion, energy methods, buckling. It counts toward three interest areas at once.
Structures and computational mechanicsAeronautics and spaceMiniaturised systems and materials - 0542-4011Semester A · 3h
Research project for honours students 1
פרויקט מחקר למצטיינים 1
The honours research project, and the most direct on-ramp to a thesis in the catalogue. You pick a supervisor, produce results, and frequently continue the same problem into a masters.
Structures and computational mechanicsMechatronics and roboticsMiniaturised systems and materialsAeronautics and spaceEnvironment and energyFlow and thermal designMechanical design - 0542-4012Semester B · 3h
Research project for honours students 2
פרויקט מחקר למצטיינים 2
The continuation of the honours project, where the results get deep enough to defend. Under the direct track this is already the first part of the masters thesis.
Structures and computational mechanicsMechatronics and roboticsMiniaturised systems and materialsAeronautics and spaceEnvironment and energyFlow and thermal designMechanical design - 0542-4221Semester B · 4h
Introduction to theory of elasticity
מבוא לתורת האלסטיות
The theory floor under every serious solid-mechanics result. Stress and strain as tensors, boundary-value problems formulated and solved, and the classical two-dimensional solutions.
Structures and computational mechanicsAeronautics and space
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