Prerequisite/Recommended prerequisite for
participation in the module
The module adds to the knowledge obtained in 1st Semester.
Content, progress and pedagogy of the
module
Learning objectives
Knowledge
- Have gained an in-depth understanding of energy and variational
methods and classical principles of stationarity to derive
governing equations of statics and dynamics, and their application
for solution of general problems in structural mechanics,
including:
- Energy methods and energy minimization principles as the
foundation of the finite element method
- Variational methods (methods of Ritz, Galerkin, Rayleigh and
Rayleigh-Ritz)
- Different applications of those such as analysis of statics,
buckling and vibration of beams, plates and similar
- Dynamics of discrete multi-dof and multi-body mechanical
systems
- Exact and approximate solutions to the natural frequencies and
modal analysis problems for multi-dof/continuous vibration
systems
- Approximate methods for nonlinear mechanical
vibrations
Skills
- Be able to apply energy and variational methods for the
solution of problems in statics and dynamics involving discrete and
continuous, multi-rigid-body and multi-dof vibrational mechanical
systems
- Be able to adequately simulate and analyze dynamics of linear
and non-linear mechanical systems
Competences
- Be able to apply energy minimization / maximization principles
to derive the relationships between stresses, strains,
displacements, material properties, and external effects (e.g.,
tractions and volume forces) in the form of balance of the kinetic
and potential energies and the work done by internal and external
forces.
- Be able to use the variational calculus as a convenient and
robust tool for formulating the governing equations of statics and
dynamics of rigid and solid bodies in applied mechanics.
- Be able to apply the energy and variational methods to find
approximate analytical and numerical (e.g. finite element)
solutions of complex problems in statics, stability and dynamics of
mechanical systems
- Be able to formulate equations of motion for multi-body
mechanical systems and for discrete multi-dof and continuous
vibration systems using Lagrange and Newton-Euler equations.
- Be able to understand and analyze the dynamic behavior (mode
shapes and eigenfrequencies) of linear vibration systems
- Be able to use appropriate (e.g., harmonic balance) methods to
analyze behavior of nonlinear vibration systems.
Type of instruction
The teaching is organized in accordance with the general form of
teaching. Please see the programme cirruculum §17.
Extent and expected workload
Since it is a 5 ECTS course module the expected workload is 150
hours for the student.
Exam
Exams
Name of exam | Energy and Variational Methods with Applications |
Type of exam | Written or oral exam |
ECTS | 5 |
Assessment | 7-point grading scale |
Type of grading | Internal examination |