# Multibody Dynamics

The course teaches the ability to mathematically describe arbitrary mechanisms including the physical effects occurring therein, such as elasticity, damping and friction, and to analyze the motion behavior of such systems.

In the course, mainly vibrations of linear multibody systems are analyzed. The matrix calculation is used for a clear and computer-friendly investigation of the systems with several degrees of freedom. The systematic approach taught in the lecture has the advantage that it can be applied to almost any technical system and can be carried out in suitable programs with few instructions.

The course is offered in German as Dynamik der Mehrkörpersysteme and in English as Multi Body Dynamics.

### Key Info

#### Basic Information

Degree:
Master
Semesters:
Summersemester
Organizational Unit:
Institute of Mechanism Theory, Machine Dynamics and Robotics
Lecturer:
Univ.-Prof. Dr.-Ing. Dr. h. c. Burkhard Corves
Language:
German, English

Lecture

work
+49 241 80 95553

E-Mail

Exercises

work
+49 241 80 99792

E-Mail

## Course Content

Creating Models for Technical Systems

Vibration models are especially needed in mechanical systems: for example to be able to build controllers for active suspension systems. In the lectures of vibration technology you learn how to build multi-body models for real systems which are as simple as possible and still consider all significant effects.

Also, an efficient method to determine planar and spatial kinematics of general moving multibody systems is presented as well as methods to form the equations of motion by using the Lagrange-Equation or the Newton-Euler-Equation. The second order equation of motion can be transformed to an equivalent first order equation of state.

Analysis of Technical Systems

The equations of motion and states are mathematical models of systems and are valuable tools to get secure information on parameter influences and parameter optimization especially in dealing with dynamic systems. In vibration technology you learn how to solve the equations of motion and states with the help of matrix calculus to analyse multibody systems.

Free Vibrations

Eigenvalues and eigenvectors are calculated to analyze the intrinsic behavior. They give information on vibration amplitudes and frequencies as well as on the decay of free oscillations. In addition, stability statements are based on simple eigenvalue stability criteria. The lectures of vibration technology teach you how to do necessary calculations by hand or with the help of computer programs.

Forced Vibrations

Technical systems often perform forced vibrations. You learn how to solve non-homogeneous state and motion equations of specific excitation functions. During the operation of technical systems periodic excitations occur, for example because of unbalanced forces or occurring wave-like movements. In such cases, critical excitation frequencies or drive speeds and the frequency-dependent system behavior need to be calculated. Another special excitation function is the step function excitation, for example in form of a run over the curb. The vibration response to such impulse functions are often used to compare and evaluate vibration systems and can easily be calculated with the equation of state.

A very wide range of practice-relevant analysis of movements can be covered by the previously introduced special solution methods which gives closed solutions for state and motion equations. But general forms of excitation require the calculation of the general equation of the non-homogeneous state equation. This is often only numerically possible and meaningful. Therefore the lecture deals with the numerical aspects to solve the equations of state with the help of fundamental matrices.