cod. 1005619

Academic year 2022/23
1° year of course - Second semester
- Elisabetta MANCONI
Academic discipline
Meccanica applicata alle macchine (ING-IND/13)
Ingegneria meccanica
Type of training activity
48 hours
of face-to-face activities
6 credits
hub: PARMA
course unit

Learning objectives

Knowledge and ability to understand:
through the lectures held during the course, the student will acquire the skills necessary to describe the dynamics and vibrations of machines and mechanical systems and to understand their modelling and analysis criteria. The student will also learn the principal methodologies to obtain analytical and numerical solutions also through practical applications of interest for mechanical engineering.

Applying knowledge and understanding: through practical exercises, the student will learn how to apply the acquired knowledge in a real design context. The students will be involved, in groups, in a year's project that will allow them to extend and apply, through practical activities, the theoretically acquired knowledge.
Making judgments:
the student will be able to understand and critically evaluate the main problems related to vibrations of mechanical systems. In particular, the student will be able to choose the appropriate modelling methodology to predict their behaviour, evaluating the computational performance and accuracy of the selected solution.

Communication skills:
through the lectures and the year's project, the student will acquire specific vocabulary related to the course. It is expected that, at the end of the course, the student will be able to communicate, in oral and written form, the main contents of the course, e.g. ideas, engineering problems and related solutions. The student will be able to communicate his/her knowledge adequately and understand and use common tools, such as tables, schemes, and software.

Learning skills:
the student who has attended the course will be able to enhance his/her knowledge through the autonomous consultation of specialized texts, scientific or popular magazines, technical catalogues, etc., to deal with more complicated problems and be prepared for his/her chosen career or further specific training courses in the same field


There are no mandatory propaedeutics. Basic knowledge of Mechanics and Mathematical Analysis are required.

Course unit content

The course provides the concepts and methods for modelling the dynamics and vibratory behavior of machines and mechanical systems. In particular, the principal methodologies to obtain analytical and numerical solutions for the study of the vibrations of discrete and continuous systems are presented, also considering practical applications of interest for mechanical engineering. The exercises use software for numerical calculation and simulation to learn the specific contents of the course.

Full programme

Vibrations of single degree of freedom systems.
Vibration isolation.
Vibrations of systems with concentrated parameters with many degrees of freedom.
Writing of the equations of motion in matrix form.
Free vibration of conservative systems, reduction of the eigenvalue problem in standard form. Definite matrices and semidefinite.
Properties of frequencies and natural modal forms.
Normalization, orthogonality, expansion theorem.
Linear transformations of coordinates and modal coordinates; forced solution of the problem. Proportional damping and modal damping.
Non-proportional damping: method of the transition matrix. Complex modes.
Practical examples of experimental modal analysis in laboratory.
Technical applications and exercises.


All the PowerPoint presentations and the material presented during the lectures are available in the platform Elly.

In addition to the shared material, the student can find some of the topics presented during the course in the following books:
S. S. Rao, Mechanical Vibrations, 5th edition, Prentice Hall, 2011
J.P. Den Hartog, Mechanical Vibrations, 2nd edition, Dover Publications, 1956
L. Meirovitch, Analytical Methods in Vibrations, Macmillan Publishing Co., 1967
M. Petyt, Introduction to finite element vibration analysis, Cambridge, University Press, 1990

Teaching methods

The course counts 6 CFUs (one CFU, University Credits equals one ECTS credit and represents the student's workload during educational activities to pass the exams), corresponding to 48 hours of lectures. The didactic activities are composed of frontal lessons and exercises. During the frontal lectures, the course topics are presented from the theoretical and modelling point of view. Students will also apply theoretical knowledge to exercises and real case studies.
The slides and notes used to support the lectures will be uploaded to the Elly Platform. To download the slides from Elly, enrolling in the online course is required.
All the shared material is part of the didactic material. For non-attending students, it is important to stay up-to-date on with the course content, information and announcements through the Elly platform, which is the teacher/student tool used for this course. On this platform, day by day, the topics discussed in the lesson are uploaded, providing the students with the contents for the final exam.

Assessment methods and criteria

Learning assessment takes place through an individual or group project and its oral discussion.
The project content is agreed with the teacher at the beginning of the course and consists of a practical problem according to the main contents of the lectures. The project is completed with the delivery of the work (e.g. source code of a program) and a technical report.
The project must be delivered one week before the official exam date the student intends to take.

The project is evaluated as follows.
Project development (max 10 points): understanding of the project requirements and objectives, prerequisite analysis, the definition of functionality, performance and constraints; design; realization; integration, test and validation.
Working method (max 10 points): independency, proactivity, creativity; research, analysis, evaluation and selection of different solutions; systematicity and essentiality; communication within the group and with the tutor.
Results (max. 5 points): fulfilment of the original project's objectives.
Documentation (max 5 points): structure; completeness and correctness; style.
The final grade is equal to the sum of obtained points. The achieved points must be confirmed during the oral test, which aims to verify the actual personal contribution of the student.
An exam is considered to be passed successfully if the final grade is equal to or higher than 18/30. In the event of a full grade (30/30), the Examination Board may grant honours (lode) based on the quality of the documentation and the oral presentation.

Other information