Civil engineering
Study-unit Code
Federico Cluni
  • Federico Cluni
  • 42 ore - Federico Cluni
Course Regulation
Coorte 2023
Learning activities
Ingegneria civile
Academic discipline
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Dynamics of single-degree-of-freedom systems. Free and forced vibrations.
Response to arbitrary forces. Response spectrum.
Equation of motion of multi-degree-of-freedom systems. Modal shapes and pulsations. Modal analysis.
Applications to seismic analysis.
Equation of motion of the beam and taut string. Modal shapes and pulsations of beam and taut string.
Reference texts
* English books
- A. Chopra, "Dynamics of Structures", Prentice Hall
- R.W. Clough, J. Penzien, "Dynamics of Structures", McGraw-Hill
- A. Zingoni, "Vibration Analysis and Structural Dynamics for Civil Engineers", CRC Press
* Italian books
- L. Facchini, "Elementi di Dinamica delle Strutture", Editrice Esculapio
- I. Iervolino, "Dinamica delle strutture e ingegneria sismica. Principi e applicazioni", Hoepli
- G. Muscolino, "Dinamica delle strutture", McGraw-Hill (out of print, copies at the Engineering Library)
- C. Gavarini, "Dinamica delle strutture", ESA (out of print, copies at the Engineering Library)
Educational objectives
The course presents the base elements and the conceptual and analytical tools for the study of the dynamics of the structures in civil engineering.
The main aim of the course is to provide students with the conceptual bases and the the instruments to study the dynamics of the structures in civil engineering, with a particular reference to those responding linearly to the actions.
Main knowledge acquired will be:
- comprehension of the behavior of single-degree-of-freedom systems.
- response in free and forced vibration.
- response to arbitrary forces.
- meaning and use of response spectrum
- comprehension of the behavior of multi-degree-of-freedom systems
- features of pulsations and modal shapes.
- knowledge of modal analysis.
- comprehension of the behavior of beams and taut strings.
The main competence (i.e. the ability to apply the acquired knowledge) will be:
- study the response of single-degrre-of-freedom system to arbitrary force.
- find the pulsations and modal shapes of a multi-degree-of-freedom system.
- apply the modal analysis to obtain the response under arbitrary forces.
- find the response under seismic actions by means of response spectrum.
- find the pulsations and modal shapes of a continuous system, beam or taut string.
The Course is in the first year.
The topics of the Course require the ability to solve ordinary
and partial differential equations and simpe integrals.
Knowledge of these techniques represents a mandatory prerequisite for students planning to follow the course with profit.
Teaching methods
The course is organized as follows:
- Face-to-face lectures on all subjects of the course.
The lecture notes will be available at: https://www.unistudium.unipg.it/unistudium/
Other information
Learning verification modality
The exam consists of an oral test consisting on an interview about half an hour long, aiming to ascertin the knowledge level and the understanding capability acquired by the student on theoretical and methodological contents as indicated on the program (elementary oscillator, discrete systems, continuous systems).
The oral exam will also test the student communication skills and his autonomy in the organization and exposure of the theoretical topics.
Extended program
Single-degree-of-freedom system
The laws of motion. Principle of D'Alembert. Undamped free oscillations. Free and forced oscillations with damping. Harmonic forces. Amplification factor and phase shift. Resonance. Power dissipated by the damper. Pseudo-acceleration. Response spectrum. Base displacements. Accelerometers and seismometers. Response to arbitrary force. Duhamel's integral. Solution with Fourier series. Nonlinearity: nonlinear damping (hysteresis and friction). Oscillator with nonlinear (elastic-plastic) reaction.
Multi-degree-of-freedom systems
Equations of motion for discrete systems. Solution in free oscillations. Properties of the eigenvectors: natural modes. Normal and principal coordinates. Modal Analysis. Rayleigh's damping. Applications of modal analysis. Modal participation factors. Modal contribution factors. Respone to base displacements. Modal analysis for seismic actions (response spectrum analysis). Push-over analysis. Mass participation factors.
Continuous systems
Equation of motion of the beam and taut string. Free oscillations of the beam. Mode orthogonality. Examples: simply supported beam, cantilever. Forced oscillations of the beam. Influence of axial force on the modes. Oscillations of the taut string. Respone to base displacements.
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