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AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
This lecture starts with a recap on the topics that have been discussed so far. Thereafter, the phenomenon of resonance is introduced and elaborated. This is a special case of the solution for forced vibration problems.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
In this lecture, the analysis of forced vibration is continued. This time, forced motion with base excitation is discussed. The critical speed at which resonance occurs is elaborated, where a phase change of 180 degrees exists. Corresponding to the forced motion with base excitation, an example is worked out by the lecturer. Lastly, the beat phenomenon is explained.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
Up until now, undamped mass-spring systems have been analyzed and in the following lecture the concept of damping (dissipation) is introduced. The topic that is treated is called “damped second-order systems”. First, the general solution of free vibration of a damped system is derived and from this, specific damping cases are discussed.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
This lecture continues with the analysis of free vibration of damped systems. Recall that in the previous lecture, the case of underdamped motion was introduced. In this lecture, A.S.J. Suiker expands this case to find the response parameters from the initial conditions. Thereafter, the second and third case of damped motion is treated. Finally, a quick overview of the three cases is given.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
In this lecture, the case of underdamped free vibration is considered again. The lecturer shows how to determine (viscous) damping by means of the logarithmic decrement. After a general introduction, two examples are worked out.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
In this lecture, the special case of harmonic forced vibration of damped systems is explained. It is shown that the principle is similar to the cases that have been treated before. The response of the differential equation is then shown in a graph.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
In this lecture, the final equations of the particular solution of the case of harmonic forced vibration of damped systems are written down as a recapitulation of the previous lecture. Thereafter, the homogeneous part of the solution is introduced for an underdamped system. Also, other types of damping are discussed.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
This lecture continues on the homogeneous part of the solution of harmonic forced vibration of damped systems. The lecturer starts by correcting a mistake that was made during the previous lecture. Thereafter, the energy dissipation per cycle is explained for two different types of damping. This explanation is followed by an example on hysteretic damping. Finally, it is shown how to compute the solution of such problems.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
In this lecture, the lecturer starts with a recapitulation of what is treated so far in this course.

AE2914. This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
In this lecture, frictional damping is explained (also known as Coulomb damping). This is done by means of an example. Again, a graph is drawn that schematically displays the response of systems with frictional damping.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
This lecture deals with the topic of the general forced response. System responses are analyzed when subjected to non-periodic load. After an introduction on this topic, the unit impulse function is elaborated.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
This lecture continues with the introduction of general forced responses. In the previous lecture the unit impulse was treated and now the response to a step function is elaborated. First, the characteristics of a unit step loading are given and then it is shown how to compute the response of a system subjected to a unit step load. Also, a graph off the step response is given.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
In this lecture, Laplace transforms are explained. First, the impulse and step responses that were introduced in the last two lectures are shortly revisited. Next to these two types of responses, one more non-periodic loading is introduced: the rectangular pulse loading. Thereafter, it is explained how transform methods can be used to solve difficult problems in an easy way. The Laplace transform method is then further elaborated.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
In this lecture, the lecturer starts with a recapitulation of what is treated so far in this course. A final example on viscous damping is then given.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
This lecture is about the convolution integral.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
In this lecture, general periodic loadings are treated. Fourier series are introduced and the three mathematical expressions are given. Next, it is shown how to compute the response for a periodic loading using the Fourier series approximation. Also, an example on the Fourier series is given.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
This lecture starts with graphical representations of responses, corresponding to the three (Laplace, convolution integral and Fourier) methods that have been treated in this module. The response to a sawtooth pulse, computed with the Laplace transform method, is given first. Another graph of the Laplace method is given for the exponential decaying load example. Thereafter, the response to an exponentially saturating load computed with the convolution integral is elaborated. The block loading example of the previous lecture, computed with Fourier series, is given next.

AE2914 - This course is about being able to do basic analyses and design of vibrations problems in engineering practice. The four essential learning goals of the course are: schematization of engineering structure into mass-sping-dashpot model, construct governing (set of) differential equation(s) for this model, derive the appropriate solution and a practical interpretation of the solution (parameter variations).
This lecture continues on the coupled equations of motion that were found in the previous lecture for a two degree-of-freedom system. First, it is shown how to solve the system when no loads are applied. It is shown how to compute the non-trivial solution for such a system (i.e. eigenfrequencies). Thereafter, the lecturer shows how to compute the eigenmodes corresponding to the eigenfrequencies.