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Videos uploaded by user “Efstratios Nikolaidis”
Sequential Quadratic Programing
 
14:00
The lecture presents a method for constrained optimization that uses a quadratic polynomial approximation. The method applies to problems with a single ofjective function.
Views: 10517 Efstratios Nikolaidis
Lecture 14. Orthogonality of Model Shapes
 
01:07:28
The lecture shows that the mode shapes of a multi-degree of freedom system are orthogonal with respect to the mass and stiffness matrix. Then it explains how to take advantage of this orthogonality property to simplify the calculation of the free vibration response of a dynamic system.
Views: 2598 Efstratios Nikolaidis
Lecture 8. Forced vibration response to harmonic and periodic excitation
 
59:06
The lecture explains and demonstrates the calculation of the transient response of a single degree of freedom system to harmonic and periodic excitations.
Views: 4115 Efstratios Nikolaidis
Reliability Calculations, Part 2: Monte Carlo Simulation
 
01:15:09
Standard Monte Carlo Simulation is Explained and Demonstrated
Views: 5621 Efstratios Nikolaidis
Lecture 2: Estimation of the volume of a sphere using Monte Carlo Simulation
 
22:47
The lecture demonstrates the calculation of the volume of a sphere using simulation.
Views: 1858 Efstratios Nikolaidis
Lecture 21: Finite Element Analysis in Structural Dynamics; Part II
 
01:11:54
The mass and stiffness matrices of a beam element are derived by using energy principles.
Views: 3840 Efstratios Nikolaidis
Lecture 12.Free Vibration of Multi-Degree of Freedom Systems: Part I
 
48:29
The lecture presents the derivation of the equations for the free vibration of a multi-degree of freedom system. It explains the concept of mode shapes, and expresses the displacement in terms of the mode shapes.
Views: 6144 Efstratios Nikolaidis
Lecture 8A. Optimization using response surfaces
 
11:40
One method to optimize systems that are expensive to analyze is to use a response surface appromation. This demonstrates this method on the problem of optimizing the units delivered by the postal service.
Views: 10141 Efstratios Nikolaidis
Lecture 6. Forced Vibration of a Single Degree of Freedom System
 
01:04:49
This first lecture on forced vibration response studies the steady-state response of a system to a sinusoidal excitation.
Views: 6503 Efstratios Nikolaidis
Lecture 9. Vibratory Response of  SDOF System to Arbitrary Excitation
 
01:22:17
This video explains how to find the vibratory response of a single degree of freedom system to an arbitrary force. To do so the convolution integral is used calculated. The method is demonstrated on finding the response to a rectangular pulse function.
Views: 1765 Efstratios Nikolaidis
Lecture 4. Free vibration of single degree of freedom systems, Part I
 
01:05:55
Equations for the free vibration response are derived. Three system types are considered: overdamped, critically damped, and underdamped.
Views: 1965 Efstratios Nikolaidis
Reliability Design and Markov Chain Monte Carlo Simulation
 
01:06:23
The example on fatigue reliability of the torsion bar of a truck hood is completed in this lecture. Then the acceptance-rejection method and Markov Chain Monte Carlo simulation is introduced.
Views: 2002 Efstratios Nikolaidis
Reliability Calculations Using Standard Monte Carlo Simulation and Importance Sampling
 
01:16:40
Standard Monte Carlo Simulation and Importance Sampling and explained and demonstrated. The issue of the high computational cost when the probabilities are very low (e.g. one per hundred thousand) is discussed.
Views: 2840 Efstratios Nikolaidis
Lecture 17. Forced Vibration of Multi Degree of Freedom Systems, Part II
 
01:13:06
The lecture explained and demonstrates the calculation of the steady state response of a system to harmonic forces.
Views: 1553 Efstratios Nikolaidis
Lecture 3. Equations of Motion of a Single Degree of Freedom System
 
01:11:35
The lecture explains Newton's law and energy methods for deriving the equations of motion of a system with one degree of freedom
Views: 1320 Efstratios Nikolaidis
Subjective Probability-Part 1
 
58:38
Decisions involve one-time events. There is no data to estimate their relative frequencies. Subjective probability is the decision maker's degree of belief that an event will materialize. We estimate this probability by finding out how much money she agrees to bet that the event will materialize.
Views: 1785 Efstratios Nikolaidis
Lecture 23: Transformation of Mass and Stiffness Matrices of a Vibratory System
 
51:15
A method to transform the mass and stiffness matrices from the element to the global coordinate system is presented, The method is based on energy principles.
Views: 2778 Efstratios Nikolaidis
A Kind and Gentle Introduction to Markov Chain Monte Carlo Simulation: Part 1
 
01:01:39
The calculation of a very low probability of failure (for example 0.0001) using Monte Carlo simulation is very expensive. Here is how to circumvent this difficulty by decomposing the problem into two: 1) estimation of a higher probability (say 0.01) using standard MCS, and 2) the a conditional probability using Markov Chain Monte Carlo.
Views: 6415 Efstratios Nikolaidis
Lecture 15. Free Vibration Analysis of Multi-Degree of Freedom Systems-Orthogonality of Modes
 
01:12:41
The lecture explains how to find the free vibration response of a multi-degree of freedom system efficiently by taking advantage of the orthogonality of the mode shapes.
Lecture 17: Example of Nonlinear Optimization
 
13:29
The Lecture Demonstrates the Solution a Nonlinear Optimization Problem With One Objective
Operations Research: Perishable goods problem under uncertainty
 
11:36
The lecture presents and demonstrates a method to optimize the amount of goods that an entrepreneur should order to maximize the expected profit.
Lecture 5. Free Vibration Analysis: Part II
 
01:01:32
In this lecture we study the response of single degree of freedom systems because of initial displacements and velocities. No external forces are applied. We consider three cases: over damped, critically damped and under damped systems. A method to estimate damping from a record of the vibratory response is explained and demonstrated.
Lecture 7. Forced Vibration of Dynamic Systems Part II
 
01:03:32
This lecture explains and demonstrates the calculation of the response of a single-degree-of-freedom system to harmonic excitation.
Lecture 2. Derivation of the equation of motion of a single degree of freedom (SDOF) system
 
01:09:46
This lecture lecture presents a method to derive the equation of motion by finding the equivalent stiffness, mass and damping of the system.
Views: 1577 Efstratios Nikolaidis
A Kind and Gentle Introduction to Markov Chain Monte Carlo Simulation: Part 2
 
01:03:59
The lecture explains and demonstrates the calculation of a confidence intervals of the probability of an event estimated by Markov Chain Monte Carlo simulation.
Views: 1032 Efstratios Nikolaidis
Lecture 11. Equations of Motion of Systems with Multiple Degrees of Freedom
 
01:08:06
The derivation of the equations of motion is explained and demonstrated. Two methods based on Newton's Law and Energy Principles are Explained.
Views: 1133 Efstratios Nikolaidis
Lecture 20: Finite Element Analysis, Part I
 
56:48
This is the first lecture that explains how to predict the vibratory response of a dynamic system by developing and solving a finite element model of the system.
Views: 1030 Efstratios Nikolaidis
Lecture 13: Game Theory, Non-Constant Sum Games, Prisoners’ Dilemma
 
41:38
The total reward of the players in most real life games is not constant. The lecture introduces the concept of such games.
Lecture 10. Multi degree of Freedom Systems: Equations of Motion
 
53:03
This lecture explains the derivation of the equations of motion of systems with multiple degrees of freedom.
Lecture 8: How Airlines Optimize Policy for Accepting Reservations
 
14:42
Airlines often accept more reservations than the available seats to optimize profit. The lecture explains and demonstrates and optimization method that increments the number of accepted reservations until it starts losing money.
Lecture 13. Free Vibration of Multi-Degree of Freedom Systems, Part II
 
56:11
The free vibration response of a multi-degree of freedom system is derived by solving the equations of motion.
Lecture 19: Forced Vibration of Multi-Degree of Freedom Systems
 
01:02:25
The mode superposition and mode acceleration methods are explained and compared.
Movie 12: Games Without Equilibrium, Randomized Strategies
 
34:41
Some games have no equilibrium point. The game of odds and evens odds is an example. The lecture explains how to solve this problem considering a randomized strategy.
Markov Chain Monte Carlo Simulation-Part 1
 
01:13:07
Markov Chain Monte Carlo Simulation enables an analyst to generate sample values from complex probability densities. An example is a probability density which is non zero only for those combinations of values of the random variables that cause failure.
Lecture 1. Mechanical Vibration: Class Overview
 
57:56
This is the overview of a graduate class on Mechanical Vibration. Modeling of dynamic systems, and free and forced vibration of systems are covered in this class.
Views: 7337 Efstratios Nikolaidis
Lecture 16: Forced Vibration of Multi-Degree of Freedom Systems
 
53:53
The frequency response function method is explained and demonstrated.
Movie 7: Optimization of Reservations that an Airline Accepts
 
56:11
The lecture explains how airlines can maximize their expected profit by optimizing the reservation policies
Subjective Probability-Part 2
 
01:10:25
We continue the presentation of subjective probability and explain how to elicit it. To do so, we observe how a decision bets on the event of interest. The more money he bets the higher his probability is.
Lecture 16: Nonlinear Optimization
 
08:41
The Lecture Presents the Definition of a Nonlinear Optimization Problem With One Objective
Lecture 18. Forced Vibration of Systems to Arbitrary Forces
 
56:51
By expressing the system's response in terms of the mode shapes we calculate efficiently the response to arbitrary forces.
Lecture 17: Eliciting One's Utility Function To Plan For Retirement
 
45:44
In order to decide how much one needs to save for retirement, one must quantify her/his risk attitude. The lecture presents an example of estimating the utility function of an investor. Disclaimer: In order to decide how much one needs to save for retirement, one must quantify her/his risk attitude. The lecture presents an example of estimating the utility function of an investor. Disclaimer: The objective of the lecture is only to demonstrate concepts of decision analysis. Do not use the material in the lecture to make financial decisions.
Lecture 24: Finite Element Analysis, Part V
 
01:02:23
The lecture explains how to assemble the mass and stiffness matrices of a vibratory system and account for the boundary conditions.