Videos uploaded by user “Efstratios Nikolaidis”

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

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

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

Standard Monte Carlo Simulation is Explained and Demonstrated

Views: 5621
Efstratios Nikolaidis

The lecture demonstrates the calculation of the volume of a sphere using simulation.

Views: 1858
Efstratios Nikolaidis

The mass and stiffness matrices of a beam element are derived by using energy principles.

Views: 3840
Efstratios Nikolaidis

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

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

This first lecture on forced vibration response studies the steady-state response of a system to a sinusoidal excitation.

Views: 6503
Efstratios Nikolaidis

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

Equations for the free vibration response are derived. Three system types are considered: overdamped, critically damped, and underdamped.

Views: 1965
Efstratios Nikolaidis

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

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

The lecture explained and demonstrates the calculation of the steady state response of a system to harmonic forces.

Views: 1553
Efstratios Nikolaidis

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

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

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

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

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.

Views: 834
Efstratios Nikolaidis

The Lecture Demonstrates the Solution a Nonlinear Optimization Problem With One Objective

Views: 798
Efstratios Nikolaidis

The lecture presents and demonstrates a method to optimize the amount of goods that an entrepreneur should order to maximize the expected profit.

Views: 166
Efstratios Nikolaidis

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.

Views: 460
Efstratios Nikolaidis

This lecture explains and demonstrates the calculation of the response of a single-degree-of-freedom system to harmonic excitation.

Views: 506
Efstratios Nikolaidis

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

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

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

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

The total reward of the players in most real life games is not constant. The lecture introduces the concept of such games.

Views: 132
Efstratios Nikolaidis

This lecture explains the derivation of the equations of motion of systems with multiple degrees of freedom.

Views: 841
Efstratios Nikolaidis

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.

Views: 144
Efstratios Nikolaidis

The free vibration response of a multi-degree of freedom system is derived by solving the equations of motion.

Views: 347
Efstratios Nikolaidis

The mode superposition and mode acceleration methods are explained and compared.

Views: 295
Efstratios Nikolaidis

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.

Views: 114
Efstratios Nikolaidis

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.

Views: 783
Efstratios Nikolaidis

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

The frequency response function method is explained and demonstrated.

Views: 802
Efstratios Nikolaidis

The lecture explains how airlines can maximize their expected profit by optimizing the reservation policies

Views: 68
Efstratios Nikolaidis

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.

Views: 232
Efstratios Nikolaidis

The Lecture Presents the Definition of a Nonlinear Optimization Problem With One Objective

Views: 164
Efstratios Nikolaidis

By expressing the system's response in terms of the mode shapes we calculate efficiently the response to arbitrary forces.

Views: 198
Efstratios Nikolaidis

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.

Views: 186
Efstratios Nikolaidis

The lecture explains how to assemble the mass and stiffness matrices of a vibratory system and account for the boundary conditions.

Views: 347
Efstratios Nikolaidis

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