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Formulas For Natural Frequency And Mode Shape

You must turn in your code as well as output files. Please generate a report that contains the code and ouput in a single readable format. Getting Started  You may want to download Irfanview image viewing software. It handles pretty much any image type, lets you convert, and provides batch processing.  Download the sample images from the class website. The following question operates on the city.jpg image. (a) Perform image smoothing using a 7×7 averaging filter and a Gaussian filter with σ = 0.5 and 3. Compare the outputs. (b) Perform edge enhancement using the Sobel operator (Matlab's default parameters). Repeat using the Laplacian and Laplacian of Guassian operators. Compare the outputs 2. Frequency Domain Filtering The following question operates on the city.jpg image. (a) Find the Fourier transform of the image. Be sure to center the frequencies. (b) Perform image smoothing in the frequency domain using the filters defined in the previous problem. Compare the output images from the two methods (spatial and frequency) and the time for operation. (c) Perform edge enhancement using the filters defined in the previous problem. (d) Define a lowpass filter in the frequency domain with radius of 1/4 the height. Show the result. Repeat with a similar sized Guassian and compare the results. Give the σ parameter you used and show the output transform image. (e) Repeat with a rectangular filter with the same dimension as the ideal lowpass. Compare the results between the ideal filter and the rectangular approximation. 3. Canny Edge Detection (a) Give the convolution kernels for determining the gradient. You may examine the function gradient.m to help with the explanation. (It may be easiest to apply the gradient to an impulse and inspect the results. (b) Implement the simplified version of the Canny edge detector (single scale). The syntax of the function should be where E contains the detected edges, M the smoothed gradient magnitude, A contains the gradient angle, I is the input image, sig is the σ parameter for the smoothing filter, and tau= [τ h , τ l ] is the two element vector containing the hysteresis thresholds. See Algorithm 6.4 for non-maximal suppression and Algorithm 6.5 for hysteresis thresh-olding. (It may be more efficient to implement the hysteresis as edge tracking)

http://ieeexplore.ieee.org/iel5/5/31355/01457626.pdf

Multidimensional digital signal processing

Dynamic load data have been Valuable for bridge and pavement design. Traditional ways to acquire truck axle and gross weight information are expensive and subject to bias, and this has led to the development of Weigh-in-Motion (WIM) techniques. Most of the existing WIM systems have been developed to measure only the static axle loads. This paper aims to introduce a method to identify moving dynamic loads on bridges using the bridge responses caused by such loads. A closed-form solution can be obtained to identify moving constant loads, while numerical methods must be used to identify the time-varying moving loads. The set of equations that leads to the solution is based on Euler's equation of beams. A two-axle vehicle model is developed to generate the theoretical responses and the corresponding interactive moving forces. Studies were carried out to check whether the proposed method could recover the original interactive moving forces and the method was found to be feasible.

An interpretive method for moving force identification

Enhanced band-gap properties of an acoustic metamaterial beam with periodically variable cross-sections

Computer program aids in reduction and analysis of data. It determines critical loading conditions for critical values of reactions, applied loads, deflections, stresses, internal loads, etc. Input to program must be in one of specified three-part format.

Finite-element structural analysis

Vibration of a beam subjected to a moving force: Frequency-domain spectral element modeling and analysis

Dynamic analysis of a multi-span beam subjected to a moving force using the frequency domain spectral element method

The modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey reveals that the necessary information reported in the existing literature is sometimes very limited or incomplete, even for simple beam models such as Timoshenko beams. Thus, we present complete information on the natural frequencies, three types of mode shapes, and the orthogonality of the mode shapes for simply supported Timoshenko beams. Based on this information, we use the MAM to derive the forced vibration responses of a simply supported Timoshenko beam subjected to arbitrary initial conditions and to stationary or moving loads (a point transverse force and a point bending moment) in analytical closed form. We then conduct numerical studies to investigate the effects of each type of mode shape on the long-term dynamic responses (vibrations), the short-term dynamic responses (waves), and the deformed shapes of an example Timoshenko beam subjected to stationary or moving point loads.

/pdf/forced-vibration-of-a-timoshenko-beam-subjected-to-2sqc8y7xiz.pdf

Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

Modified one-element method for exact dynamic responses of a beam by using the frequency domain spectral element method

We propose a new spectral element model for finite rectangular plate elements with arbitrary boundary conditions. The new spectral element model is developed by modifying the boundary splitting method used in our previous study so that the four corner nodes of a finite rectangular plate element become active. Thus, the new spectral element model can be applied to any finite rectangular plate element with arbitrary boundary conditions, while the spectral element model introduced in the our previous study is valid only for finite rectangular plate elements with four fixed corner nodes. The new spectral element model can be used as a generic finite element model because it can be assembled in any plate direction. The accuracy and computational efficiency of the new spectral element model are validated by a comparison with exact solutions, solutions obtained by the standard finite element method, and solutions from the commercial finite element analysis package ANSYS.

/pdf/frequency-domain-spectral-element-model-for-the-vibration-2m29s9v34z.pdf

Taehyun Kim

Papers

Vibration of a beam subjected to a moving force: Frequency-domain spectral element modeling and analysis

Dynamic analysis of a multi-span beam subjected to a moving force using the frequency domain spectral element method

Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

Modified one-element method for exact dynamic responses of a beam by using the frequency domain spectral element method

Frequency Domain Spectral Element Model for the Vibration Analysis of a Thin Plate with Arbitrary Boundary Conditions