Question: You are modeling a beam with a step discontinuity in cross-section located at x/L= 0.35. You wish to use the Rayleigh-Ritz method to approximate

You are modeling a beam with a step discontinuity in cross-section located at x/L= 0.35. You wish to use the Rayleigh-Ritz method to approximate the first five natural frequencies of the structure. The boundary conditions of the structure are clamped at both ends. a) One of your classmates suggests the following set of shape functions to use in your model: cos(2x/L)-1, cos(3x/L)-1, cos(4x/L)-1, cos(5mx/L)-1.... Could this set of functions be used in the Rayleigh-Ritz analysis of your structure? Why or why not? b) What is the lower bound on the number of shape functions required for this analysis? c) How do you know whether you have used enough shape functions to produce reliable results?

Step by Step Solution

★★★★★

3.40 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a One of your classmates suggests the following set of shape functions to use in your model cos2 xL1 cos3 xL1 cos4 xL1 cos5 L1 Could this set of funct... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Civil Engineering Questions!

John Parsons ( 1 2 3 - 4 5 - 6 7 8 1 ) and George Smith ( 1 2 3 - 4 5 - 6 7 8 2 ) are 7 0 % and 3 0 % owners, respectively, of Premium, Inc. ( 1 1 - 1 1 1 1 1 2 0 ) , a candy company located at 1 0 0...

Jupiter is 7.8108 km from the Sun and has an albedo of0.73. Its atmosphere is mostly hydrogen and helium. a) Calculate the surface temperature of Jupiter, assuming thatthe Sun is the only energy...

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

This case provides students with a real-world, hands-on experience in developing a balanced scorecard. It is different from other balanced scorecard cases in that it takes place in a charitable...

Respond to at least two colleagues by explaining a strategy social workers might use to advocate for fair benefits within this program for the populations your colleagues selected.

Jones & Bartlett Learning, LLC. NOT FOR RESALE OR DISTRIBUTION CHAPTER Hot Spot Analysis 10 LEARNING OBJECTIVES C A R R Provide a working definition of a \"hot spot.\" , Be able to explain different...

5, Putting Together an Evaluation Matrix An evaluation plan is a written document that describes the cWill/mat\Questions to ask yourself when putting together an evaluation matrix: Evaluation...

Draw the moment diagram for the beam. Follow the sign convention Show me step by step and explain how to draw it . Thanks Draw the moment diagram for the beam. Follow the sign convention. Click on...

1 ) Draw the influence line for the vertical reaction at A . Indicate the values of the influence line at each marked point along the beam. Draw discontinuity lines at each marked point along the...

Draw the shear and moment diagrams for the beam in ( Figure 1 ) . Follow the sign convention. Fin re Part B Draw the moment diagram for the beam. Click on "add discontinuity" to add discontinuity...

Draw the shear and moment diagrams for the beam inDraw the shear and moment diagrams for the beam in ( Figure 1 ) . Follow the sign convention. Figure Draw the shear diagram for the beam. Click on...

The latest weather report includes the following statement: The temperature is 78F, barometric pressure is 29.9 inches, and the relative humidity is 87%. From this information, estimate the mole...

Kim works for a clothing manufacturer as a dress designer. During 2019, she travels to New York City to attend five days of fashion shows and then spends three days sightseeing. Her expenses are as...

8.4 In the circuit of Fig. 8.65, find: (a) v (0+) and i (0+), (b) d v (0+) dt and di (0+) dt , (c) v () and i (). 302 0.25 H ww m 4u(-) V ( 0.1 F HE ww +V- 5 4u(t) A

Suppose that the widget market consists of three equally efficient sellers, each with a marginal cost of $1. a. Assume that competition is well described by the "pure" Bertrand model. If two of these...

Mention common modes of failure of reinforced concrete buildings?

Two players play an asymmetric prisoners dilemma. Each can Cooperate or Defect. The payoffs from each pure strategy profile are as follows: for (c, c), (2, 4); for (c, d), (0, 5); from (d, c), (4,...

GMC INC. is a US oil refinery that operates on a multinational scale in both producing and selling crude oil. It is currently August 31 2020, and the firm anticipates selling 500,000 barrels of crude...

Whats the interest rate of a 9-year, annual $3,300 annuity with present value of $20,000?(Use a time value of money calculator or a spreadsheet. Round your answer to 2 decimal places.)

If you run a multi-objective optimization and generate a Pareto optimal set of solutions, what work do you still have to do to determine the best solution for your supply chain?

In the mathematical formulation, why can Y be a continuous linear variable and still give a legitimate solution? (For example, what does a Y value of 0.45 mean?)

You are starting a network modeling project. When you ask the project manager what the objective of the study is, you get the answer, We want to optimize the entire end-to-end supply chain. Why...

4. How does light reset the biological clock?

9. Why do most antihistamines make people drowsy? 10. What would happen to the sleepwake schedule of someone who lacked orexin?

21. How does L-dopa relieve the symptoms of Parkinsons disease?