Calculate the first three natural frequencies of a cantilever steel beam (E=210 GPa, 7800Kg/m^3) of length...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Calculate the first three natural frequencies of a cantilever steel beam (E=210 GPa, 7800Kg/m^3) of length L = 0.45 m. Assume that the beam has a rectangular cross-section with, d = 0.003 m, and b = 0.02 m. Recall that I = b bh³. A SDOF oscillates freely once the following IC are provided x(0) = 1, x(0) = 0, The amplitudes of two consecutive peaks of X(t1) = 0.545385m and X(t2) = 0.296315m, where t1=1.0049 sec, and t2=2.0098 sec. (a) Use the logarithmic decrement to calculate the value of the damping ratio . (b) Calculate the natural frequency of the system wn. Calculate the first three natural frequencies of a cantilever steel beam (E=210 GPa, 7800Kg/m^3) of length L = 0.45 m. Assume that the beam has a rectangular cross-section with, d = 0.003 m, and b = 0.02 m. Recall that I = b bh³. A SDOF oscillates freely once the following IC are provided x(0) = 1, x(0) = 0, The amplitudes of two consecutive peaks of X(t1) = 0.545385m and X(t2) = 0.296315m, where t1=1.0049 sec, and t2=2.0098 sec. (a) Use the logarithmic decrement to calculate the value of the damping ratio . (b) Calculate the natural frequency of the system wn.
Expert Answer:
Answer rating: 100% (QA)
Solution a The logarithmic decrement is defined as lnXt2Xt1 t2 t1 Using the given values ... View the full answer
Related Book For
Intermediate Algebra
ISBN: 9780134895987
13th Edition
Authors: Margaret Lial, John Hornsby, Terry McGinnis
Posted Date:
Students also viewed these general management questions
-
Aleksander is a trader with a financial year end of 30 June. He buys containers of sunflower seeds for $100 each. Some of these he ships to his agent Benji in northern Europe. He pays Benji a...
-
Mr. Butler runs a lawnmowing business. Recently his manager Ms Natalie reported that one of the mowers has to be replaced. After analysing the prices of different mowers, Ms Natalie finally came up...
-
The first three natural frequencies of an organ pipe are 126 Hz, 378 Hz, and 630 Hz. (a) Is the pipe an open or a closed pipe? (b) Taking the speed of sound in air to be 340 m/s, find the length of...
-
Find f x (x, y) and f y (x, y). f(x, y) = 2x + 5y 3x + y
-
Composite materials are now being utilized extensively in sports equipment. (a) List at least four different sports implements that are made of, or contain composites. (b) For one of these...
-
Ontario Traveller Magazine completed the following transactions during 2017: Aug. 31 Sold one-year subscriptions, collecting cash of $1,500, plus HST of 13%. Dec. 31 Remitted (paid) HST to Canada...
-
How can the impact of share repurchases on stock price be evaluated?
-
Calafs Drillers erects and places into service an off-shore oil platform on January 1, 2011, at a cost of $10,000,000. Calaf is legally required to dismantle and remove the platform at the end of its...
-
A relatively low (compared to other communities) tax leverage factor (operating expenditures / own revenue sources) indicates that if external funding sources are reduced, taxes will decrease. a...
-
Assume the following date for Water and Sewer Enterprise Fund after preliminary closing entries have been prepared. The CFO asks your assistance in allocating the assets and liabilities to the...
-
Problem 11-49 (LO 11-3, LO 11-4, LO 11-5) (Algo) Shimmer Incorporated is a calendar-year-end, accrual-method corporation. This year, it sells the following long-term assets: Asset Building Sparkle...
-
Max Company manufactures and sells a single product. The following costs were incurred during the company's first year of operations: Variable cost per unit: Production: Direct Materials Direct Labor...
-
If you cover a white light with a specially designed green plastic gel so that only the green light passes through, which color plastic cover gel do you need to add to the pure green light to make it...
-
What challenges might an organization face when trying to connect observed changes in behavior on the job to a specific program or initiative? How can these challenges be addressed to accurately...
-
Briefly describe the procedure you followed when carrying out face point testing.
-
INTRODUCTION TO DATABASES i) In your own words, explain Strategic Database Planning [2 marks] ii) Discuss (giving at least four reasons) why Database Planning is important. [4 marks] A B I
-
TASK (B) DEPRECIATION (13 POINTS) On January 24th, the Korab Inc. acquired a new packing machine for the production line with an estimated useful life of ten years. The price of the machine was...
-
Whats the difference between an ordinary annuity and an annuity due? What type of annuity is shown below? How would you change the time line to show the other type of annuity?
-
A company has determined that the cost y to make x (thousand) computer tablets is and that the revenue y from the sale of x (thousand) tablets is Find the break-even point, where cost equals revenue....
-
A student solved the following equation and obtained the proposed solutions x = -3 and x = 6. She gave { -3, 6} as the solution set. Give the correct solution set. V3x + 18 x =
-
Let (x) = x 2 + 4, g(x) = 2x + 3, and h(x) = x - 5. Find each of the following. (hog) (-2)
-
Describe the four steps in the closing process. LO15
-
Why are only the statement of financial position accounts permanent? LO17
-
Distinguish between a sunk cost and an opportunity cost. R-2
Study smarter with the SolutionInn App