Home / Questions / Flight vehicles such as airplanes and rockets are unconstrained and therefore they can und...
Flight vehicles such as airplanes and rockets are unconstrained, and therefore they can undergo rigid body motion. The free-free uniform beam gives some insight into the behavior of such free-free structures. Consider transverse vibration of the uniform beam (El = constant, pA = constant) shown in Fig. P13.6. (a) Show that the beam has two zero-frequency (i.e., rigid-body) modes, one mode in translation and one in rotation. (b) Determine the characteristic equation governing the nonzero frequencies. Your answer should contain the parameters λ and L. where λ is defined by Eq. 13.13. (Note that this is the same equation as obtained in Problem 13.5 for a uniform clamped-clamped beam.) (c) Determine an expression for the fundamental nonzero frequency of the beam (ω_{3} rad/s). (Note: For the rigid body modes, ω_{1}, = ω_{2} = 0.) (d) Determine an expression for the fundamental flexible transverse-vibration mode shape, φ_{3} (x ), and use M a t l a b , or another computer program, to plot the fundamental flexible mode. Scale the mode so that its maximum value is 1.0.
Problem 13.5
Consider transverse vibration of the uniform clamped-clamped beam shown in Fig. P13.5.' (a) Determine the characteristic equation for transverse vibration. Your answer should contain the parameters λ and L, where λ is defined by Eq. 13.13. (b) Determine an expression for the fundamental transverse-vibration frequency of the beam (tus rad/s), (c) Determine an expression for the fundamental transverse-vibration mode shape, φ_{1}(x) and use M a t l a b , or another computer program, to plot the fundamental mode. Scale the mode so that its maximum value is 1.0. (d) Using the results of Example 13.2, compare the fundamental frequency of the clamped-clamped beam with that of a simply supported beam. What is the effect of adding the slope constraints to the beam at x = 0 and x = L?
Example 13.2
Determine the natural frequencies and natural modes of a uniform beam that is simply supported at both ends, as shown in Fig. 1.
May 19 2020 View more View Less
Find the angle between the planes x+2y+3z=0 and 3x+2y+z=0.
Aug 08 2020When the price of a cake is $4, the price of pasta is $8 a dish, and Martha has $24 a week to spend, she buys 2 cakes and 2 dishes of pasta. Does she maximize her total u...
Jun 02 2020Collect the latest annual reports of Two (2) ASX listed companies for the last 3 financial years. Based on your collected annual reports, do the following tasks: (i) Iden...
Jan 31 2020Mouse Pad Computer Company, in addition to its retail sales, conducts night classes in computer technology. Mouse Pad has provided you the following information: Number o...
Mar 31 2020Turnbull is considering a project that requires an initial investment of $270,000. The firm will raise the $270,000 in capital by issuing $100,000 of debt at a before-tax...
May 02 2020Write a research essay of around 10 pages on the topic stated below in bold:In recent years, the Fijian government has resorted towards public-private partnership (PPP) i...
Dec 29 2019Evaluate the efficiency and profitability of the company by computing the following: (a) Net profit margin, (b) Total asset turnover, and (c) Return on total assets. Comm...
Mar 30 2020Shell lengths of sea turtles. Refer to the Aquatic Biology (Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise 2.83 (p. 65)...
Jul 31 2020The Morris Company is attempting to determine its costof capital in order to evaluate several proposed capital projectsand set its capital budget for next year. The follo...
Dec 01 2019MindToCengage Leaming X Grade 15FA ECONODA X + /nb/u/evo/index.htmlISBN 9781337096546bd1265972 an d 12650723-5374654356 Problems & Applications (Ch 04) Back to Assignment...
Jan 05 2020