Q2 The vibration in the vertical direction of an airplane and its wings can be modelled as a three-degree-of-freedom system with one mass corresponding to the right wing, one mass for the left wing, and one mass for the fuselage. The stiffness connecting the three masses corresponds to the wing and is a function of the modulus E of the wing. The equation of motion is: [100x₁ EI m0N 0₂ + -3 0 0 1 m where N=2.5 (i.e. the fuselage mass is N=2.5 times the wing mass). The model is shown in Fig. 2. Calculate the natural frequencies and mode shapes. Interpret the mode shapes in terms of the airplane's deflections in each mode. Use the following data: E=(7.1.10¹) Pa, l=3.5 m, m=3000 kg, and I= (1.05.10-5) m¹. k= 3 -3 6 0 -3 3EI 7³ Nxm m x₁(t) x₂ (1) Figure 2 EI 0 313-8 -3 x₂ k= 3EI x₂ (1) Nxm m x₂ (1) EI m x₂ (1)

Q2 The vibration in the vertical direction of an airplane and its wings can be modelled as a three-degree-of-freedom system with one mass corresponding to the right wing, one mass for the left wing, and one mass for the fuselage. The stiffness connecting the three masses corresponds to the wing and is a function of the modulus E of the wing. The equation of motion is: [100x₁ EI m0N 0₂ + -3 0 0 1 m where N=2.5 (i.e. the fuselage mass is N=2.5 times the wing mass). The model is shown in Fig. 2. Calculate the natural frequencies and mode shapes. Interpret the mode shapes in terms of the airplane's deflections in each mode. Use the following data: E=(7.1.10¹) Pa, l=3.5 m, m=3000 kg, and I= (1.05.10-5) m¹. k= 3 -3 6 0 -3 3EI 7³ Nxm m x₁(t) x₂ (1) Figure 2 EI 0 313-8 -3 x₂ k= 3EI x₂ (1) Nxm m x₂ (1) EI m x₂ (1)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

See similar textbooks

Similar questions

Consider a mass-and -spring system containing two masses m1=1 and m2=1 whose displacement functions x(t) and y(t) satisfy the differential equations : x'' = -10x + 2y y'' = 3x -15y Assume that the two masses start in motion with the initial conditions x(0) =32, x'(0)=6, and y(0)=36, y'(0)=3 and are acted on by the same force F1(t)=F2(t)=-1320cos(7t). Describe the resulting motion as a superposition of oscillations at the three different frequencies. The three frequencies consist of lower, higher, and the forcing frequency. For each one please compare the magnitude of m2 to m1.
A spring is stretched 175 mm by an 8-kg block. If the block is displaced 100 mm downward from its equilibrium position and given a downward velocity of 1.50 m/s,determine the differential equation which describes the motion. Assume that positive displacement is downward.Also, determine the position of the block when t = 0.22 s.
The period of vibration for a cylindrical barrel floating in salt water is foundto be τ1 s when the barrel is empty and τ2 s (≥ τ1) when it is filled with Llitres of crude oil. The density of the oil is ρc kgm−3Determine the following:a) The cross – sectional area of the barrel A in m2 b) The mass of the crude oil c) The mass of the empty barrel d) The density of the salt water, ρsw in kgm−3
A 9-kg block is suspended from a spring having a stiffness of k = 200 N/m. If the block is given an upward velocity of 0.4 m/s when it is 95 mm above its equilibrium position, determine the maximum upward displacement of the block measured from the equilibrium position. Assume that positive displacement is downward.
The maximum amplitude and the maximum acceleration of the foundation of an industrial fan were found to be x_max = 0.4 mm and max acceleration = 0.25g. Determine the operating speed of the fan.
mass 1 is excited by a harmonic force whose maximum value and frequency are 2 N and 50 Hz, respectively. Where m1 = 5 kg, m2 = 5 kg, k1 = 2000 N/m and k2 = 2000 N/m. Which answer represents the amplitude X1 and X2?
but change the spring constant (k) of spring DB to 310 N/m
A spring has a spring constant of k=18N/m, hung with a weight of mass m=½ kg. If the load is in an equilibrium position, then it is pulled and released with a speed of 3 m/s, then determine the equation of motion of the object if it does not experience friction or damping.
A reciprocating pump, of mass 68.6 kg, is mounted at the middle of a steel plate of thickness 0.8 cm, width 50.4 cm, and length 279 cm, clamped along two edges as shown in the accompanying figure. During operation of the pump, the plate is subjected to a harmonic force F(t)=301 cos(84.60t) N. Find the amplitude of vibration of the plate. Given that the equivalent stiffness of the plate can be calculated as k=192EI / l^3and the young modulus is E=200 GPa.
An 8-lb weight stretches a spring 4 ft. The spring–mass systemresides in a medium oering a resistance to the motion equal to1.5 times the instantaneous velocity. If the weight is released ata position 2 ft above its equilibrium position with a downwardvelocity of 3 ft > sec, find its position relative to the equilibriumposition 2 sec later.
k = 2.4 N/cm, W = 24N, L1 = 12cm, L2 = 8cmThe total weight of the object shown in the figure is W.Find the period of small amplitude vibrations of the object. (The bar thicknesses will be neglected)
The mass of the car is 1400 kg, which is evenly distributed over the four springs. The car's own weight compresses the springs into a pile for a distance of 20 cm. What is the characteristic frequency of car vibration in Hertz to one decimal place?