Q1 The torsional vibration of one of the wings of an airplane is modelled as in Figure 1. Write the equation of motion in matrix form and calculate the natural frequencies in terms of the rotational inertias (J₁ and J₂) of the engines and rotational stiffnesses (k₁ and k₂) of the wing. model one wing as → Figure 1 J₂ K₁ pazg=29 K₂

Q1 The torsional vibration of one of the wings of an airplane is modelled as in Figure 1. Write the equation of motion in matrix form and calculate the natural frequencies in terms of the rotational inertias (J₁ and J₂) of the engines and rotational stiffnesses (k₁ and k₂) of the wing. model one wing as → Figure 1 J₂ K₁ pazg=29 K₂

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

Related questions

Q: A ship with metacentric height 0.36 m is cruising in sea. The Captain of the ship asked an engineer…

A: Given, Metacentric height = GM = 0.36 m Radius of gyration = K = 0.9 m Period of oscillation…

Q: Derive the expression for the frequency trasfer functions X,(i w)/F (i w) and 0(i w)/F(i w) and…

A: Given : To find : Transfer function

Q: The dynamic system below has the following parameters: m₁ = 20 kg, m₂ = 15 kg, m3 = 10 kg, k₁ = 100…

A: Given:To find:Mathematical modelTransfer functionState space representation

Q: Derive a model for the mechanical system represented below. The input being the force F and the…

Q: The vibration model is subjected to the force shown in the figure. Find the response of the system…

Q: Q6. For a point at distance 50 m and angle 450 to the axis which of the following are correct?…

A: Given data: a = 5 cm = radius of the piston q = 45° = angle between the axis of the piston and the…

Q: Please solve this problem by showing the manual calculation and choose the correct answer(SUBJECT:…

A: Given: →m1=1.8 Kg ; →m2=0.7Kg→k1=250 N/m→k2=700 N/m→k3=100 N/m And the give vibration is free…

Q: An automobile is modeled as shown in Figure below. Derive the equations of motion, build the…

A: FOR solution refer below images.

Q: particle of mass m is constrained to move under gravity on a smooth surface given by the equation:…

A: Given that h(x,y)=x2+y2-xyKinetic energy is T=12mx˙2+12my˙2Potential energy is V=mghx,y…

Q: ) Based on the vibration signal shown in Figure determine the damping ratio, natural frequency and…

Q: Q3 Assume that the 300kg trailer shown below in figure Q3 is fitted with two springs and two shock…

A: Given: m = 300 kgy = 40 mmζ=0.28ωn=10k=30000 To find: Range of driving speeds

Q: A 100-kg tumbler produces a harmonic force of magnitude 5000 N. The stiffness coefficient of the…

A: Write the magnitude of harmonic force. F=5000 N Write the stiffness coefficient of the support.…

Q: The figure below shows an aircraft fighter. Each wing of the aircraft may be modelled as a clamped…

Q: In order to evaluate the suspension unit, a test was carried out where the hammer is dropped onto…

A: Solution: Given Data:

Q: Recall the two coupled masses undergoing linear oscillations in Example 8, p.22-25. Solve a simple…

A: For solution refer below images.

Q: In this lab, we will observe the free response of a first order mechanical system: a rotating…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Find the equation of motion and the initial conditions for the following system: 1/s 1 s²+55+6 x} X…

A: We must do the inverse Laplace transform of the transfer function, which is denoted as follows, in…

Q: What is the dynamic model of the following system? Force F m Displacement x K₁ 5 ееее ееее elle O a.…

A: option-b :

Q: Consider the single degree of freedom spring–mass system shown in Fig. where k = 4 x 10$ N/m and m =…

A: Given data Consider the single degree of freedom spring-mass system shown in Fig. where k = 4 x 105…

Q: For the system below, the mass, m is attached to the end of a cantilever beam of length, l,…

Q: t. Design the following application case The mechanical vibration system is shown in Figure (a).…

Concept explainers

Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.

Question

Q1
The torsional vibration of one of the wings of an airplane is modelled
as in Figure 1. Write the equation of motion in matrix form and calculate the natural
frequencies in terms of the rotational inertias (J₁ and J₂) of the engines and
rotational stiffnesses (k, and k₂) of the wing.
44
model one wing as →
Figure 1
العالم
K₁₁
K₂

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given

VIEW

Step 2: Calculation of natural frequencies and equation in matrix form

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

Similar questions

Need help with parts C and D plssss
3
III) A relatively well-praised model for a car suspension is depicted in Figure 5: 4 4 Body Mass MW Suspension Mass b₂ ↑" Figure 5 - Model of the suspension of a car. Considering it is a system with two degrees of freedom, WRITE the equations that model the free vibrations of this system.
A simple harmonic oscillator, of mass and natural frequency , experiences anoscillating driving force . Therefore, its equation of motion is where is its position. Given that at we have , , find thefunction . Describe the solution if is approximately, but not exactly, equal to .
damping, c Sliding Crate with Bumper Stop A crate of mass m enters a lubricated slide at a loading dock with a velocity v, to the right and an initial position x(0) = x, in the diagram shown above. The sliding motion is lubricated, characterized by a linear damping coefficient C. At a distance x = L the crate contacts a bumper stop characterized by a spring constant k and a damping coefficient c. Numerical values for the system parameters are: C = 8 N-s/m k = 1000 N/m m = 50 kg X = 0 Vo = 5 m/s L= 20 m Ca is to be experimentally determined in completing this assignment Bumper: Assignment 1) Given these parameters, determine the governing dynamic equation for the crate position. 2) Convert the governing equation to state variable form. This requires two first-order equations: a. dv/dt f:(x,v) b. dx/dt = f.(x,v) where f, is a function of the states, x and v. where f, is a different function of the states, x and v. Make two sets of the above equations, one each depending on whether there…
The ideal gas law, discovered experimentally, is an equation of state that relates the observable state variables of the gas--pressure, temperature, and density (or quantity per volume): PV = NkBT (or pV = nRT), Figure L₂ Lx 1 of 1 Part A Find the magnitude of the average force (F) in the x direction that the particle exerts on the right-hand wall of the container as it bounces back and forth. Assume that collisions between the wall and particle are elastic and that the position of the container is fixed. Be careful of the sign of your answer. Express the magnitude of the average force in terms of m, vr, and L₂. ► View Available Hint(s) Submit Part B IVE ΑΣΦ ? Imagine that the container from the problem introduction is now filled with N identical gas particles of mass m. The particles each have different x velocities. but their average x velocity squared. denoted
Please show steps
Given an oscillator of mass 2.0kg and spring constant of 180N/m, what is the period without damping? Use numerical methods to model this oscillator with an additional friction force equal to where c is a positive damping constant. Using c=5.0, what is the new period of oscillation. What about for c=10? Assume initial position is 0.2m and initial velocity is zero. Please find the period using the position versus time plot and use the first full cycle of the motion.
HELP!!! ASAP!!! DIFERENTIAL EQUATION
III) A relatively well-praised model for a car suspension is depicted in Figure 5: 4 4 Body Mass MW Suspension Mass b₂ ↑" Figure 5 - Model of the suspension of a car. Considering it is a system with two degrees of freedom, WRITE the equations that model the free vibrations of this system.
3. Consider the vibrating system described below (t) 4 -2 -2 1 [ói]x+ [ $ ? ]x= 11 * 0 Compute the mass - normalized stiffness matrix, the eigenvalues, the normalized eigenvectors, the matrix P, and show that PTP I and PTKP is the diagonal matrix of eigenvalues A.
1. A thin disk attached to the end of an elastic beam has three uncoupled modes of vibration. The longitudinal motion, transverse motion and the torsional oscillations are all kinematically independent. Calculate the following for the system shown. a. Longitudinal stiffness b. Transverse stiffness c. Torsional stiffness mumm 65 cm r= 10 mm E-200 x 10° N/m² G=80 x 10º N/m²