Rayleigh's damping model has been used to evaluate the damping matrix, C=aM+ BK, for a fixed-fixed bar, split in 3 elements, and subject to axial vibration. M and K are the mass and stiffness matrices respectively. Please select all the answers that apply: The coupled equations of motion can now be decoupled into single mode equations. The damping is stiffness dominated when ß is large. Following observations through experimental testing, a=ß in most cases. We will obtain large damping at high frequencies only if a large. Following observations through experimental testing, ß is always null.

Rayleigh's damping model has been used to evaluate the damping matrix, C=aM+ BK, for a fixed-fixed bar, split in 3 elements, and subject to axial vibration. M and K are the mass and stiffness matrices respectively. Please select all the answers that apply: The coupled equations of motion can now be decoupled into single mode equations. The damping is stiffness dominated when ß is large. Following observations through experimental testing, a=ß in most cases. We will obtain large damping at high frequencies only if a large. Following observations through experimental testing, ß is always null.

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

Given the vibrating system below: K4 Y(t) =Ysin30t where for = 30 and Y=20mm Find the following K1 K2 m C3 H C2 C1 C5 C4 1. Frequency Ratio 2. Displacement Transmissibility Ratio 3. Absolute displacement of the mass 4. Type of Damping 5. Equation of motion x(t). Assume Initial conditions for displacement and velocity 6. Graph 2 cycles of the vibrating system. You can use third party app for this. M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2=40 Ns/m C3= 35Ns/m C4= 15 Ns/m C5= 10 Ns/m
A structure has a mass of 10 kip/g and a stiffness of 10 kip/in. The acceleration of gravity, g, is 386.1 in/s2. What is the value of damping assumed by the code?
Given the vibrating system below: K1 K3 K4 Find the following 1. Keq 2. Ceq 3. Natural angular velocity K2 m C1 C3 C5 C2 C4 4. Damped angular velocity 5. Type of Damping 6. Equation of motion x(t). Assume Initial conditions for displacement and velocity Graph 2 cycles of the vibrating system. You can use third party app for this. 7. M = 10 kg K1=100 N/m K2= 80 N/m K3=75 N/m K4= 120 N/m C1 = 20Ns/m C2= 40 Ns/m C3= 35Ns/m C4= 15 Ns/m C5= 10 Ns/m
Q1 A vibration model of a machine system that consists of three levers connected by lightweight linkages (represented by spring) is shown in Figure Q1. Each lever has a length, L with the distance of linkage from pivot point is given as ´a’. Important: Please provide the final answer equation of motion in the matrix form of unknown m, k, a and L. (a) By using Lagrange equation, determine the equation of motion of the system by considering 0,, 02 and 03 are very small. (b) Prove the answer from Q1(a) by using Newton's second law. Use a free body diagram to support the answer.
The following model describes material model as a viscous damper in parallel with an elastic stiffness (spring) and both are in series with another spring. E E, C Drive the governing equation of the model (stress-strain relation) • Drive the creep behaviour of the model under constant load Drive the strass relaxation of the model under constant strain
Calculate the natural frequencies and vibration modes of a free-vibrating 2-GDL spring-mass system, using the matrices of this system presented below. mass matrix stiffness matrix [":] m 2k -k M K: %3D т ーk 2k
1. Suppose you are riding your bicycle on a bumpy road having a surface profile that varies harmonically with +/- 6 cm undulations. The distance between consecutive peaks of these undulations is 2 m. When you sit on the seat of your bike for your casual ride, the springs deflect 5 cm. When you are seated, the damper under the seat provides an equivalent linear viscous damping of 10% of the critical damping. A simple representation of your ride on the "never-ending" rough road is shown below. (a) If you are riding your bicycle at a horizontal speed of 2.5 m/sec, how much bumping up and down will you experience? (b) Next day, you are carrying a backpack which increases your on-seat weight by 20%. Assuming that you are still able to ride with same speed, will this "loaded" ride be more or less comfortable than your previous, "no backpack" ride? M k/23 k/2 6 cm 2 m
O choose 1/2 dynamics model or whole- car dynamic model of the automobile O obtaion the motion differential equations of the chosen model and the equations of non-damping free vibration O calculate the natural frequencies and natural modes by Matlab program 1/2 dynamic model of the automobile parameters O% body mass M 690kg O mass moment of inertia J, = 1222kgm O wheel mass M= 40.5kg. M= 45.4kg O tire stiffness k =k, - 192000N/m O sispension stiffness ky 17000N/m. k, =2000ONim O suspension damping coefficient c c, = 1500Ns/m O geometry dimensions a= 1.25m, b= 1.51m whole-car dynamic model of the automobile Xe kater el kel lee kal te parameters O body mass m,-1380kg O mass moment of inertia of pitch 1,-2444kgm O mass moment of inertia of roll 1,-3800kgm O Viwheel distance t-0.74m O the other parameters are the same as the l/2 dynamic model
Q2 The angular position c of a mass is controlled by a servo system through a referen signal °r. The moment of inertia of moving parts referred to the load shaft, J, is 150 kebo and damping torque coefficient referred to the load shafi(B, is 4.5 x 103 Nw-m fraden The torque developed by the motor at the load s 7.2 x 10* Nw-m per radian of error (a)Obtain the response of the system to a step input of 1 rad and determine the peak time, peak overshoot and frequency of transient oscillations. Also find the steady state error for à constant angular velocity of 1 revolution / minute. (b)If a steady torque of 1000 Nwm is applied at the load shaft, determine the steady Kan state error. 5(J5+ B) 03 For the system shown, apply a proportional controller to move the time constant to a sixth of its open loop value. R(s) + E(s) U(s) Kp 'Y(s) s +0.333 10
4. A convenient way to measure damping in a single-degree-of-freedom system is called logarith- mic decrement of free response. Consider the free response given by (4). Let's denote t₁ and t2 denote the times corresponding to two consecutive displacements ₁ and 2 measured one cycle apart, i.e., where t₂ = t₁ + T 2π Wd According to (4), show that the logarithmic decrement dis T = x1 8 = log = x2 where log has base e. Combine (5), (7), and (8) to obtain = (WnT 8 4π² +8² Will this method work for other initial conditions? why?
A student is asked to design a four bar crank-rocker mechanism that satisfied Grashof mechanism with following condition: time ratio is 1:1.4, rocker is 70 mm and maximum oscillation angle is 60 degree. (ii) Solve the angles a, ß and ô for crank-rocker mechanism following the condition given. (iii) Based on information in Q2(ii), design the four bar crank-rocker that satisfied all the condition given. Please label all the links and angles a, ß and ô in your design. (iv) If time ratio of this mechanism becomes 1, construct the kinematics diagram of the crank- rocker mechanism. Please label all the links and angles a, ß and d in your design.
A body of mass 100 kKg is suspended by a spring of stifness of 30KN/m and a dashpot of damping constant 1000 N.s/m. Vibration is excited by harmonic force ft)=80 cos (67tt) 1- Write the equation of motion of the system using Lagrange's equation. 2- Find the natural frequency and the driving frequency. 3- Write the complete solution of the vibrating system.