suspension or You are requested to design an aut shock absorber system. In order to simplify the problem to one dimensional multiple mass-spring-damper system, a quarter vehicle model is used. The system parameters and free-body diagram of such system is shown below. M₁: Automobile body mass M₂: Wheel and suspension mass K₁: Spring constant of suspension system K₂: Spring constant of wheel and tire B: Damping constant of shock absorber = 2500 kg = 320 kg = 80,000 N/m = 500,000 N/m = 350 N-s/m Automobile- Suspension system Wheel- M₁₂ M₂ Rn Ka x₁(1) x₂(1) Tire

suspension or You are requested to design an aut shock absorber system. In order to simplify the problem to one dimensional multiple mass-spring-damper system, a quarter vehicle model is used. The system parameters and free-body diagram of such system is shown below. M₁: Automobile body mass M₂: Wheel and suspension mass K₁: Spring constant of suspension system K₂: Spring constant of wheel and tire B: Damping constant of shock absorber = 2500 kg = 320 kg = 80,000 N/m = 500,000 N/m = 350 N-s/m Automobile- Suspension system Wheel- M₁₂ M₂ Rn Ka x₁(1) x₂(1) Tire

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

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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
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
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?
A spring system is shown here: k₁ 3 Ę k3 2 K₂ www ma 4 Ę₂ Part 1: For this specific system, develop the: a. Global stiffness matrix . b. Boundary condition vector • c. Load vector • d. Reduced system of equations • e. Reaction force equations (i.e., the equations eliminated by the boundary conditions) Part 2: Given: k1 = 70 N/mm, k2 = 110 N/mm, k3 = 165 N/mm, F1 = 150 N, F2 = 100 N, and nodes 1 and 3 are fixed; calculate the: a. Global stiffness matrix b. Displacements of nodes 2 and 4 c. Reaction forces at nodes 1 and 3 d. Spring force in each of the springs
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
Find the differential equation of the mechanical system in Figure 1(a) To obtain the differential equation of motion of the mass and spring system given in Fig. 1. (a) one may utilize the Newton's law for mass and spring relations defined as shown in Fig. 1. (b) and (c) use f = cv for viscous friction, where v is the velocity of the motion and c is a constant. Z/////// k M F. F, F F F, F, k EF=ma F = k(x, - x,) = kx (b) (c) Figure 1: Mass-spring system (a), Force relations of mass (b) and spring (c)
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
2. Below is a picture of a car suspension system with additional springs (in red) added in series. Assume the car remains "level" (i.e. no rotational motion of the car body, only vertical motion). The original springs are ks modeling tire/road interaction). The car mass is m = 2,000 kg. 20, 000 N/m (the suspension spring), and kt 100, 000 N/m (the spring %3D The springs are all in equilibrium when d = 0.4 m. Ignore gravity in this problem. The point of the additional spring k is to make the ride more "bouncy" (some people like it that way). However, you need to make sure the car does not "bottom out" (i.e. hit the bump). It is known that when the springs are unstretched/uncompressed, the marimum vertical velocity can be is 1 m/s. What is the minimum value of the spring constant k (of the additional red spring) so that the car does not hit the bump during its vertical oscillations. Hint: Use energy balance. kis k's kt Figure 4: Simplified car model with upper springs representing…
The car's corner mass is m₁ = 220 kg and the unsprung mass is m₂ = 16 kg . The suspension spring stiffness is k = 13000 N/m and the tire stiffness is k, = 150000 N/m. a) Find the ride rate, RR, in N/m. b) Find the bounce natural frequency, f, in Hz for this corner of the car. c) Find the value of the suspension damping coefficient, c, that corresponds to a suspension damping ratio of 5 = 0.5. d) Find the damped natural frequency, fa, in Hz if the damping ratio is 5 = 0.5. m₂ k₂ m₁ III Jizz Z2 z, (t) = A, sin ot
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
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): A. Use Laplace transform of the differential equation to determine the transfer function of the system.
A velocity of a vehicle is required to be controlled and maintained constant even if there are disturbances because of wind, or road surface variations. The forces that are applied on the vehicle are the engine force (u), damping/resistive force (b*v) that opposing the motion, and inertial force (m*a). A simplified model is shown in the free body diagram below. From the free body diagram, the ordinary differential equation of the vehicle is: m * dv(t)/ dt + bv(t) = u (t) Where: v (m/s) is the velocity of the vehicle, b [Ns/m] is the damping coefficient, m [kg] is the vehicle mass, u [N] is the engine force. Question: Assume that the vehicle initially starts from zero velocity and zero acceleration. Then, (Note that the velocity (v) is the output and the force (w) is the input to the system): 1. What is the order of this system?