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) Consder asimped quarter model of a paenger carpenson system ashown the fere 2. For amore accurate calulation, in general, damping dcharacterities and pring sines of the nytem should be modelled by considering a 200F nytem, a shown in the feure 2. However, for the sake of simplicity, let's consider anlyingita 1DOF ytem, hownin the fre below whed

) Consder asimped quarter model of a paenger carpenson system ashown the fere 2. For amore accurate calulation, in general, damping dcharacterities and pring sines of the nytem should be modelled by considering a 200F nytem, a shown in the feure 2. However, for the sake of simplicity, let's consider anlyingita 1DOF ytem, hownin the fre below whed

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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A numerical with a and parts solution given just do b c d parts

a) Consider a simplified quarter model of a passenger car suspension system as shown in the figure 2(a). For a more accurate calculation, in general, damping characteristikcs and spring stiffness of the system should be modelled by considering a 2-DOF system, as shown in the figure 2b). However, for the sake of simplicity, let's consider analysing it as a1-DOF system, as shown in the figure 2e) below: w wheel Spring Ccar body Read C (a) te) Figure 2 (a) Suspension system of a simplified Quarter-car model (b) The representative system considering 2-DOF (e) Simplified 1-DOF model Write the equations of motion for displocement x for the 1-DOF medel. b) If the displacement created by a rough road is represented by the following equation, 6() - (0.019) sin (6.5321) m And, the suspension system damping coefficient e 39 x 10 kg/s, equivalent spring stiffness of k= 389 kN/m, the mass the car = 1153 kg (with only the driver inside the car when the car was running). Calculate the amplitude of the maximum displacement xm of the car. e) Consider the same car with wo more added passengers, 150 kg is added to the total mas of the car. What is the change in natal fequency, velocity amplitade, and acceleration amplitude if the absolute maximum deflection a to remain same after adding the passengers as you've calculated in part "7 d) Now consider another car (Car 2) which is 400 kg heavier than the first car considered in part "e". Both cars have same passengers, same usprosion system ie similar demping coefficient and equivalent spring constant). ir he variable creating a forced fiequency or-02875v, wheee is the speed o calculate the deflections xi (for car 1) and e (for car 2) when both can. 50, 70, 100, and 110 kmh and fill eut the following table ei Deflection Deflection Frequency ratio for car 2, Car Frequency ratio for car 1. speed (m/s) Deflection due to the road condition follows the following function, where, 0.019 Also, what is the impact of increasing the speed in both cars? e) From a design perspective, is the suspension system wed for the second can appropriate? How would you adjust the values of damping coefficient e nd spring constant k such that the amplitude transmitted to the passenger compartment is kept to as low as possible?
Transcribed Image Text:a) Consider a simplified quarter model of a passenger car suspension system as shown in the figure 2(a). For a more accurate calculation, in general, damping characteristikcs and spring stiffness of the system should be modelled by considering a 2-DOF system, as shown in the figure 2b). However, for the sake of simplicity, let's consider analysing it as a1-DOF system, as shown in the figure 2e) below: w wheel Spring Ccar body Read C (a) te) Figure 2 (a) Suspension system of a simplified Quarter-car model (b) The representative system considering 2-DOF (e) Simplified 1-DOF model Write the equations of motion for displocement x for the 1-DOF medel. b) If the displacement created by a rough road is represented by the following equation, 6() - (0.019) sin (6.5321) m And, the suspension system damping coefficient e 39 x 10 kg/s, equivalent spring stiffness of k= 389 kN/m, the mass the car = 1153 kg (with only the driver inside the car when the car was running). Calculate the amplitude of the maximum displacement xm of the car. e) Consider the same car with wo more added passengers, 150 kg is added to the total mas of the car. What is the change in natal fequency, velocity amplitade, and acceleration amplitude if the absolute maximum deflection a to remain same after adding the passengers as you've calculated in part "7 d) Now consider another car (Car 2) which is 400 kg heavier than the first car considered in part "e". Both cars have same passengers, same usprosion system ie similar demping coefficient and equivalent spring constant). ir he variable creating a forced fiequency or-02875v, wheee is the speed o calculate the deflections xi (for car 1) and e (for car 2) when both can. 50, 70, 100, and 110 kmh and fill eut the following table ei Deflection Deflection Frequency ratio for car 2, Car Frequency ratio for car 1. speed (m/s) Deflection due to the road condition follows the following function, where, 0.019 Also, what is the impact of increasing the speed in both cars? e) From a design perspective, is the suspension system wed for the second can appropriate? How would you adjust the values of damping coefficient e nd spring constant k such that the amplitude transmitted to the passenger compartment is kept to as low as possible?
(a) S- extemal exi cation enungy T(x,) the and caternal fo reing and dipatie forus l i,x) kinetfe potlentional V() V(x) = 1 k Cact)") pex, á)- -cá Ct) +E %3D 2. deorngugre dagrange's lqua tón dor IDDF :- dt Equation of motion mä(t)+cé (t) +k XIt) =S,. S(t)- 0.019 )sin (6.5329 SLE) A Sin lwtto) SLt): A sin lwt +o SLE) - Asin Cwt) (0.019) SiR (G.532t) Marimum amplitude A =0.019.
Transcribed Image Text:(a) S- extemal exi cation enungy T(x,) the and caternal fo reing and dipatie forus l i,x) kinetfe potlentional V() V(x) = 1 k Cact)") pex, á)- -cá Ct) +E %3D 2. deorngugre dagrange's lqua tón dor IDDF :- dt Equation of motion mä(t)+cé (t) +k XIt) =S,. S(t)- 0.019 )sin (6.5329 SLE) A Sin lwtto) SLt): A sin lwt +o SLE) - Asin Cwt) (0.019) SiR (G.532t) Marimum amplitude A =0.019.
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