Mechanical Engineering

We consider the ordinary differential equation of second order beam bending:

q(x)=E*I*w”’-Fn*w” The homogenous solution is: w(x)=c1+c2*x+c3*sin(k*x)+c4*cos(k*x) with k =−(Fn)/(E*I) Determination of the integration constants leads to a linear equation system of theformA(k)∙c = bThese non-trivial solutions can be determined with the conditiondet A(k) = 0With the following steps determine the buckling load and buckling shape of thedepicted Euler cases I-IV.1. Determine the boundary conditions (at …

We consider the ordinary differential equation of second order beam bending: Read More »

The spur gear is subjected to the two forces caused by contact with other gears. Determine the resultant of the two forces and express the result as a Cartesian vector.

EXPERT ANSWER General guidance Concepts and reason The representation of the force in a Cartesian vector is the force with both magnitude and the direction of the force acting. Vector: Vector is used represent a quantity in terms of magnitude and direction. Resultant force: “The Resultant force is defined as the total force acting on …

The spur gear is subjected to the two forces caused by contact with other gears. Determine the resultant of the two forces and express the result as a Cartesian vector. Read More »

Q1 (a) Referring to the system shown in Figure 1, determine the values of K and k such that the system has a damping ratio of 0.7 and an undamped natural frequency Wy of 4 rad/sec. (4 marks) R(s) C(s) K (s + 2) k Figure 1: Block diagram of a system (b) Calculate the rise time, peak time, maximum overshoot, and settling time in the unit-step response of a closed-loop system given by C(s) 36 R(S) 52 + 2s + 36 (8 marks) (c) A feedback system is shown in Figure 2 i Determine the steady-state error for a unit step when K = 0.4 and Gy(s)-1. (8 marks) Select an appropriate value for Gr(s)so that the steady-state error is equal to zero for the unit step input. (5 marks) R(s) Y(s) G (8) к s(8 + 2) (5 + 3) (s + 0.1) Figure 2: Block diagram of a feedback system

EXPERT ANSWER while y(r)<1.0001; r=r+1; end; rise_time=(r-1)*0.005 [ymax,tp]=max(y); peak_time=(tp-1)*0.005 max_overshoot=ymax-1 s=1001; while y(s)>0.98&y(s)<1.02; s=s-1; end settling_time=(s-1)*0.005 step: 8 MATLAB ouput:

To determine the strength of the riveted joints in a cylindrical vessel, tensile tests were performed on the 6-in wide specimens as shown in the figure. the tensile force p at failure was found to be 32 kips for the longitudinal joint specimen and 16 kips for the circumferential joint specimen . determine the largest allowable inner diameter of the cylinder that can support a pressure of 150 psi with a factor of safety of 2.0

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