Problem: Lagrangian and Eulerian DescriptionThe motion of a body is given byX = X, +aX,tx, = X, +aX,tx; = X;with a constantwith (x1, x2, X3) being the coordinates of a material point M in the current configuration at a time"t", while (X1, X2, X3) are the coordinates at t=0 (initial configuration)a) Determine the displacement vector u(X1, X2, X3), the velocity vector v(X1, X2, X3) in theLagrangian description.b) Determine the displacement vector u(x1, x2, X3), the velocity vector v(x1, X2, X3) in theEulerian description.ôx,c) Calculate the deformation gradient F (F,).d) Calculate the right Cauchy Green strain tensor C and the finite strain tensor E

Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Answered: The motion of a body is given by X; =…

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

2. As a traffic engineer, you have been asked to investigate the dynamic response of the road sign (in Figure a below) to wind gusts. In particular, you are to stu-the bending and torsional response of the support pole for the sign due to initial velocity conditions due to a wind gust (Figure b). Derive the equation of motion using Lagrange's equation and show it in matrix form (neglect gravity). (25) San Diego Fwy Speed Limit 55 (White Ford Broncos 25) (a) Front View (b) Top View G M. Ic 0
Q: for the following equation, what are the units of x., u, and a if X, is the distance in m. t, is the time in second? [X. x3 = + u?t +
If f(x.y,z) = xy+ yz + xz. The maximum rate of change of f at the point P(1,2,3) is: %3D 50 O 11 O 5V2 32
A = (A1)ï+ (A2)J + (A3)k A = 2, B = 3 B = (B1)ï + (B2)J + (B3)k ĀxB = ? Ā.B= ? JÃ×B]= ?
A four-bar mechanism is used to transmit power to slider E. Link AC rotates counterclockwise at 100 rpm. A and B are fixed points. The following linkages are measured in cm: AC=35, AB=70, CD=45, BD=45, DE=40. Find the instantaneous velocity of slider E in cm/s 1.Draw the mechanism in appropriate scale on your paper2. Find the instantaneous linear velocity of C3. Find a point on your paper to draw the velocity polygon and scale the magnitude of the computed linearvelocity4. Use the relative velocity equation for finding the linearvelocity of D; ? = ? + ?? ? ?/?5. Remember that although the magnitudes are unknown, their directions can be identified6. Obtain the magnitudes of the unknown velocities from the velocity polygon7. For Link DE, repeat the process by using ? = ? + ??the line as much as needed8. Remember that E is a SLIDER therefore it can only goin the direction where its movement is not constrained? . Add the vector ? to the head of ? and extend?/? ?/??
Find a vector equation and parametric equations for the line segment that joins P to Q. P(3.5, −2.4, 2.1), Q(1.8, 0.3, 2.1) vector equationr(t)= parametric equations (x(t), y(t), z(t)) =
mecha
: For the square object of points: P1-(1,1,2), P2- (3,1,2), P3= (3,3,2), P4 (1,3,2), find the final transformation matrix when the object is translated by [4 2 0], rotated about z-axis by 45° CW, then reflected through XY plane
2. A kilogram mass is attached to the end of the spring with spring constant 2 N/m. Find the equation of motion if the mass is initially released (set in motion) from rest from a point 1 meter above equilibrium position. (Use the convention that displacements measured below the equilibrium position are positive.) (a) Write the initial-value problem which describes the position of the mass. (b) Find the solution to your initial-value problem from part (a). (c) Graph the solution found in (b) on (0
Q2 (a) The uniformly loaded beam ABC has simple supports at A and B and an overhang BC (see Figure Q2(a)). Values X, Y and Z are given in Table Q2 (a). (i) Determine the support reaction of the beam. (ii) Draw the shear diagram and determine the point on the beam where the zero shear occurs. (iii) Draw the moment diagram and determine the points where the zero moment occurs. Table Q2(a): Parameter Parameter 1000 N/m Y 0.9 m Z 0.6 m
Q6 (a) Figure Q6(a) shows an example of pressure vessel with radius of r, and yield stress Oy. Suppose the vessel is subjected to uniform internal pressure p, determine the minimum thickness to sustain the pressure according to: (i) Von Mises yield criterion (ii) Tresca yield criterion
Q1 A three-level offshore platform located in the Helang Oilfield area has a 1500 kg floor steel grating supported at each level. The structure sometimes is subjected to a vertical ocillation movement during rough sea waves given by function of y(t) = Y sin wt. If the steel grating only moves in the vertical direction and is supported by one equivalent spring and damper at each steel grating pole level with stiffness, k1 = (300 x 4) N/m, k2= (200 × 4) N/m and k3= (100 x 4) N/m while damping, c= (15 × 8) Ns/m, c2 = (10 x 8) Ns/m and c3 = (5 × 8) Ns/m, respectively, as simplified in Figure Q1. Neglect the effect of gravitational force. (a) Sketch a free body diagram for each steel grating that includes the mass's action and reaction forces. (b) Determine the equation of motion in a matrix form using Newton's second law, [m]ÿ + [c]ý + [k]y = F. (c) By omitting the damping and external force parameter, deduce and express the general solution in the form of ([k] – w?[m]D{Y} = 0.

SEE MORE QUESTIONS

Recommended textbooks for you

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Elements Of Electromagnetics

Mechanical Engineering

ISBN:

9780190698614

Author:

Sadiku, Matthew N. O.

Publisher:

Oxford University Press

Mechanics of Materials (10th Edition)

Mechanical Engineering

ISBN:

9780134319650

Author:

Russell C. Hibbeler

Publisher:

PEARSON

Thermodynamics: An Engineering Approach

Mechanical Engineering

ISBN:

9781259822674

Author:

Yunus A. Cengel Dr., Michael A. Boles

Publisher:

McGraw-Hill Education

Control Systems Engineering

Mechanical Engineering

ISBN:

9781118170519

Author:

Norman S. Nise

Publisher:

WILEY

Mechanics of Materials (MindTap Course List)

Mechanical Engineering

ISBN:

9781337093347

Author:

Barry J. Goodno, James M. Gere

Publisher:

Cengage Learning

Engineering Mechanics: Statics

Mechanical Engineering

ISBN:

9781118807330

Author:

James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher:

WILEY

SEE MORE TEXTBOOKS