Solve problem 5.22 by using example 5.2
5.2. A rigid bar of mass per unit length m carries a point mass M at its right end. The bar is supported by two springs, as shown in Fig. 5.21. Derive the differential equations for the translation and rotation of the mass center. Assume small motions. A F(t) k2 4 4 FIGURE 5.21 Mass supported by springs through a rigid bar
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5.22. Verify that the natural modes in Example 5.2 are orthogonal with respect to both the mass m...
A mass block of mass m1 is attached to the rigid and weightless bar ABC whose...
A mass block of mass m1 is attached to the rigid and weightless bar ABC whose other end is pin-connected to the wall The bar is supported by a spring of spring constant of k3 at its midpoint B. AB BC-a-1m. Another block of mass m2 is connected to the first block by a spring of spring constant k1 and is connected to the fixed ground by a spring of spring constant k2. The size of both blocks are ignored....
displacement g bout 1t A block of mass m and mass moment of inertia i wb...
displacement g bout 1t A block of mass m and mass moment of inertia i wb springs as shown in Fig. 6.3.9(a). The block can have rectilinear displacement (a) Determine the flexibility matrix and write the differential equation of monion (b) Determine the sti (e) Show angular displacement. matrix form in terms of flexibility matrix. ffhess matris and write the differential equation of matrix form in terms of stiffness matrix. ofher that the flexibility matrix and the stiffness matrix are...
ke Slender bar of mass m As shown in Figure 1, a uniform slender bar with...
ke Slender bar of mass m As shown in Figure 1, a uniform slender bar with mass m and length L is supported by a vertical spring at its right end while a mass block 2m suspended from its left end through a spring is supported by another spring. All these three vertical springs have the same stiffness k. If the downward vertical displacement x of the mass block and the clockwise rotation angle 8 of the bar are assumed...
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1....
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1. The hinges are free to rotate. 0 denotes the rotational angle of the rod, and 0-0 when all springs are not stretched. The mass of the bar and the size of the mass are negligible. Neglect gravitational force, and assume 0 is very small. 1) Derive the equation of motion for this system with Lagrange's method. (20pt) 2) Find the natural frequency of the...
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - ...
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - 5 sin 2t (N) f2(t)-t (N) l. Formulate an IVP for vibration analysis in terms of xi (t) and x2(t) in a matrix form. Assume that the 2. Solve an eigenvalue problem to find the natural frequencies and modeshape vectors of the system 3. What is the modal matrix of the system? Verify the orthogonal properties of the modal matrix, Ф, with system...
A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the ver...
A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the vertical deformation of the spring if the spring constant is 700 kN/m. (ans: 21.43 mm) 2. A steel cable with a nominal diameter of 25 mm is used in a construction yard to lift a bridge section weighing 38 kN. The cable has an...
A mass block of mass m1 is attached to the rigid and weightless bar ABC whose other end is pin-connected to the wall The bar is supported by a spring of spring constant of k3 at its midpoint B. AB BC-a-1m. Another block of mass m2 is connected to the first block by a spring of spring constant k1 and is connected to the fixed ground by a spring of spring constant k2. The size of both blocks are ignored....
displacement g bout 1t A block of mass m and mass moment of inertia i wb springs as shown in Fig. 6.3.9(a). The block can have rectilinear displacement (a) Determine the flexibility matrix and write the differential equation of monion (b) Determine the sti (e) Show angular displacement. matrix form in terms of flexibility matrix. ffhess matris and write the differential equation of matrix form in terms of stiffness matrix. ofher that the flexibility matrix and the stiffness matrix are...
ke Slender bar of mass m As shown in Figure 1, a uniform slender bar with mass m and length L is supported by a vertical spring at its right end while a mass block 2m suspended from its left end through a spring is supported by another spring. All these three vertical springs have the same stiffness k. If the downward vertical displacement x of the mass block and the clockwise rotation angle 8 of the bar are assumed...
1. Springs and a mass are attached to a rigid bar, as shown in Fig 1. The hinges are free to rotate. 0 denotes the rotational angle of the rod, and 0-0 when all springs are not stretched. The mass of the bar and the size of the mass are negligible. Neglect gravitational force, and assume 0 is very small. 1) Derive the equation of motion for this system with Lagrange's method. (20pt) 2) Find the natural frequency of the...
For the following 2DOF linear mass-spring-damper system r2 (t) M-2kg K -18N/m C- 1.2N s/m i(t) - 5 sin 2t (N) f2(t)-t (N) l. Formulate an IVP for vibration analysis in terms of xi (t) and x2(t) in a matrix form. Assume that the 2. Solve an eigenvalue problem to find the natural frequencies and modeshape vectors of the system 3. What is the modal matrix of the system? Verify the orthogonal properties of the modal matrix, Ф, with system...
A 3 m rigid bar AB is supported with a vertical translational spring at A and a pin at B The bar is subjected to a linearly varying distributed load with maximum intensity g Calculate the vertical deformation of the spring if the spring constant is 700 kN/m. (ans: 21.43 mm) 2. A steel cable with a nominal diameter of 25 mm is used in a construction yard to lift a bridge section weighing 38 kN. The cable has an...
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