Question

In: Mechanical Engineering

(i) Write down the wave equation and find the general solution for longitudinal vibration of a...

(i) Write down the wave equation and find the general solution for longitudinal vibration of a beam using the method of separation of variable separation.

(ii) Find three lowest natural frequencies of longitudinal vibration of 1.5m beam with free-free boundary conditions at the ends. The modules of elasticity is 200e^9 N/m and density 7500 kg/m3.

Solutions

Expert Solution


Related Solutions

Find the general solution to the equation ?″+4?=1
Find the general solution to the equation ?″+4?=1
Write down a general expression relating the number of nodes in a standing wave to value...
Write down a general expression relating the number of nodes in a standing wave to value of n. Write down a general expression relating the number of antinodes in a standing wave to the value of n. Imagine that you have a string of fixed length that has a standing wave on it that has two segments, n=2. If you were unable to change the frequency of your generator, how could you change to a standing wave with n=4? In...
An aluminum rod, 1.0 m long, is held lightly in the middle. One end is struck head-on with a rubber mallet so that a longitudinal pulse —a sound wave—travels down the rod. The fundamental frequency of the longitudinal vibration is 2.55 kHz.
An aluminum rod, 1.0 m long, is held lightly in the middle. One end is struck head-on with a rubber mallet so that a longitudinal pulse —a sound wave—travels down the rod. The fundamental frequency of the longitudinal vibration is 2.55 kHz. (a) Describe the locations of the displacement and pressure nodes and antinodes for the fundamental mode of vibration. (b) Calculate the speed of sound in aluminum from the information given in the problem. (c) The vibration of the...
Find the general solution of the equation: y^(6)+y''' = t
Find the general solution of the equation: y^(6)+y''' = t
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation. y''+2y'+5y=3sin(2t)
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation. y''+4y=3csc2t   
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation. y''+2y'+y=2e^t
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation.
Use Method of Undetermined Coefficients te find a particular solution of the non-homogeneous equation. Find general solution of the non-homogeneous equation. y''+2y'+y=2e^{-t}
Use the one solution given below to find the general solution of the differential equation below...
Use the one solution given below to find the general solution of the differential equation below by reduction of order method: (1 - 2x) y'' + 2y' + (2x - 3) y = 0 One solution: y1 = ex
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT