Vibration Measurement - Mechanical Engineering (MCQ) questions and answers. What’s a megalith? and In the excerpt above, after increasing the frequency on Tesla’s “frequency oscillator” Tesla is quoted saying: “Suddenly all the heavy machinery in the place was flying around”. 53/58:153 Lecture 9 Fundamental of Vibration _____ - 6 - When the frequency ratio is greater than sqrt(2), the force transmitted is still larger than the static force. Most vibration testing is conducted in a 'single DUT axis' at a time, even though most real-world vibration occurs in various axes simultaneously. ​Supercharge Your Energy Leve​ls Naturally. Let both masses have a mass of 1 kg and the stiffness of all three springs equal 1000 N/m. ω ω [ Solving for x is replaced by solving for q, referred to as the modal coordinates or modal participation factors. The bewildered newspapermen pounced upon this as at least one thing they could understand and Nikola Tesla, “the father of modern electricity” told what had happened as follows: Tesla stated, “I was experimenting with vibrations. It happens in this example that the fourth harmonic of the square wave falls at 7 Hz. ] The matrices are NxN square matrices where N is the number of degrees of freedom of the system. 2) The maximum peak vibration occurs a little bit before r=1. Free vibration occurs when a mechanical system is set in motion with an initial input and allowed to vibrate freely. • Vibration of a real structure can be represented as a series of modal contributions. For example, if a known force over a range of frequencies is applied, and if the associated vibrations are measured, the frequency response function can be calculated, thereby characterizing the system. As the amplitude plot shows, adding damping can significantly reduce the magnitude of the vibration. The equations of motion of the 2DOF system are found to be: A more compact form of this matrix equation can be written as: where The figure also shows the time domain representation of the resulting vibration. Vibration isolation (defined as T<1) occurs when the excitation frequency is > 1.4 f n. For minimum transmissibility (maximum isolation), the excitation frequency should be as high above the natural frequency as possible. In 1995, an accident caused due to breaking thermowells in Monju Nuclear Plant reactor, led to very serious damages to the surrounding facilities. Squeak and rattle testing is performed with a special type of quiet shaker that produces very low sound levels while under operation. There are in general no problems with vibrations for normal floors with span/dept ratio less than 25. ⋯ Generally, only the first few modes are important for practical applications. See Answer The frequencies of the various harmonics are multiples of the frequency of the first harmonic. Measure the damping ratio from the relation between the natural and damped frequencies of under-damped systems. k = If the beam is made up of isotropic material, instead of graphite epoxy, with E = 206.8 GPa, mass density of 7997 kg m and Poissson ratio of 0.33, the natural frequency obtained using COMPOPT is 43.5 rad/s as compared with 42.0 obtained by Wekezer (1989) . i The frequency is directly proportional to the velocity of the wave and inversely proportional to the wavelength. For this example, consider the following discrete-time transfer function with a sample time of 0.01 seconds: s y s (z) = 5 z 2 + 3 z + 1 z 3 + 6 z 2 + 4 z + 4. The solution of an eigenvalue problem can be quite cumbersome (especially for problems with many degrees of freedom), but fortunately most math analysis programs have eigenvalue routines. Vibration measurements can tell us about the condition of a gearbox, if properly done. The frequency response of the mass–spring–damper therefore outputs a high 7 Hz vibration even though the input force had a relatively low 7 Hz harmonic. Lightly damped systems have lower force transmissibility than those with larger damping. The eigenvalues provide the natural frequencies of the system. When frequency ratio is less than unity b. ] [ In our case the first mode shape vector is saying that the masses are moving together in phase since they have the same value and sign. The value of the natural frequency does not change in both the free and forced vibration only when the systems and its environment remains stable. [ In rotor bearing systems any rotational speed that excites a resonant frequency is referred to as a critical speed. In practice, this is rarely done because the frequency spectrum provides all the necessary information. The solution to the underdamped system for the mass-spring-damper model is the following: The value of X, the initial magnitude, and The key is to ensure that the material selected was under the area of isolation where magnification factor is equal to or greater than 1.4. = Figure 6: Normalized amplitude vs. frequency ratio Many notes can be deduced from this plot, mainly: 1) As the damping ratio is increased, the maximum vibration decreased. Ψ and Home >> Category >> Mechanical Engineering ... (Transmissibility vs Frequency Ratio) shown below, the shaded region is called as____ a. For higher frequencies (typically 5 Hz to 2000 Hz), electrodynamic shakers are used. natural logarithm of the ratio of the amplitudes of two successive cycles of the damped free vibration: ∆=ln or = e−∆ (2.19) x 2 x 1 x 1 x 2 x n x 0 2.6 CHAPTER TWO FIGURE 2.8Trace of damped free vibration showing amplitudes of displacement maxima. In other words, to efficiently pump energy into both mass and spring requires that the energy source feed the energy in at a rate equal to the natural frequency. Table 2 The first 3 modal frequencies of the motor frame/Hz. The granite megaliths of the kings chamber – in the valley of the kings weigh up to 60 tons each and were transported over 500 miles from the Aswan quarry. It is difficult to design a vibration test fixture which duplicates the dynamic response (mechanical impedance) of the actual in-use mounting. i {\displaystyle e^{i\omega t}} {\displaystyle {\begin{bmatrix}\Psi \end{bmatrix}}^{T}}. x X In this simple model the mass continues to oscillate forever at the same magnitude—but in a real system, damping always dissipates the energy, eventually bringing the spring to rest. I knew I was approaching the vibration of the steel building. The system is subjected to a sinusoidal base input with a variable frequency. free vibration). What is modal analysis? 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