A Shock Response Spectrum (SRS) [1] is a graphical representation of a shock, or any other transient acceleration input, in terms of how a Single Degree Of Freedom (SDOF) system (like a mass on a spring) would respond to that input. The horizontal axis shows the natural frequency of a hypothetical SDOF, and the vertical axis shows the peak acceleration which this SDOF would undergo as a consequence of the shock input. [2]
The most direct and intuitive way to generate an SRS from a shock waveform is the following procedure: [2]
The resulting plot of peak acceleration vs test system frequency is called a Shock Response Spectrum. It is often plotted with frequency in Hz, and with acceleration in units of g
Consider a computer chassis containing three cards with fundamental natural frequencies of f1, f2, and f3. Lab tests have previously confirmed that this system survives a certain shock waveform—say, the shock from dropping the chassis from 2 feet above a hard floor. Now, the customer wants to know whether the system will survive a different shock waveform—say, from dropping the chassis from 4 feet above a carpeted floor. If the SRS of the new shock is lower than the SRS of the old shock at each of the three frequencies f1, f2, and f3, then the chassis is likely to survive the new shock. (It is not, however, guaranteed.)
Any transient waveform can be presented as an SRS, but the relationship is not unique; many different transient waveforms can produce the same SRS (something one can take advantage of through a process called "Shock Synthesis"). Due to only tracking the peak instantaneous acceleration the SRS does not contain all the information in the transient waveform from which it was created. [3]
Different damping ratios produce different SRSs for the same shock waveform. Zero damping will produce a maximum response. Very high damping produces a very boring SRS: A horizontal line. The level of damping is demonstrated by the "quality factor", Q which can also be thought of transmissibility in sinusoidal vibration case. Relative damping of 5% results in a Q of 10. An SRS plot is incomplete if it doesn't specify the assumed Q value. [3]
An SRS is of little use for fatigue-type damage scenarios, as the transform removes information of how many times a peak acceleration (and inferred stress) is reached. [3]
The SDOF system model also can be used to characterize the severity of vibrations, with two criteria:
Like many other useful tools, the SRS is not applicable to significantly non-linear systems.
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of a periodically applied force is equal or close to a natural frequency of the system on which it acts. When an oscillating force is applied at a resonant frequency of a dynamic system, the system will oscillate at a higher amplitude than when the same force is applied at other, non-resonant frequencies.
A mechanical or physical shock is a sudden acceleration caused, for example, by impact, drop, kick, earthquake, or explosion. Shock is a transient physical excitation.
A spectrum analyzer measures the magnitude of an input signal versus frequency within the full frequency range of the instrument. The primary use is to measure the power of the spectrum of known and unknown signals. The input signal that most common spectrum analyzers measure is electrical; however, spectral compositions of other signals, such as acoustic pressure waves and optical light waves, can be considered through the use of an appropriate transducer. Spectrum analyzers for other types of signals also exist, such as optical spectrum analyzers which use direct optical techniques such as a monochromator to make measurements.
An accelerometer is a tool that measures proper acceleration. Proper acceleration is the acceleration of a body in its own instantaneous rest frame; this is different from coordinate acceleration, which is acceleration in a fixed coordinate system. For example, an accelerometer at rest on the surface of the Earth will measure an acceleration due to Earth's gravity, straight upwards of g ≈ 9.81 m/s2. By contrast, accelerometers in free fall will measure zero.
In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency-domain representation can also include information on the phase shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time signal.
A voltage-controlled oscillator (VCO) is an electronic oscillator whose oscillation frequency is controlled by a voltage input. The applied input voltage determines the instantaneous oscillation frequency. Consequently, a VCO can be used for frequency modulation (FM) or phase modulation (PM) by applying a modulating signal to the control input. A VCO is also an integral part of a phase-locked loop. VCOs are used in synthesizers to generate a waveform whose pitch can be adjusted by a voltage determined by a musical keyboard or other input.
Torsional vibration is angular vibration of an object—commonly a shaft along its axis of rotation. Torsional vibration is often a concern in power transmission systems using rotating shafts or couplings where it can cause failures if not controlled. A second effect of torsional vibrations applies to passenger cars. Torsional vibrations can lead to seat vibrations or noise at certain speeds. Both reduce the comfort.
Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples include viscous drag in mechanical systems, resistance in electronic oscillators, and absorption and scattering of light in optical oscillators. Damping not based on energy loss can be important in other oscillating systems such as those that occur in biological systems and bikes.
A response spectrum is a plot of the peak or steady-state response of a series of oscillators of varying natural frequency, that are forced into motion by the same base vibration or shock. The resulting plot can then be used to pick off the response of any linear system, given its natural frequency of oscillation. One such use is in assessing the peak response of buildings to earthquakes. The science of strong ground motion may use some values from the ground response spectrum for correlation with seismic damage.
In a variety of applications, a shock mount or isolation mount is a mechanical fastener that connects two parts elastically. They are used for shock and vibration isolation.
In mechanical engineering, random vibration is motion which is non-deterministic, meaning that future behavior cannot be precisely predicted. The randomness is a characteristic of the excitation or input, not the mode shapes or natural frequencies. Some common examples include an automobile riding on a rough road, wave height on the water, or the load induced on an airplane wing during flight. Structural response to random vibration is usually treated using statistical or probabilistic approaches. Mathematically, random vibration is characterized as an ergodic and stationary process.
A mechanical amplifier, or a mechanical amplifying element, is a linkage mechanism that amplifies the magnitude of mechanical quantities such as force, displacement, velocity, acceleration and torque in linear and rotational systems. In some applications, mechanical amplification induced by nature or unintentional oversights in man-made designs can be disastrous. When employed appropriately, it can help to magnify small mechanical signals for practical applications.
Shock pulse method (SPM) is a technique for using signals from rotating rolling bearings as the basis for efficient condition monitoring of machines. From the innovation of the method in 1969 it has been further developed and broadened and is a worldwide accepted philosophy for condition monitoring of rolling bearings and machine maintenance.
The 7 post shaker is a piece of test equipment used to perform technical analysis on race cars. By applying shaking forces the shaker can emulate banking loads, lateral load transfer, longitudinal weight transfer and ride height sensitive downforce to emulate specific racetracks.
Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem. The oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road.
Pyroshock, also known as pyrotechnic shock, is the dynamic structural shock that occurs when an explosion or impact occurs on a structure. Davie and Bateman describe it as: "Pyroshock is the response of a structure to high frequency, high-magnitude stress waves that propagate throughout the structure as a result of an explosive event such as an explosive charge to separate two stages of a multistage rocket." It is of particular relevance to the defense and aerospace industries in that they utilize many vehicles and/or components that use explosive devices to accomplish mission tasks. Examples include rocket stage separation, missile payload deployment, pilot ejection, automobile airbag inflators, etc. Of significance is the survival and integrity of the equipment after the explosive device has activated so that the vehicle can accomplish its task. There are examples of flight vehicles Boeing-The Aerospace Corp which have crashed after a routine explosive device deployment, the cause of the crash being determined as be a result of a computer failure due to the explosive device. The resultant energies are often high g-force and high frequency which can cause problems for electronic components which have small items with resonant frequencies near those induced by the pyroshock.
The Extreme Response Spectrum (ERS) is defined as a curve giving the value of the highest peak of the response of a linear Single Degree of Freedom System to vibration, according to its natural frequency, for a given damping ratio. The response is described here by the relative movement of the mass of this system in relation to its support. The x-axis refers to the natural frequency and the y-axis to the highest peak multiplied by the square of the quantity, by analogy with the relative displacement shock response spectrum.
Spectral acceleration (SA) is a unit measured in g that describes the maximum acceleration in an earthquake on an object – specifically a damped, harmonic oscillator moving in one physical dimension. This can be measured at different oscillation frequencies and with different degrees of damping, although 5% damping is commonly applied. The SA at different frequencies may be plotted to form a response spectrum.
A shock data logger or vibration data logger is a measurement instrument that is capable of autonomously recording shocks or vibrations over a defined period of time. Digital data is usually in the form of acceleration and time. The shock and vibration data can be retrieved, viewed and evaluated after it has been recorded.
Anelasticity is a property of materials that describes their behaviour when undergoing deformation. Its formal definition does not include the physical or atomistic mechanisms but still interprets the anelastic behaviour as a manifestation of internal relaxation processes. It's a special case of elastic behaviour.
FreeSRS, http://freesrs.sourceforge.net/, is a toolbox in the public domain to calculate SRS.