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Dynamics of linear elastic SDOF oscillators
Published in Mark Aschheim, Enrique Hernández-Montes, Dimitrios Vamvatsikos, Design of Reinforced Concrete Buildings for Seismic Performance, 2019
Mark Aschheim, Enrique Hernández, Dimitrios Vamvatsikos
Resonance is the tendency of a system to oscillate with large peak amplitude under forced vibration at particular frequencies, known as the system’s resonant frequencies. Resonance occurs for an undamped SDOF system if the system’s natural frequency (ω) coincides with the frequency of harmonic loading (i.e., Ω = ω). Response amplitudes approach infinity for undamped systems, but practically speaking, as the amplitude increases a point will be reached where the physical properties of the system change, thus creating a nonlinear problem. For damped SDOF systems, resonance occurs at frequencies Ω slightly less than ω, as can be observed in Figure 3.4. While damping causes a reduction in peak response amplitudes relative to the undamped case (e.g., Figure 3.4), resonant amplitudes can still be quite large, compared with other cases of forced vibration.
Factors Affecting Mirror Performance
Published in Daniel Vukobratovich, Paul Yoder, Fundamentals of Optomechanics, 2018
Daniel Vukobratovich, Paul Yoder
Damping is the energy loss from the system during oscillation. A system is critically damped if it does not oscillate when released after being perturbed from equilibrium. The amount of damping CC required for critical damping is given by 2(km)½, where k is the system spring stiffness and m is the system mass. Alternatively, CC = 2mωN = 4πmfn, where ωn is the angular natural frequency (in radians per second) and fn is the natural frequency (in hertz). Optomechanical systems are generally poorly damped and their damping is given in terms of the critical damping ratio ζ, which is the ratio of the actual system damping C to CC required for critical damping, i.e., ζ = C/CC.
Clock Synchronization in Distributed Systems Using NTP and PTP
Published in Richard Zurawski, Industrial Communication Technology Handbook, 2017
Reinhard Exel, Thilo Sauter, Paolo Ferrari, Stefano Rinaldi
A clock can be considered an instrument to measure, keep, and indicate time. Practically, all clocks are built as a two-part device: An oscillating device for defining a reference time interval (e.g., a second or fraction thereof) and a counter device, which accumulates the number of time intervals and provides a time indication. Mechanical oscillators, such as a pendulum or balance wheel, have been widely used for timekeeping until the invention of electronic oscillators. Quartz-crystal oscillators are today the most widely used oscillators, thanks to their low price, ruggedness, and low power consumption. Atomic clocks provide a much better stability than Quartz oscillators or any mechanical oscillator. They exploit the quantum effect, where the transition between two energy levels in an atom requires exactly a certain amount of energy to emit a photon. As the frequency of the emitted photon and its energy are connected by the Planck’s constant, the atomic resonance can be exploited to create a well-defined frequency. Due to the stability of the quantum transition, the SI unit second was defined in 1967 as the duration of 9,192,631,770 periods of the radiation of the two hyperfine levels of the ground state of the cesium-133 atom [2].
Applications of Elzaki decomposition method to fractional relaxation-oscillation and fractional biological population equations
Published in Applied Mathematics in Science and Engineering, 2023
Lata Chanchlani, Mohini Agrawal, Rupakshi Mishra Pandey, Sunil Dutt Purohit, D. L. Suthar
In physical, chemical and biological processes, an oscillator is something that exhibits a rhythmic periodic reaction. Many real mechanical, radio-technical, biological and other things have oscillatory processes in which a slow smooth transition of an object’s status over a finite length of time shifts to an irregular change of status over an incredibly short period. The behaviour of a physical system returning to equilibrium after being disrupted provides the basis for a relaxation oscillation. A damped oscillating system is an oscillator that fades away over time owing to energy loss, such as a swinging pendulum, a weight on a spring or a resistor-inductor-capacitor circuit. Relaxation and damped oscillations are described by ordinary differential equations of order one and two, respectively.
Surge and heave hydrodynamic coefficients for a combination of a porous and a rigid cylinder in motion in finite ocean depth
Published in Waves in Random and Complex Media, 2021
Abhijit Sarkar, Swaroop Nandan Bora
Solving radiation problems for ocean waves yields the important hydrodynamic coefficients, namely, added mass and damping coefficients. These coefficients arise as the real and imaginary parts of the hydrodynamic reaction loads on the body due to the prescribed body motions. In physical sense, the added mass is the weight added to a system in a fluid due to the fact that an accelerating or decelerating body must move some volume of surrounding fluid with it as it moves. Damping is an influence within or upon an oscillatory system that has the effect of reducing, restricting or preventing its oscillations. The hydrodynamic forces in the x- and z-directions (i.e. for surge and heave motions) due to the motion of the cylinder in modes m = 1, 2 can be found out by integrating the corresponding pressure over the cylinder. For this configuration, only surge motion is considered. The following explains why heave motion is not considered for this problem:
Dynamic interaction of a freight car body and a three-piece bogie during axle load increase
Published in Vehicle System Dynamics, 2022
It is well known that the movement of railway rolling stock, even along straight track sections, is not rectilinear. In this case, oscillations of three types have the greatest intensity: lateral motion of bogie frame, hunting, and rolling motion of the rail vehicle bolster structure. These oscillations can occur separately, but often occur simultaneously and are interrelated. When the oscillation frequencies are equal, their amplitude increases significantly, the phenomenon of resonance occurs.