Technology & Engineering
Transmissibility
Transmissibility refers to the ability of a mechanical system to transmit forces and motion from one part to another. It is a measure of how efficiently a force applied to one part of a system is transmitted to another part. The transmissibility of a system can be affected by factors such as the stiffness and damping of the system.
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4 Key excerpts on "Transmissibility"
eBook - PDFVibration Analysis and Control
New Trends and Developments
- Francisco Beltran-Carbajal(Author)
- 2011(Publication Date)
- IntechOpen(Publisher)
10 Whys and Wherefores of Transmissibility N. M. M. Maia 1 , A. P. V. Urgueira 2 and R. A. B. Almeida 2 1 IDMEC-Instituto Superior Técnico, Technical University of Lisbon 2 Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa Portugal 1. Introduction The present chapter draws a general overview on the concept of Transmissibility and on its potentialities, virtues, limitations and possible applications. The notion of Transmissibility has, for a long time, been limited to the single degree-of-freedom (SDOF) system; it is only in the last ten years that the concept has evolved in a consistent manner to a generalized definition applicable to a multiple degree-of-freedom (MDOF) system. Such a generalization can be and has been not only developed in terms of a relation between two sets of harmonic responses for a given loading, but also between applied harmonic forces and corresponding reactions. Extensions to comply with random motions and random forces have also been achieved. From the establishment of the various formulations it was possible to deduce and understand several important properties, which allow for diverse applications that have been envisaged, such as evaluation of unmeasured frequency response functions (FRFs), estimation of reaction forces and detection of damage in a structure. All these aspects are reviewed and described in a logical sequence along this chapter. The notion of Transmissibility is presented in every classic textbook on vibrations, associated to the single degree-of-freedom system, when its basis is moving harmonically; it is defined as the ratio between the modulus of the response amplitude and the modulus of the imposed amplitude of motion. Its study enhances some interesting aspects, namely the fact that beyond a certain imposed frequency there is an attenuation in the response amplitude, compared to the input one, i.e., one enters into an isolated region of the spectrum.
eBook - PDFMechatronics
An Integrated Approach
- Clarence W. de Silva(Author)
- 2004(Publication Date)
- CRC Press(Publisher)
Two types of Transmissibility functions —force Transmissibility and motion Transmissibility —can be defined. Due to a reciprocity characteristic in linear systems, it can be shown that these two transfer functions are equal and, consequently, it is sufficient to consider only one of them. Let us first consider both types and show their equivalence. 2.12.4.1 F orce Transmissibility Consider a mechanical system supported on a rigid foundation through a suspension system. If a forcing excitation is applied to the system it is not directly transmitted to the foundation. The suspension system acts as an “isolation” device. Force Transmissibility determines the fraction of the forcing excitation that is transmitted to the foundation through the suspension system at different frequencies, and is defined as Note that this function is defined in the frequency domain, and accordingly F s and F should be interpreted as the Fourier spectra of the corresponding forces. A schematic diagram of a force Transmissibility mechanism is shown in Figure 2.73. The reason for the suspension force f s not being equal to the applied force f is attributed to the inertia paths (broken line in Figure 2.73) that are present in the mechanical system. FIGURE 2.73 Force Transmissibility mechanism. Force Transmissibility = Suspension Force Applied Force T F F f s Suspension Foundation Forcing Excitation f ( t ) Inertia Force Path Mechanical System f s 168 Mechatronics: An Integrated Approach 2.12.4.2 Motion Transmissibility Consider a mechanical system supported through a suspension mechanism on a structure, which may be subjected to undesirable motions (e.g., seismic disturbances, road distur-bances, machinery disturbances). Motion Transmissibility determines the fraction of the support motion which is transmitted to the system through its suspension at different frequencies. It is defined as The velocities V m and V are expressed in the frequency domain, as Fourier spectra.
eBook - PDFVibration
Fundamentals and Practice, Second Edition
- Clarence W. de Silva(Author)
- 2006(Publication Date)
- CRC Press(Publisher)
Two types of Transmissibility functions—force trans-missibility and motion Transmissibility—can be defined as given in Table 3.1. Because of a reciprocity characteristic in linear systems, it can be shown that these two transfer functions are equal and, consequently, it is sufficient to consider only one of them. Let us, however, consider both types first and show their equivalence. 3.5.1 Force Transmissibility Consider a mechanical system that is supported on a rigid foundation through a suspen-sion system. If a forcing excitation is applied to the system, this force is not directly transmitted to the foundation. The suspension system acts as a vibration isolation device and will alter the transmitted force. Force Transmissibility determines the fraction of the forcing excitation that is transmitted to the support structure (foundation) through the suspension, at different excitation frequencies, and is defined as Force Transmissibility T f ¼ Force transmitted to support F s Applied force F ð 3 : 91 Þ Note that this is a ‘‘dynamic’’ function, which is defined in the frequency domain. Accordingly, F s and F should be interpreted as the Fourier spectra of the corresponding forces. A schematic representation of the force Transmissibility mechanism is shown in Figure 3.11a. The fact that the suspension force f s and the applied force f are unequal is attributed to the inertia paths (broken line in the figure) that are present in a mechanical system. 3.5.2 Motion Transmissibility Consider a mechanical system that is supported through a suspension on a structure that may be subjected to undesirable motions (e.g., guideway deflections, vehicle motions, or seismic disturbances). Motion Transmissibility determines the fraction of the support motion that is transmitted to the system through its suspension at different frequencies.
eBook - PDF- Clarence W. de Silva(Author)
- 2007(Publication Date)
- CRC Press(Publisher)
As a result, the concepts of force Transmissibility and motion Transmissibility may be studied using just one common Transmissibility function T : Simple examples of force isolation and motion isolation are shown in Figure 7.4(c) and (d). For both cases, the Transmissibility function is given by T ¼ k þ b j v ð k 2 m v 2 þ b j v Þ ð 7 : 5 Þ where v is the frequency of vibration excitation. Note that the model (Equation 7.5) is not restricted to sinusoidal vibrations. Any general vibration excitation may be represented by a Fourier spectrum, which is a function of frequency v : Then, the response vibration spectrum is obtained by multiplying the excitation spectrum by the Transmissibility function T : The associated design problem is to select the isolator parameters k and b to meet the specifications of isolation. Equation 7.5 may be expressed as T ¼ v 2 n þ 2 zv n v j ð v 2 n 2 v 2 þ 2 zv n v j Þ ð 7 : 6 Þ where v n ¼ ffiffiffiffiffi k = m p ¼ undamped natural frequency of the system z ¼ b 2 ffiffiffiffi km p ¼ damping ratio of the system (a) (b) Z s M s 1 = Z m M m 1 = Inertial System (Isolated System) Isolator Received Vibration Motion v m Applied Vibration Motion v ( t ) Moving Platform (c) (d) v ( t ) m k v m b m k b f ( t ) f s f s Generated Vibration Force f ( t ) Inertial System (Source) Isolator Transmitted Vibration Force f s Fixed Supporting Structure (Isolated System) Z m Z s FIGURE 7.4 (a) Force isolation; (b) motion isolation; (c) force isolation example; (d) motion isolation example. Vibration Design and Control 7 -7 Equation 7.6 may be written in the nondimensional form: T ¼ 1 þ 2 z rj 1 2 r 2 þ 2 z rj ð 7 : 7 Þ where the nondimensional excitation frequency is defined as r ¼ v = v n The Transmissibility function has a phase angle as well as magnitude. In practical applications, the level of attenuation of the vibration excitation (rather than the phase difference between the vibration excitation and the response) is of primary importance.
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