ASHRAE AN-04-2-1-2004 Vibration Isolation Harmonic and Seismic Forcing Using the Wilson Theta Method《隔振 被迫使用威尔逊太塔 法谐波和地震》.pdf
《ASHRAE AN-04-2-1-2004 Vibration Isolation Harmonic and Seismic Forcing Using the Wilson Theta Method《隔振 被迫使用威尔逊太塔 法谐波和地震》.pdf》由会员分享,可在线阅读,更多相关《ASHRAE AN-04-2-1-2004 Vibration Isolation Harmonic and Seismic Forcing Using the Wilson Theta Method《隔振 被迫使用威尔逊太塔 法谐波和地震》.pdf(8页珍藏版)》请在麦多课文档分享上搜索。
1、AN-04-2-1 Vibration Isolation: Harmonic and Seismic Forcing Using the Wilson Theta Method James A. Carlson, P.E. Associate Member ASHRAE Joseph Turner, Ph.D. ABSTRACT It is well known that equipment can causeunwantedvibra- tions in buildings. Springs have been used to isolate these vibrations and re
2、duce transmitted forces to building struc- tures. For simple vertical harmonic motion and free vibration, theproblem is easily evaluated using simple charts andjgures. Evaluation of spring-isolated equipment responding to earth- quakes is not simple. A numerical method is included to eval- uate resp
3、onse of equipment to earthquakes and harmonic forcing functions. Conjguration of equipment on springs is simplijied for numerical analysis. A simplijied approach and associated equations of motion can be developed to evaluate the response of the equipment with vertical and horizontal forcing functio
4、ns. Response of spring isolation in the vertical direction is based on the vertical forcing function acting on the center of mass and results in the translation of the total mass (up and down). Horizontal forcing functions result in a change in the angle around the center of mass. Ifthe mass of the
5、equip- ment is ofset from the center of mass, then the vertical and angular responses are coupled. Resulting tension and compression forces at the spring can be directly related to the center of mass vertical and rotational displacements and velocities. Results of this numerical method may be used t
6、o vertfi simplijied methods. INTRODUCTION Dynamic response of equipment to earthquake ground motion is becoming an active topic in the HVAC industry. Code requirements and equipment failures during recent earthquakes drive this growing attention. Code requirements focus on the seismic evaluation of
7、the anchorage and opera- tional effects in a very simple format. New building codes have been enhanced and are adopting more stringent requirements for both when to apply a seismic restraint design and increas- ing the earthquake forces applied to equipment. In some cases, the code requirements may
8、also require a shake table to prove operability. But for most code design considerations, the seis- mic restraint andlor anchorage is the only concern. For anchorage, the International Building Code (ICC 2000) endorses a static analysis, but will allow computational methods. A simplified static anal
9、ysis for calculating earth- quake forces acting on anchor bolts has been developed by ASHRAE for anchor bolt selection. But these equations are limited to very simple installations and only look at the peak response and estimated anchor bolt forces (tension, compres- sion, and shear) based on a stat
10、ic analysis and spring acceler- ation multipliers. Finite-element analysis programs have been used to look at more complex installations. These approaches also have drawbacks for the typical HVAC design engineer selecting spring isolators and anchorage systems. Finite-element programs are very compl
11、ex and are time consuming. Simpli- fied static analysis of complex systems may be too simple with unreasonable assumptions and results. One other analysis method includes calculating or measuring the impulse response and solving by convolution. This paper looks at a rigorous implicit evaluation of s
12、pring-isolated equipment that can be employed to evaluate simple and complex installation response to any input forcing functions. Several different input excitation functions are evaluated. Harmonic forcing functions (sine waves) are applied with frequencies from 1 to 30 Hz in the vertical, horizon
13、tal, and a combination of both. The seismic forcing function used for demonstration of the methodology is in terms of acceleration James A. Carlson is with the Omaha Public Power District, Fort Calhoun, Nebraska. Joseph Turner is at the University ofNebraska, Lincoln. 02004 ASHRAE. 321 tvg L 63 X t
14、Figure 1 Simple spring-isolated equipment mass Figure 2 Free body diagram of spring-isolated equipment. representation. using the El Centro earthquake data (Donea 1980). Future evaluations can be made with input excitations developed from earthquake peak response spectrum as defined in the building
15、codes. Design engineers can gain insight into the resultant forces at the spring and anchorage by looking at the system response. SPRI NG-ISOLATED EQUIPMENT Spring-isolated equipment is simplified for the analysis. A simple configuration for equipment is two masses resting on springs and dashpots (s
16、nubbers) and attached to the ground. The forcing functions (horizontal and vertical accelerations) are applied at the ground and represent forces generated by an earthquake. Equations of motion can be developed for this system. Structural engineers, looking at buildings, have already derived similar
17、 equations of motion. But buildings are uniform with the center of mass very near the center of the building. For equipment, the equations of motion are compli- cated by offset centers of mass. Figure 1 shows a typical instal- lation with springs mounted at the comers. The total mass is separated in
18、to two masses. The first mass is for the equipment elevated above the base by some height (hcg). The second mass represents a structural base. For equipment installed without a base, the base mass is simply zero for this analysis. The earthquake accelerations acting on the ground are represented by
19、v, and h, as seen in Figure 2. Intuitively, the horizontal oscillating forcing function will induce a rocking motion or a change in the angle defection of spring. The vertical acceleration will cause a translation of the total mass. The system selected to represent the typical equipment isolation sy
20、stem contains some information about the equip- ment and inherent features. These features include the stiff- ness (K,) and the damping coefficient (Ce) of the equipment in response to the horizontal forcing functions as shown in Figure 1. Damping coefficients for the equipment are typically assumed
21、 to be 5%. For this analysis the equipment effect and x motion are expected to be small and have an insignificant effect on the total mass translation and rocking motion. Future work will look at the stiffness and damping effects of the equipment. This work is looking at the motion at the springs an
22、d resulting spring compression and tension forces. Devel- opment of the free body diagram is completed without the equipment stiffness and damping. From Figure 2, the free body diagram, equations of motion (EOM) may be developed. SYSTEM RELATIONSHIPS There are several relationships that are used in
23、the devel- opment of the EOM. Inputs to the equations of motion use relationships of the displacement and mass as identified by the coordinate system selected. If there is an offset of the equip- ment mass as previously discussed, the center of mass of the system will not coincide with the equipment
24、 mass. This equip- ment mass offset is defined as a vector rAc as shown in Figure 2. Vector rAc is a simple summation problem determined by the relationship as shown in Equation 1. the base due to the equipment mass (M) and not the total mass (M+m). The horizontal force acts on the mass of the base
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