Research scheme of optical table dynamic characteristic: 1, 2, 3, 4, 5, 6 – vibration transducers; 7 – platform (base); 8 – vibrator; 9 – sup- ports of vibration isolation; 10 – optical table with experimental of vibration isolation; 11 – impulse generator; 12 – amplifier; 13 – gen- erator; 14 – computer with analyser 

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... coating procedure can be a viable approach in optimal damping designs. A semi-analytical finite element for doubly curved, multi-layered shells of revolution, based on an extension of the dis- placement field proposed by Wilkins et al, is proposed in paper [14]. Numerical analysis is done to study the vibration and damping charac- teristics of multi-layered fluid filled shells with alternating elastic and viscoelastic layers. The effect of varying the number of viscoelastic layers on the vibration and damping characteristics is also studied. The effect of the fluid is incorporated by the added mass concept. The effect of shear parameter on natural frequency and modal loss factor is studied for various circumferential and axial modes. The vibration and damping characteristics of free–free composite sandwich cylin- drical shell with pyramidal truss-like cores have been conducted using the Rayleigh-Ritz model and FEM is presented in paper [22]. The pre- dictions for the modal properties of composite sandwich cylindrical shell with pyramidal truss-like cores showed good agreement with the experimental tests. The influences of fiber ply angles on the natural frequency and damping loss factor were investigated. Three types of such composite sandwich cylindrical shells were manufactured using a hot press moulding method and the relevant modal characteristics of various sandwich cylindrical shells could be obtained by modal tests. The natural frequencies of composite sandwich cylindrical shell increased with the increasing of the ply angle of the inner and outer curve face sheets, whereas the damping loss factors of present shells did not increase monotonically. The natural frequencies of composite sandwich beams with lattice truss core are investigated by combining the Bernoulli–Euler beam theory and Timoshenko beam theory were analysed by Xu and Qiu [21]. Latterly, the scientists concerning honeycomb sandwich structures have been focused on effective numerical modelling methods, vibra- tion properties, crash- worthiness, damage, and failure and impact response. Researchers Adams and Maheri[1] investigated the damp- ing of composite honeycomb sandwich beams in steady-state flexural vibration using the method extended from that for monolithic beams. The material properties such as elastic modules and strengths are various in different directions, and even the compressive and tensile properties are different in the thickness-direction, primarily due to the initial deflection of cell walls. Vibration frequencies and mode shapes of honeycomb sandwich panels with various structural parameters were studied by Qunli Liu and Yi Zhao [7] using computational and experimental methods. Two computational models were used to pre- dict the mode shapes and frequencies of honeycomb sandwich panels. Plate elements were used for honeycomb cell walls to reflect the geo- metric nature of the hexagonal cells. Optical table vibrations typically are between 2 Hz and 7 Hz, because it is eigen-frequency at which the optical table resonates. However, especially for low (from 0.7 Hz) frequencies a better insu- lator, working with scanning probe microscopy and interferometry is required. Existing quasi-zero (negative) stiffness isolators resonates from 0.5 Hz [6].This frequency has almost no power, because it would be very unusual to find large oscillations at 0.5 Hz[18]. Optical tables and active systems do not work very well when placed in a vacuum, especially at high or low temperature and radiation. Such an environ- ment occurs during specific investigations of semiconductors. Quasi- zero stiffness system can work in vacuum, high and low temperatures and under radiation [6]. Optical tables with pneumatic vibration isolators are suitable for laser centres. Theoretical analysis of vibration parameters and analy- sis of experimental results allows to assess of honeycomb systems reliability. Comprehensive analysis of vibration theoretical methods are described by scientists Cveticanin, Mester and Biro [2], Siljak, Subasi [16] and Wicher, Więckowski [19]. A lot of studies presented in bibliographic sources are related to one of the attributes (high strength/weight or increased energy absorp- tion) mentioned above. With regard to the development of a honey- comb panels, one issue that has been overlooked is the scaling of hon- eycomb properties with respect to cell size. The variation in cell size may have a large influence on the dynamic properties of honeycomb panels. The goal of this study was to reveal the effect of cell size on the fundamental frequency of honeycomb panels. The results of the experimental investigation are presented and discussed. Nevertheless, authors described the determination of mechanical passive isolation systems ability to isolate low (from 0.7 to 50 Hz) and higher (from 500 to 1200 Hz) frequency oscillations. The experimental research combination of optical table with pneumatic vibration insulators is shown in Fig. 1. Top and bottom countertop surfaces of analysed optical table are made of cold-rolled ferro-magnetic steel sheets, which combine light- weight structure made of corrosion resistant cellular steel, giving the table exceptional toughness. The optical table is usually mounted on special vibration isolating supports. The optical table structures resist to static and dynamic forces not only vertically, but also horizontally considered being highly important defining quality factors. Idealized “seismic” mounting system of optical tables is a rigid table, mounted on a massive foundation or on the supports that inhibit vibrations. Various types of vibration isolation bearings with com- pressed air dampers are used in world practice. These supports must ensure the stability of the table in vertical and horizontal directions. Horizontal environmental vibration effect is particularly striking when the laboratories are installed on the upper floors of the buildings. The lightweight honeycomb structures for manufacture objects that are resistant to the dynamic and static forces are widely used. Honeycomb cells are characterized by the size, wall thickness, the ma- terial from which they are made, etc. Typical features of honeycomb structures are lightness and resistance to compression and bending. These qualities are especially important when it is required for optimal characteristics ratio of mass and stiffness. Therefore cellular structures are used in aircraft, helicopters, and other plant production. This type of structures is widely used for optical laboratory tables also. Cellular tables have good vibration damping properties, they are much lighter than the massive tables made of granite. In most cases not resistant for mechanical loads heavy granite table, but lightweight cellular structure have been chosen. The most important quality criteria of insulating pillars is char- acteristics of mechanical vibration transmission from a base supports the table top. These characteristics determine the applicability of vari- ous experimental techniques. The specific method is selected accord- ing to a number of factors, among which the more important one is dominant frequency range. Study includes analysis and measurement of vibration and other dynamic properties by using “Brüel&Kjær” firm equipment. The port- able measurement results processing device connected with computer, and vibration sensors (type 8341 and 8306) with vibration meter 2511 were used as well. An experimental part of modal analysis was carried out by using this equipment as well. The vibration excitation platform with a vibrator and other spe- cial test equipment were used in and tested for research of dynamic parameters of pneumatic isolator of vibrations. Easily tuned vibration excitation platform has been built, allowing the test subject to excite vibrations of (1–50) Hz frequency range in any of three directions: vertical transverse, horizontal transverse and horizontal longitudinal directions. Using aforementioned equipment modal analysis of top plate of table was performed. This analysis was done with purpose to obtain eigen-frequencies of top plate which are unwelcome in precise meas- uring process. During experiment top plate of vibro-isolating table was treated as single deformable body instead of construction with supports. The results of typical damping (Fig. 1) of vibration isolation sup- ports excited by harmonic vibrations, impulse and white noise, shown in Fig. 2. (a, b, c, d, e).Oscillations are not isolated when there is a harmonic excitation at 2 Hz; isolation starts with 4 Hz. Thus, optical tables are not effective for frequencies up to 4 Hz. Following are presented the most important results of vibration isolating supports at 1–50 Hz frequency range at different sizes of load (transmission dependence on frequency curves T v , correspond- ing resonant frequency of the f vr and transmissibility coefficient values at resonance 5 Hz to 10 Hz frequencies). Maximum value of transmissibility coefficient at different loads varies from 3 to 4 Hz: without load – 2.9 Hz; 100 kg – 2.7 Hz; 250 kg – 2.4 Hz; 500 kg – 2.1 Hz. This shows that the vibration isolating supports with the load forms an elementary single mass vibrating system. Resonance frequency decreases by increasing the load of vibration isolating sup- ports. With increasing frequency above the resonance transmissibility steadily decreases, and at frequencies of 50 Hz is less than 0.01. Further results of modal analysis are provided.The experimental results were compared with the analytical model of the vibro-isolating table; approximate simplified model of vibro-isolating table built. This analytical model is thoroughly described in paper [6]. In current pa- per mathematical model of vibro-isolating table was built in ANSYS environment and modal analysis was performed. The table top was modelled using SHELL63 finite element; mesh of 25x25 elements, which gave ...

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... 0.5 Hz[18]. Optical tables and active systems do not work very well when placed in a vacuum, especially at high or low temperature and radiation. Such an environ- ment occurs during specific investigations of semiconductors. Quasi- zero stiffness system can work in vacuum, high and low temperatures and under radiation [6]. Optical tables with pneumatic vibration isolators are suitable for laser centres. Theoretical analysis of vibration parameters and analy- sis of experimental results allows to assess of honeycomb systems reliability. Comprehensive analysis of vibration theoretical methods are described by scientists Cveticanin, Mester and Biro [2], Siljak, Subasi [16] and Wicher, Więckowski [19]. A lot of studies presented in bibliographic sources are related to one of the attributes (high strength/weight or increased energy absorp- tion) mentioned above. With regard to the development of a honey- comb panels, one issue that has been overlooked is the scaling of hon- eycomb properties with respect to cell size. The variation in cell size may have a large influence on the dynamic properties of honeycomb panels. The goal of this study was to reveal the effect of cell size on the fundamental frequency of honeycomb panels. The results of the experimental investigation are presented and discussed. Nevertheless, authors described the determination of mechanical passive isolation systems ability to isolate low (from 0.7 to 50 Hz) and higher (from 500 to 1200 Hz) frequency oscillations. The experimental research combination of optical table with pneumatic vibration insulators is shown in Fig. 1. Top and bottom countertop surfaces of analysed optical table are made of cold-rolled ferro-magnetic steel sheets, which combine light- weight structure made of corrosion resistant cellular steel, giving the table exceptional toughness. The optical table is usually mounted on special vibration isolating supports. The optical table structures resist to static and dynamic forces not only vertically, but also horizontally considered being highly important defining quality factors. Idealized “seismic” mounting system of optical tables is a rigid table, mounted on a massive foundation or on the supports that inhibit vibrations. Various types of vibration isolation bearings with com- pressed air dampers are used in world practice. These supports must ensure the stability of the table in vertical and horizontal directions. Horizontal environmental vibration effect is particularly striking when the laboratories are installed on the upper floors of the buildings. The lightweight honeycomb structures for manufacture objects that are resistant to the dynamic and static forces are widely used. Honeycomb cells are characterized by the size, wall thickness, the ma- terial from which they are made, etc. Typical features of honeycomb structures are lightness and resistance to compression and bending. These qualities are especially important when it is required for optimal characteristics ratio of mass and stiffness. Therefore cellular structures are used in aircraft, helicopters, and other plant production. This type of structures is widely used for optical laboratory tables also. Cellular tables have good vibration damping properties, they are much lighter than the massive tables made of granite. In most cases not resistant for mechanical loads heavy granite table, but lightweight cellular structure have been chosen. The most important quality criteria of insulating pillars is char- acteristics of mechanical vibration transmission from a base supports the table top. These characteristics determine the applicability of vari- ous experimental techniques. The specific method is selected accord- ing to a number of factors, among which the more important one is dominant frequency range. Study includes analysis and measurement of vibration and other dynamic properties by using “Brüel&Kjær” firm equipment. The port- able measurement results processing device connected with computer, and vibration sensors (type 8341 and 8306) with vibration meter 2511 were used as well. An experimental part of modal analysis was carried out by using this equipment as well. The vibration excitation platform with a vibrator and other spe- cial test equipment were used in and tested for research of dynamic parameters of pneumatic isolator of vibrations. Easily tuned vibration excitation platform has been built, allowing the test subject to excite vibrations of (1–50) Hz frequency range in any of three directions: vertical transverse, horizontal transverse and horizontal longitudinal directions. Using aforementioned equipment modal analysis of top plate of table was performed. This analysis was done with purpose to obtain eigen-frequencies of top plate which are unwelcome in precise meas- uring process. During experiment top plate of vibro-isolating table was treated as single deformable body instead of construction with supports. The results of typical damping (Fig. 1) of vibration isolation sup- ports excited by harmonic vibrations, impulse and white noise, shown in Fig. 2. (a, b, c, d, e).Oscillations are not isolated when there is a harmonic excitation at 2 Hz; isolation starts with 4 Hz. Thus, optical tables are not effective for frequencies up to 4 Hz. Following are presented the most important results of vibration isolating supports at 1–50 Hz frequency range at different sizes of load (transmission dependence on frequency curves T v , correspond- ing resonant frequency of the f vr and transmissibility coefficient values at resonance 5 Hz to 10 Hz frequencies). Maximum value of transmissibility coefficient at different loads varies from 3 to 4 Hz: without load – 2.9 Hz; 100 kg – 2.7 Hz; 250 kg – 2.4 Hz; 500 kg – 2.1 Hz. This shows that the vibration isolating supports with the load forms an elementary single mass vibrating system. Resonance frequency decreases by increasing the load of vibration isolating sup- ports. With increasing frequency above the resonance transmissibility steadily decreases, and at frequencies of 50 Hz is less than 0.01. Further results of modal analysis are provided.The experimental results were compared with the analytical model of the vibro-isolating table; approximate simplified model of vibro-isolating table built. This analytical model is thoroughly described in paper [6]. In current pa- per mathematical model of vibro-isolating table was built in ANSYS environment and modal analysis was performed. The table top was modelled using SHELL63 finite element; mesh of 25x25 elements, which gave converged results of eigen-frequencies (see Fig. 3). Table was measured in 16 points using same equipment as in previous experiments. As top plate of the vibro-isolating table is per- mitted to freely bend, there are many different shapes in which the top plate can bend. An eigen-mode describes the shape of bended top plate; an eigen-frequency describes how fast bending occurs. Eigen-mode vibrates at its eigen-frequency and the total bending and frequency of the top plate is their sum. Eigen-modes depend on the support configuration of the vibro-isolating table, and the natural fre - quencies depend on the stiffness and mass components of the top plate and its shape. Natural modes with the highest frequencies are usually not very important because their amplitude is relatively small. Only four lowest eigen-frequencies of the vibro-isolating table are consid- ered to be significant. Eigen-mode shapes of experiment match ones of mathematical model. Results of mathematical model showed good corresponding with experiment;i.e. discrepancy does not exceed 2.9% between re- sults of experimental and mathematical tests (Table 1). As seen in Table 1, the discrepancy of theoretical and experimen- tal results varies from 1.7 % up to 2.9 %. This shows enough high reliability of above mentioned modelling ...