Dynamic deformation of a cylindrical composite shell with filler subject to radial two-frequency excitation

Abstract

We discuss test data on the nonlinear dynamic deformation of the elastic wall of a cylindrical glassfiber-reinforced shell (empty or filled) subject to radial two-frequency excitation. It is revealed that such processes can be accompanied (especially at the lowest resonant frequencies) by the cyclic variation in the amplitude and deformation mode between traveling and standing circumferential wave Introduction. An important task of solid mechanics is to study the nonlinear vibrations (with large (of the order of the thickness) deflections) of thin-walled shells made of laminated composites among which glass-reinforced plastics are most popular [16]. Many publications [1-3, 5-9, 11-16, etc.] address the deformation of shell structures and nonlinear and resonant phenomena caused by the superimposed and nonlinearly interacting flexural vibration modes, which create preconditions for the occurrence of complex deformation modes (such as traveling circumferential waves, chaotic processes, etc. under single-frequency excitation). When in service, however, real shell structures used in aircraft and rocket technology, space transportation systems, chemical engineering etc., are subjected to combined vibratory loading. In this connection, some tests were performed to study the dynamic behavior of shells filled with a fluid and subjected to longitudinal-and-transverse and compound two-frequency vibrational excitation [4,10,17,18].Here we will discuss test data on the nonlinear dynamic deformation of the elastic wall of a glassfiber-reinforced plastic shell (empty or filled) subjected to two-frequency vibrational excitation. Our primary task is to find the combination of the two excitation frequencies and the natural frequencies of the "dry" and filled shells and the amplitude of the vibrational load that cause the most intensive deformation of the shell wall and to analyze the associated processes and the effect of the filler on them.1. Test Specimen, Equipment, and Procedure. The test specimen was an elastic glassfiber-reinforced plastic cylindrical sandwich shell with length N sh = 900 mm, inside diameter D sh = 320 mm, and wall thickness d sh = 0.68 mm. The shell was fixed vertically, with its lower end inserted into the ring groove filled with epoxy resin in a disk and the upper end free. The disk was fixed to a foundation. A VEDS-100 electrodynamic shaker was used to excite transverse vibrations of the shell. The shaker table was in elastic contact with the lateral surface of the shell at a point located at 0.3N sh from the lower end. To produce two-frequency vibrational excitation, we used a generator built in the frame of the shaker and an external Robotron generator (one of them was used for single-frequency excitation). The vibroaccelerations of the shaker table and the shell wall were measured with IS-318 and D-14 transducers operating with the measuring unit of the shaker and an AD-1 microtransducer (with a mass of about 1 g) with a VShV-3 device. The signals (amplitudes, frequencies) from the transducers were a...

Experimental Study of the Vibrations of a Composite Cylindrical Shell with a Filler Subject to Two-Frequency Excitation

“…The signals (amplitudes, frequencies) from the transducers were analyzed and measured with a Bruel & Kjaer type 2031 low-frequency analyzer and V3-56 millivoltmeter. A measured wedge [1,11] was used to measure the amplitude of the vibrating end of the shell in the antinode zone.…”

“…are subjected to combined vibratory loading of various types. The dynamic behavior of shells filled with a fluid is more intensive under combined two-frequency vibratory loading [10,11] than under single-frequency loading [8,12].Here we will discuss test data on the nonlinear dynamic deformation of a glassfiber-reinforced plastic shell (empty or filled) subjected to longitudinal kinematic two-frequency vibrational excitation. Our primary task is to establish and analyze the relationship between the two excitation frequencies and the natural frequencies of the shell and the amplitude of the kinematic loading that cause the most intensive deformation of the shell and to analyze the effect of the filler and the way the excitation frequency varies on these processes.…”

“…are subjected to combined vibratory loading of various types. The dynamic behavior of shells filled with a fluid is more intensive under combined two-frequency vibratory loading [10,11] than under single-frequency loading [8,12].…”

Dynamic behavior of gas inclusions in a liquid under biharmonic loading

“…The solution of many engineering problems such as degasification, extraction, dispersion, and heat-exchange intensification involves the study of multiphase media that are mixtures of fluid and gas inclusions subjected to external periodic vibratory or acoustic loads. In [2,3,[5][6][7][8], problems of the nonlinear vibrations of multiphase media are formulated and the possibility for the occurrence of stable or unstable equilibrium positions of the components of the disperse phase in a liquid subject to single-frequency periodic loading is examined. However, real objects containing gas-liquid media are often subjected to complex periodic vibrations.…”

“…into(7) and averaging the result over explicit time, we obtain first approximation, where the formal small parameter m is omitted; x is the slow one-direction displacement of bubble centers along the Oõ-axis ; x 1 is the velocity of this motion; A and B are the slowly varying amplitudes of pulsations of bubbles with frequency W.Equating the right-hand sides of system (9) to zero, we obtain solutions, i.e., the localization of gas bubbles, can be found from the first equation of this system: a transcendental equation and it is impossible to solve it analytically. Let us examine some special cases in which it is possible to obtain stationary solutions.…”