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

Abstract

Experimental results on the nonlinear dynamic deformation of the elastic wall of a glassfiber-reinforced plastic cylindrical shell (either "dry" or filled) during beating caused by kinematic two-frequency loading are discussed. It is revealed that the nonlinear deformation of a shell undergoing beating, especially at the two close frequencies of the modes n = 3 and n = 5, can be accompanied by the alteration of amplitude and deformation mode between one mode n = 3 and combined mode (n = 3) + (n = 5) and the alternation of one mode n = 3 between a traveling wave and a standing wave Introduction. The deformation of elastic cylindrical shells is strongly dependent on major factors (external periodic loading) and other factors. For example, the presence of a filler (fluid or loose material) in thin-walled cylindrical shells may result in compound multimode or multiwave dynamic deformation under certain conditions (free vibraions or external periodic loads). Many theoretical and experimental studies [2, 3, 6-9, 12-14] address the deformation of shell structures and nonlinear and resonant phenomena caused by the imposition and nonlinear interaction of several 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. It was established that even the mode shape a shell takes under purely harmonic loads can affect its dynamic instability domains (DID) [4]. For example, the principal DID of a cylindrical shell is located lower on the frequency axis and is considerably wider than the DID of a shell with alternating curvature. Such a situation is typical for composite shells [1,8]. Therefore, experimental studies of the vibratory and wave processes in composite shell structures interacting with a fluid are of current importance. As indicated in [5], experimental methods not only give a true picture of the behavior of mechanical structures under varying loads, but also make it possible to identify the limits of validity of theoretical models. This fact was confirmed by holographic interferometry studies of the natural frequencies and modes of isotropic circular cylindrical shells.An important task of solid mechanics is to study the nonlinear vibrations (with large deflections) of thin-walled laminated shells under combined vibratory loading. When in service, real shell structures with fluid used in aircraft and rocket technology, chemical engineering, etc. 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 th...