Browsing by Subject "Resonant vibration"
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Item Deterministic behavior of elevated water tanks under vertical motion(Texas Tech University, 1985-12) Gau, Jin-shyThe dynamic response of 3n elsstic structure carrying 3 rigid cylindrical tank partially filled with a liquid subjected to vertical sinusoidal harmonic excitation Is considered. The nonlinear response is determined by using an asymptotic expansion technique developed by Struble. Secular terms which give rise to parametric resonance conditions are identified. Four parametric resonance conditions are found to take place when the excitation frequency is in the neighborhood of twice the natural frequency of one of the normal modes, or close to the sum or difference of the normal mode frequencies of the system. The steady-state responses of the system are obtained for the first three parsmetric resonance conditions and show the occurrence of the jumps phenomenon at a certain critical excitation frequency. Under combination parametric resonance of difference type the method does not provide any steady state response.Item Development of a non-Gaussian closure scheme for dynamic systems involving non-linear inertia(Texas Tech University, 1985-12) Soundararajan, AravamudhanThe main objective of this investigation is to develop a non-Gaussian closure scheme adapted for the analysis of random response statistics of nonlinear dynamic systems which are subjected to parametric random excitations. The scheme is based on the asymptotic expansion of the non-Gaussian probability density. The technique is found to have two main advantages. The first is that it resolves an observed contradiction of results obtained by other techniques. The second is that it explores new response characteristics not predicted by other methods. The scheme is applied to a number of dynamic systems possessing single and two degrees-of-freedom and various types of nonlinearities. Numerical solutions are obtained and their validity is examined according to certain criteria based on the preservation of moment properties and Schwarz's inequality. Higher order terms are considered to examine the convergence of the Edgeworth expansion. It is found that the inclusion of the third and fourth order semi-invariants is adequate for the series convergence. The response of nonlinear single degree-of-freedom systems exhibits the occurrence of a jump in the response statistics at a certain excitation level which is mainly governed by the system linear damping factor. This new feature may be attributed to the fact that the non-Gaussian closure more adequately models the nonlinearity, and thus results in characteristics that are similar to those of deterministic nonlinear systems. The method is also used to determine the random response of an elevated water tower subjected to a random ground motion. The tower is represented by a two-degree-of-freedom system with cubic nonlinear coupling. In the neighborhood of the internal resonance condition r= w2/w1 =1/3, where w1 and w2 are the normal mode frequencies of the system, the nonlinear modal interaction takes the form of energy exchange between the two modes. Unlike the Gaussian solution, the non-Gaussian closure solution is found to achieve a strictly stationary response in the time domain. The response mean squares are presented as functions of the internal resonance detuning parameter r = 1/3 + 0(e), where £ is a small parameter, for various system parameters. Unbounded response mean squares are found to take place at regions above and below certain values of the internal resonance r=l/3. For regions well remote from the exact internal tuning the system exhibits the features of the linear response.Item Numerical and experimental investigation of coupled beam and pendulum oscillator(Texas Tech University, 1992-12) Cuvalci, OlkanA large number of aerospace structures and large flexible mechanical structures may be modeled as a large flexible beam with a tip-mass. Sometimes, under certain conditions (high excitation amplitude, etc.), large deformation may be produced in the structure. In the field of design, the developments have led to the use of lightweight and high strength materials in these structures. Hence, modern structures are lighter, more flexible, and provide much lower energy dissipation, leading to an intense vibration response. A vibrating (oscillating) system has a maximum response amplitude at the resonance conditions; as a result, the system should work before or beyond the resonance case. Otherwise, it has a maximum response amplitude, which may cause the system to fail. In this research, a flexible beam with an appendage, which consists of a mass-pendulum attached to its tip, is investigated. Such an appendage can be located anywhere along the beam. However, in this research, only a tip appendage is considered. The pendulum which is considered as an auto-parametric vibration absorber. The equations of the motion of a system are obtained using D'Alembert's principle. The partial differential equations are reduced to a set of ordinary differential equations using the Galerkin method. The equations are nonlinear since the analysis is based on large deflection and also coupling exists between the beam and the pendulum. Numerical simulations are performed in order to obtain frequency response curves of the beam and the pendulum. The simulations are performed for different damping coefficients, both beam and pendulum, around primary resonance and under different forcing amplitudes. Experiments are conducted for two different lengths of the beam. The longer beam is used for uninverted pendulum motion, and the shorter beam for the inverted pendulum motion. Four different pendulums are considered for the uninverted pendulum case, and one pendulum for the inverted pendulum case. The results show that an energy exchange between the beam and pendulum, and also chaotic motion, is observed for some parameters of the beam and pendulum. Hence, the pendulum may be considered as a suitable auto-parametric vibration absorber.Item Random modal interaction of a non-linear aeroelastic structure(Texas Tech University, 1985-08) Hedayati, ZhianThe modal interaction of an aeroelastic structure subjected to random wide band excitation is investigated. An analytical model, represented by three degrees of freedom, is adopted. The equations of motion are derived by employing Lagrange's equation. The Fokker-Planck equation approach is used to generate the statistical dynamic moment equations of the response. Linear and non-linear modal interactions are obtained for various system parameters. The linear modal analysis involves the determination of the normal mode eigenvalues in terms of the system parameters. The main objective of this standard analysis is to define the critical regions of internal resonance of the sum type ω3 = ω1 + ω2, where o)i are the system eigenvalues. Analytical solutions are obtained for the mean square response of the linearized system with constant and randomly varying stiffnesses. The results provide mean square stability criteria for the linear case with random stiffness. The linear response statistics are used as a reference to measure the departure of the non-linear system response in the neighborhood of the internal resonance condition. For the non-linear case the differential equations of the response moments are found to form an infinite coupled set which is closed via a cumulant-neglect scheme. The resulting closed first and second order moment equations, 27 in total, are solved by numerical integration. The response at the critical internal resonance demonstrates a deviation from the corresponding linear response. The results indicate that the autoparametric interaction takes place in the form of energy transfer between the three modes, and large amplitude motion of one mode associated with suppression of the other two modes.Item Response of two-degree-of-freedom turbine-housing system with quadratic nonlinearity(Texas Tech University, 1988-05) Anlas, GunayA 2-degree-of-freedom model of a rotating machine with nonlinear springs of quadratic type is studied. The method of Multiple Scales is used to investigate the nonlinear oscillations of the forced system where the forcing is due to the eccentricity "e" of the rotor about its center of mass. The behavior of the system for the primary resonances Q = LOI, Q = iV2, and internal resonance a;2 = 2a;i is analyzed. Other features, such as amplitude jump and saturation phenomenon, have been observed. The amplitudes versus detuning parameters for both cases are plotted. The critical values of mass ratios and spring ratios for the presence of an internal resonance are studied and interpreted for this particular application.