Nonlinear vibrations of rotating thin circular cylindrical shell

Nonlinear vibrations of thin circular cylindrical shells are investigated in this paper. Based on Love thin shell theory, the governing partial differential equations of motion for the rotating circular cylindrical shell are formulated using Hamilton principle. Taking into account the clamped-free boundary conditions, the partial differential system is truncated by using the Galerkin method. Sequentially, the effects of temperature, geometric parameters, circumferential wave number, axial half wave number and rotating speed on the nature frequency of the rotating circular cylindrical shell are studied. The dynamic responses of the rotating circular cylindrical shell are also investigated in time domain and frequency domain. Then, the effects of nonlinearity, excitation and damping on frequency responses of steady solution are investigated.     

Boundary-layer hygrothermal stresses in laminated, composite, circular, cylindrical shell panels

Free-edge effects in laminated, circular, cylindrical shell panels subjected to hygrothermal loading are studied by utilizing displacement-based technical theories. Starting from the most general displacement field of elasticity for long, circular, cylindrical shells, appropriate reduced displacement fields are determined for laminated composite shell panels with cross-ply and antisymmetric angle-ply layups. An equivalent single-layer shell theory is used to analytically determine the constant parameters appearing in the reduced displacement fields. A layerwise shell theory is then employed to analytically determine the local displacement functions and the boundary-layer interlaminar stresses in cross-ply and antisymmetric angle-ply shell panels under hygroscopic and/or thermal changes. Several numerical examples for the distributions of transverse shear and normal stresses in various shell panels under a uniform temperature change are presented and discussed.     

Internal resonances in non-linear vibrations of a laminated circular cylindrical shell

Internal resonances in geometrically non-linear forced vibrations of laminated circular cylindrical shells are investigated by using the Amabili?CReddy higher-order shear deformation theory. A harmonic force excitation is applied in radial direction and simply supported boundary conditions are assumed. The equations of motion are obtained by using an energy approach based on Lagrange equations that retain dissipation. Numerical results are obtained by using the pseudo-arc length continuation method and bifurcation analysis. A one-to-one-to-two internal resonance is identified, giving rise to pitchfork and Neimark?CSacher bifurcations of the non-linear response. A threshold level in the excitation has been observed in order to activate the internal resonance.     

基于平均法的旋转薄壁圆柱壳非线性行波振动研究

应用Donnell's简化壳理论,在考虑阻尼和几何非线性的情况下,基于平均法对旋转的薄壁悬臂圆柱壳在法向激振力作用下的非线性行波振动进行了研究.在分析过程中,首先,引入考虑阻尼及几何非线性的薄壁圆柱壳非线性波动方程,进行降阶处理后,得到模态坐标下的振动方程;其次,对模态方程进行平均化处理,确定转换矩阵,进行变量的幅值相角化,从而得到自治的标准化方程组;最后,由系统谐波共振周期解对应平均方程稳态解的原理,得到幅频特性方程.根据上述所得结果,进行了系统参数振动及稳定性研究,并进一步将结果与谐波平衡法及数值解作了比较.     

Nonlinear vibration of viscoelastic laminated composite plates

The dynamic behavior of laminated composite plates undergoing moderately large deflection is investigated by considering the viscoelastic properties of the material. Based on von Karman's nonlinear deformation theory and Boltzmann's superposition principle, nonlinear and hereditary type governing equations are derived through Hamilton's principle. Finite element analysis and the method of multiple scales are applied to examine the effect of large amplitude on the dissipative nature as well as on the natural frequency of viscoelastic laminated plates. Numerical experiments are performed for the nonlinear elastic case and linear viscoelastic case to check the validity of the procedure presented in this paper. Limitations of the method are discussed also. It is shown that the geometric nonlinearity does not affect the dissipative characteristics in the cases that have nonlinearity of perturbed order.     

Nonlinear singular traveling waves in a slightly compressible thermo-hyperelastic cylindrical shell

Nonlinear Dynamics - In this paper, we present a novel methodology for nonlinear dynamic analysis of chemical processes that are posed as differential–algebraic equations (DAE) systems. With...     

Nonlinear finite element analysis of laminated composite spherical shell vibration under uniform thermal loading

In this article, nonlinear free vibration behavior of laminated composite shallow shell under uniform temperature load is investigated. The mid-plane kinematics of the laminated shell is evaluated based on higher order shear deformation theory to count the out of plane shear stresses and strains accurately. The nonlinearity in geometry is taken in Green-Lagrange sense due to the thermal load. In addition to that, all the nonlinear higher order terms are taken in the mathematical model to capture the original flexure of laminated panel. A nonlinear finite element model is proposed to discretise the developed model and the governing equations are derived using Hamilton’s principle. The sets of governing equations are solved using a direct iterative method. In order to validate the model, the results are compared with the available published literature and the limitations of the existing models have been discussed. Finally, some numerical experimentation has been done using the developed nonlinear model for different parameters (thickness ratio, curvature ratio, modular ratio, support condition, lamination scheme, amplitude ratio and thermal expansion coefficient) and their effects on the responses are discussed in detail.     

Parametrically excited wave modes of circular cylindrical shell motion

Kiev Higher Military Aviation Engineering School. Translated from Prikladnaya Mekhanika, Vol. 25, No. 5, pp. 45–50, May, 1989.     

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping (PCLD) are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders’ thin shell theory. Numerical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.     

旋转圆环动态特性的行波解

基于固体弹性介质中的行波理论,对旋转圆环的固有频率进行了计算.以扩张弯曲梁微元体的运动方程为基础,分析了运动条件下该波导中行波的色散关系.通过分离正行波数和负行波数,解决了行波法计算旋转圆环的固有频率问题.同时给出了波数分离的判断依据,并结合简谐波动的相位封闭原理和传递矩阵建立了旋转圆环的特征方程.数值模拟研究了旋转体...     

Free vibration and critical speed of moderately thick rotating laminated composite conical shell using generalized differential quadrature method

The generalized differential quadrature method (GDQM) is employed to consider the free vibration and critical speed of moderately thick rotating laminated composite conical shells with different boundary conditions developed from the first-order shear deformation theory (FSDT). The equations of motion are obtained applying Hamilton’s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points lying on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical technique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.     

Global bifurcations and chaos of a composite laminated cylindrical shell in supersonic air flow

Nonlinear Dynamics - The global bifurcations and chaotic motions in mode interaction of a composite laminated cylindrical shell subjected to complex loads are investigated in the case of...     

Nonlinear vibration absorption of laminated composite beams in complex environment

Nonlinear Dynamics - Nonlinear vibration absorption of a laminated composite beam is investigated with the account of complex environment (moisture and temperature). A passive efficient nonlinear...     

Wave transmission through laminated composite double-walled cylindrical shell lined with porous materials

A study on free harmonic wave propagation in a double-walled cylindrical shell, whose walls sandwich a layer of porous materials, is presented within the framework of the classic theory for laminated composite shells. One of the most effective components of the wave propagation through the porous core is estimated with the aid of a fiat panel with the same geometrical properties. By considering the effective wave component, the porous layer is modeled as a fluid with equivalent properties. Thus, the model is simplified as a double-walled cylindrical shell trapping the fluid media. Finally, the transmission loss (TL) of the structure is estimated in a broadband frequency, and then the results are compared.     

THICKNESS-SHEAR VIBRATION OF CIRCULAR CRYSTAL PLATE IN CYLINDRICAL SHELL AS PRESSURE SENSOR

Based on the theory for small fields superposed on relatively larger fields in an electroelastic body, & theoretical analysis is performed on a circular plate thickness-shear crystal resonator sealed in a circular cylindrical shell for pressure measurement. A simple expression is obtained for pressure induced frequency shifts in the resonator, which is examined for design optimization. Numerical results show that the frequency shifts depend linearly on the pressure, and that a pressure sensor with a softer outer shell or a smaller thickness ratio of the crystal plate to the outer shell has higher sensitivity.     

Nonlinear vibrations of a circular cylindrical shell with multiple internal resonances under multi-harmonic excitation

The nonlinear response of a water-filled, thin circular cylindrical shell, simply supported at the edges, to multi-harmonic excitation is studied. The shell has opportune dimensions so that the natural frequencies of the two modes (driven and companion) with three circumferential waves are practically double than the natural frequencies of the two modes (driven and companion) with two circumferential waves. This introduces a one-to-one-to-two-to-two internal resonance in the presence of harmonic excitation in the spectral neighbourhood of the natural frequency of the mode with two circumferential waves. Since the system is excited by a multi-harmonic point-load excitation composed by first and second harmonics, very complex nonlinear dynamics is obtained around the resonance of the fundamental mode. In fact, at this frequency, both modes with two and three circumferential waves are driven to resonance and each one is in a one-to-one internal resonance with its companion mode. The nonlinear dynamics is explored by using bifurcation diagrams of Poincaré maps and time responses.