Beams In Thermal Environment Research Articles

Analysis of elasto-plastic postbuckling and energy release rate for delaminated fiber metal laminated beams in thermal environment

The elasto-plastic postbuckling of fiber metal laminated beams with delamination and the energy release rate along the delamination front are discussed in this paper. Considering geometrical nonlinearity, thermal environment and geometrical initial imperfection, the incremental nonlinear equilibrium equations of delaminated fiber metal laminated beams are established, which are solved using the differential quadrature method and iterative method. Based on these, according to the J-integral theory, the elasto-plastic energy release rate is studied. The effects of some important parameters on the elasto-plastic postbuckling behavior and energy release rate of the aramid reinforced aluminum laminated beams are discussed in details.

Dynamic response of functionally graded beams in a thermal environment under a moving load

ABSTRACTThe dynamic response of functionally graded (FG) beams in thermal environment subjected to moving load is investigated based on the first-order shear deformation theory (FSDT). The initial thermal stresses are determined by solving the thermoelastic equilibrium equations. The finite element method (FEM) is adopted to develop a solution procedure for FG beams with general loading and boundary conditions. The convergence behavior and accuracy of the method are shown through the different numerical examples. Finally, the influences of temperature rise, material graded index, moving load velocity, and boundary conditions on the dynamic behavior of FG beams in thermal environment is presented.

Low velocity impact response of functionally graded carbon nanotube reinforced composite beams in thermal environment

Response of functionally graded carbon nanotube reinforced composite (FG-CNTRC) beam subjected to the action of an impacting mass is analyzed. Timoshenko beam theory is used to estimate the kinematics of the beam. Material properties of the fibers and polymeric matrix are assumed to be temperature dependent. Both uniform and functionally graded distribution of CNTs are taken into account. Material properties of the composite are obtained using a refined rule of mixture. Contact force between the impactor and the beam is obtained with the aid of the conventional Hertz law. The governing dynamic equations of the system, are obtained using the conventional polynomial Ritz method applied to the total energy of the system. The solution of the resulting equations is traced in time using the well-known Runge–Kutta method. After examining the validity of the present solution, parametric studies are conducted to examine the influences of thermal environment, volume fraction of the CNTs, distribution of CNTs, initial velocity of the impactor and the impactor mass. Numerical results reveal that as the volume fraction of CNTs increases in the beam, peak contact force increases and the contact time decreases. Furthermore, temperature rise results in higher contact time duration and lower peak contact force.

In-plane free vibrations of circular beams made of functionally graded material in thermal environment: Beam theory approach

In this paper, in-plane free vibrations of FGM circular beams in thermal environment are studied via the beam theory approach. Axial deformation, shear deformation and rotatory inertia effects are taken into account. Thermal effects are taken into account by assuming the material properties as an arbitrary function of the temperature as well as the position, and by writing the equilibrium equations for the deformed shape of the beam. Necessary simplifications are made in order to obtain the differential equation system of circular beams made of FGM, in thermal environment. The system of linear differential equations with variable coefficients are solved using the matricant. Formulation is validated by comparing the results of numerous examples existing in the literature and FEM software package. Effects of temperature change, material variation, and geometrical parameters such as the ratio of thickness to the length of the beam and the opening angle on free vibration characteristics of FGM circular beams with ceramic inner surface in thermal environment are investigated. It is concluded that such structures can be analyzed with simplistic beam theory approach. Also, new results, which can be used for validation of new approaches are presented.

Nonlinear stability and bifurcations of an axially moving beam in thermal environment

The thermo-mechanical nonlinear dynamics of an axially moving beam with coupled longitudinal and transverse displacements subjected to a distributed harmonic external force is numerically investigated. This includes a case where the system is tuned to a three-to-one internal resonance between the first two transverse modes and a case where it is not is considered. Two coupled nonlinear partial differential equations for the longitudinal and transverse motions are obtained using Hamilton’s principle and constitutive relations, as well as taking into account the thermal effects. The Galerkin method is then used to discretize these equations into a set of coupled nonlinear ordinary differential equations. Two different techniques are employed to solve the resulting equations; the pseudo-arclength continuation method and direct time integration to investigate the periodic vibrations and the global dynamics of the system, respectively. The effect of different parameters on the dynamics of the system is investigated through the frequency-response curves of the system and the bifurcation diagrams of Poincaré maps. Furthermore, time histories, phase-plane portraits, and fast Fourier transforms are presented for a few different system parameter sets. It is illustrated that the system shows a broad variety of rich dynamics, depending on system parameters and the temperature rise.

The thermal effects on high-frequency vibration of beams using energy flow analysis

Abstract In this paper, the energy flow analysis (EFA) method is developed to predict the high-frequency response of beams in a thermal environment, which is a topic of concern in aerospace and automotive industries. The temperature load applied on the structures can generate thermal stresses and change material properties. The wavenumber and group velocity associated with the in-plane axial force arising from thermal stresses are included in the derivation of the governing energy equation, and the input power is obtained from the derived effective bending stiffness. In addition, effect of temperature-dependent material properties is considered in the EFA model. To verify the proposed formulation, numerical simulations are performed for a pinned–pinned beam in a uniform thermal environment. The EFA results are compared with the modal solutions for various frequencies and damping loss factors, and good correlations are observed. The results show that the spatial distributions and levels of energy density can be affected by the thermal effects, and the vibration response of beams increases with temperature.

Non-linear active control of FG beams in thermal environments subjected to blast loads with integrated FGP sensor/actuator layers

Non-linear active control of dynamic response of functionally graded (FG) beams with rectangular cross-section in thermal environments exposed to blast loadings is presented. Two FG piezoelectric layers are bonded to the beam surfaces to act as sensor and actuator. Non-linear equations of motion of the smart beam are derived based on the first-order shear deformation theory and the von Karman geometrical non-linearity. Constant velocity feedback algorithm is used to control the dynamic response of the FG beam actively through closed loop control. The generalized differential quadrature method together with the Newmark-beta scheme is utilized to solve the non-linear partial differential equations in spatial and time domains. The resulted non-linear algebraic equations are then solved using the modified Newton–Raphson method. A detailed analysis of the influence of the geometric non-linearity, material parameters and temperature field on the active vibration control of FG beams subjected to various impulsive loads is carried out.

Adaptive pole placement control for vibration control of a smart cantilevered beam in thermal environment

Piezoelectric actuators used in vibration control and high precision control have been widely used in recent years. In aeronautics and MEMS systems especially, their applications are spread from vibration suppression to position control. In this paper, a finite element model (FEM) of a piezoelectric actuator and cantilever in a thermal environment is presented to suppress vibration effectively. In other words, the FEM is namely a thermal-electrical-mechanical coupled FEM. Based on an eight-node plane finite element, the harmonic analysis and the free vibration analysis have been obtained in the current work. Therefore a transfer function model will be attained through the harmonic analysis by an identification method. In addition, a controller is designed with the adaptive pole placement control (APPC). Finally, through simulation, the thermal influence is considerable for natural frequencies, harmonic response and free vibration. Moreover, the APPC is a significant plan to vibration control in the paper.

Nonlinear analysis of buckling, free vibration and dynamic stability for the piezoelectric functionally graded beams in thermal environment

Employing Euler–Bernoulli beam theory and the physical neutral surface concept, the nonlinear governing equation for the functionally graded material beam with two clamped ends and surface-bonded piezoelectric actuators is derived by the Hamilton’s principle. The thermo-piezoelectric buckling, nonlinear free vibration and dynamic stability for the piezoelectric functionally graded beams, subjected to one-dimensional steady heat conduction in the thickness direction, are studied. The critical buckling loads for the beam are obtained by the existing methods in the analysis of thermo-piezoelectric buckling. The Galerkin’s procedure and elliptic function are adopted to obtain the analytical solution of the nonlinear free vibration, and the incremental harmonic balance method is applied to obtain the principle unstable regions of the piezoelectric functionally graded beam. In the numerical examples, the good agreements between the present results and existing solutions verify the validity and accuracy of the present analysis and solving method. Simultaneously, validation of the results achieved by rule of mixture against those obtained via the Mori–Tanaka scheme is carried out, and excellent agreements are reported. The effects of the thermal load, electric load, and thermal properties of the constituent materials on the thermo-piezoelectric buckling, nonlinear free vibration, and dynamic stability of the piezoelectric functionally graded beam are discussed, and some meaningful conclusions have been drawn.

Out-of-plane free vibration of functionally graded circular curved beams in thermal environment

Abstract A first known formulation for the out-of-plane free vibration analysis of functionally graded (FG) circular curved beams in thermal environment is presented. The formulation is based on the first order shear deformation theory (FSDT), which includes the effects of shear deformation and rotary inertia due to both torsional and flexural vibrations. The material properties are assumed to be temperature dependent and graded in the direction normal to the plane of the beam curvature. The equations of motion and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the Hamilton’s principle. Differential quadrature method (DQM), as an efficient and accurate numerical method, is adopted to solve the thermoelastic equilibrium equations and the equations of motion. The formulations are validated by comparing the results, in the limit cases, with the available solutions in the literature for isotropic circular curved beams. In addition, for FG circular curved beams with soft simply supported edges, the results are compared with the obtained exact solutions. Then, the effects of temperature rise, boundary conditions, material and geometrical parameters on the natural frequencies are investigated.

Coupled layerwise analysis of thermopiezoelectric composite beams

Previously developed discrete layer mechanics are extended to incorporate thermal effects to account for the complete coupled mechanical, electrical, and thermal response of piezoelectric composite beams. Thermal effects in both the elastic and piezoelectric media are captured at the material level. This unified representation leads to an inherent capability to model both the sensory and active responses of piezoelectric composite beams in thermal environments. Finite element equations are developed and implemented for a beam element with linear shape functions. Results from the current formulation are compared with results from a conventional thermoelastic finite element analysis and classical beam theory. Additional numerical studies demonstrate capabilities of the current formulation to predict the thermal deformation of composite beams, as well as the active compensation of these thermal deformations using piezoelectric structures. The corresponding sensory response and the resultant stress state in the piezoelectric composite beam are also presented. [Amn], [Bmn], [Dmn] b [C] {D} [d] {E} [Emn] [e] {F}