Effect of thermal environment on free vibration of cracked rectangular plate: An analytical approach
TL;DR: An analytical model for free vibration and geometrically linear thermal buckling phenomenon of a thin rectangular isotropic plate containing a continuous line surface or internal crack located at the centre of the plate using classical plate theory is proposed in this article.
Abstract: An analytical model is proposed for free vibration and geometrically linear thermal buckling phenomenon of a thin rectangular isotropic plate containing a continuous line surface or internal crack located at the centre of the plate using classical plate theory. The crack terms are formulated using Line Spring Model. The in-plane forces are due to the uniform heating of the cracked plate. Applying the Galerkin׳s method, the equation is transformed into Duffing equation which shows the effect of uniform rise in temperature on natural frequencies. A classical relation for buckling temperature for a cracked plate is also determined.
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TL;DR: An analysis of delaminated composite plates with integrated active fibre composite (AFC) actuators and sensor under hygrothermal environment has been undertaken in the present work as mentioned in this paper, where the top and bottom plies of the laminate constitute AFC actuators.
Abstract: An analysis of delaminated composite plates with integrated active fibre composite (AFC) actuators and sensor under hygrothermal environment has been undertaken in the present work. The top and bottom plies of the laminate constitute AFC actuators and sensors. In the present investigation, hygrothermal loading is taken into consideration, and the effect of moisture and temperature on the delaminated plate structures is analysed. The minimum total potential energy approach is used for arriving at the governing equation. A finite element model for centrally located delamination is developed on the basis of first order shear deformation theory. An eight noded serendipity element with five degrees of freedom per node is considered for the finite element formulation. A parametric study on the effect of stacking sequence, boundary conditions and environmental conditions in the presence of delamination on the laminated plate is studied. The key observations from the parametric study are: there will be reduction in natural frequencies in the presence of delamination and/or hygrothermal loading, and reduction in structural stiffness due to the presence of delamination can be negated by applying voltage to the active fibre actuator layer.
40 citations
TL;DR: In this paper, a nonlinear analytical model for the transverse vibration of cracked magneto-electro-elastic (MEE) thin plate was presented using the classical plate theory (CPT).
Abstract: A nonlinear analytical model for the transverse vibration of cracked magneto-electro-elastic (MEE) thin plate is presented using the classical plate theory (CPT). The MEE plate material selected is fiber-reinforced $$\hbox {BaTiO}_{3}$$
–
$$\hbox {CoFe}_{2}\hbox {O}_{4}$$
composite, which contains a partial crack at the center. The CPT and the simplified line spring model for crack terms are modified to accommodate the effect of electric and magnetic field rigidities. The analysis considers in-plane forces for the MEE plate, which makes the model nonlinear. The derived governing equation is solved by expressing the transverse displacement in terms of modal coordinates. An approximate solution for forced vibration of cracked MEE plate is also obtained using a perturbation technique. The effect of part-through crack, volume fraction of the composite on the vibration frequencies and structure response is investigated. The frequency response curves presented shows the phenomenon of hard or soft spring. Furthermore, the devised model is extended to the case of cracked MEE plate submerged in fluid. Velocity potential function and Bernoulli’s equation are used to incorporate the inertia effect of surrounding fluid. Both partially and totally submerged plate configurations are considered. The validation of the present results is carried out for intact submerged plate as to the best of the author’s knowledge the literature lacks in results for submerged-cracked plates. New results for cracked MEE plate show that the vibration characteristics are affected by volume fraction, crack length, fluid level and depth of immersion.
40 citations
TL;DR: In this paper, a non-classical analytical model is presented for free vibration of the cracked rectangular isotropic and functionally graded micro plates in the presence of thermal environment, where the crack terms are based on the Line Spring Model whereas the thermal environment is accommodated in the form of thermal moment and inplane forces.
39 citations
TL;DR: In this paper, an analytical model for vibration of a thin orthotropic plate containing two perpendicular continuous line surface cracks located at the centre of the plate in the presence of thermal environment is presented.
Abstract: An analytical model is presented for vibration of a thin orthotropic plate containing two perpendicular continuous line surface cracks located at the centre of the plate in the presence of thermal environment. Also new configuration of two perpendicular cracks as internal cracks, located along the thickness of the plate is studied by considering appropriate crack compliance coefficients based on line-spring model. Equilibrium principle based on Classical Plate Theory is used to derive the equations of motion for cracked plate, wherein the crack terms are formulated using the line spring model. The moments due to thermal environment are neglected in the results and only uniform heating of the cracked plate is considered. The solution for natural frequencies of cracked plate is obtained by Galerkin’s method. A relation for thermal buckling phenomenon for the cracked plate is also formulated. The influence of the lengths of the two cracks and their location along the thickness of the plate on critical buckling temperature and first mode natural frequency is demonstrated. The geometrically linear frequency response relation for cracked plate is formulated using the method of multiple scales. It is thus concluded that the presence of the two cracks affect the critical buckling temperature and natural frequencies.
34 citations
17 Feb 2017-Microsystem Technologies-micro-and Nanosystems-information Storage and Processing Systems
TL;DR: In this article, the transverse vibration and thermal buckling of a size-dependent functionally graded (FG) circular microplate has been investigated based on modified couple stress and classical plate theory for different boundary conditions.
Abstract: In this article, transverse vibration and thermal buckling of a size-dependent functionally graded (FG) circular microplate has been investigated based on modified couple stress and classical plate theory for different boundary conditions. Material properties of the FG microplate are supposed to be temperature-dependent and vary continuously along the thickness according to a power-law form. Axial forces are also existed in the model as the thermal ones do. Governing equation and boundary conditions have been derived using Hamiltonian’s principle. Differential quadrature method is employed to solve the governing equation. Validations are done by comparing available literatures and the obtained results that confirm the accuracy of the applied method. The obtained results represent effects of temperature changes, different boundary conditions, length scale parameter, FG index and buckling load on the first and the second nondimensional frequencies. Moreover, results determine critical values of temperature changes and other essential parameters applicable to design micromachines like micromotors and microturbines.
31 citations
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TL;DR: In this paper, an elastic plate with part-through surface crack, determining stress intensity factor for remote tensile and bending loads was used to calculate the stress intensity for bending loads.
Abstract: Elastic plate with part-through surface crack, determining stress intensity factor for remote tensile and bending loads
485 citations
TL;DR: In this article, free and forced vibration analyses for initially stressed functionally graded plates in thermal environment are presented, where material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents.
336 citations
TL;DR: In this paper, a theoretical method is developed to investigate vibration characteristics of initially stressed functionally graded rectangular plates made up of metal and ceramic in thermal environment, where material properties are assumed to be temperature dependent, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents.
270 citations