A study of the fundamental frequency characteristics of eccentrically and concentrically simply supported stiffened plates

Journal of Vibration and Control

2012

This paper undertakes a large amplitude forced vibration analysis of stiffened plates with free edges under harmonic excitation through a numerical method. The methodology adopted is an indirect one in which the dynamic system is assumed to satisfy the force equilibrium condition at peak excitation amplitude. Free vibration analysis at the deflected configuration of the same system is also carried out separately to determine the backbone curves. The mathematical formulation is based on energy principles and the governing equations in both forced and free vibration cases are derived using Hamilton’s principle. The set of nonlinear governing equations is solved by employing an iterative direct substitution method with an appropriate relaxation technique. A multidimensional quasi-Newton method, known as Broyden’s method, is separately used when the system becomes computationally stiff. The results for a reduced system are validated with the published results of other researchers. For different combinations of boundary conditions including free edge results are furnished in the dimensionless amplitude-frequency plane. The effect of in-plane end conditions is studied by considering immovable and movable edges. Response in the vicinity of the second mode is also studied. Three dimensional operational deflection shape plots along with contour plots are also provided in a few cases.

Section: Literature Reviewmentioning

confidence: 99%

Effect of in-plane boundary conditions on forced vibration analysis of stiffened plates with a free edge

Journal of Vibration and Control

2012

“…Chen et al (1994) proposed a spline compound strip method, where the plate is discretized in one direction only, for analyzing the free vibration problem of stiffened plates. Bedair and Troitsky (1997) studied the effect of variation in plate and stiffener geometric parameters on the dynamic behavior of the system. They analyzed eccentrically and concentrically stiffened simply supported plates and the fundamental frequency was determined following energy formulation and Mathematical Programming technique.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of initially deflected stiffened plates for various boundary conditions

Journal of Vibration and Control

2011

Free vibration analysis of initially deflected stiffened plates subjected to uniformly distributed loading with different flexural boundary conditions involving simply supported and clamped ends and zero displacement in-plane boundary conditions has been presented. A domain decomposition technique depending on the number, orientation and location of the stiffeners is employed to ensure sufficient number of computation points around the stiffeners. Geometric nonlinearity arising out of large deflection is accounted for by consideration of non-linear strain-displacement relations. Mathematical formulation is based on a variational form of energy principle, and a solution technique, where static analysis serves as the basis for the subsequent dynamic study, is followed. The results are validated with the published results of other researchers. The dynamic behavior has been presented in the form of backbone curves in a dimensionless frequency-amplitude plane. Vibration mode shapes along with contour plots are provided in a few cases.

“…In [Chen et al 1994] a spline compound strip method was proposed, where the plate was discretized in only one direction, for analyzing the free-vibration problem of stiffened plates. Bedair and Troitsky [1997] analyzed eccentrically and concentrically stiffened simply supported plates on the basis of energy formulation and mathematical programming techniques and studied the effect of variation in plate and stiffener geometric parameters on the fundamental frequency of the system.…”

Section: Introductionmentioning

confidence: 99%

Large-amplitude dynamic analysis of stiffened plates with free edges

J. Mech. Mater. Struct.

2011

Large-amplitude free-vibration analysis of stiffened plates subjected to uniformly distributed transverse loading with free flexural boundary conditions is presented. The free edge is taken with different combinations of clamped and simply supported end conditions for three types of stiffened plates classified according to number and orientation of stiffeners. The computational domain is divided into an adequate number of subdomains based on the number, orientation, and location of stiffeners to generate the appropriate grid of computation points. Nonlinear strain displacement relations are considered in the formulation but the effects of shear deformation have been neglected. The analysis involves two steps. First the static displacement field of the system is solved for. The second step takes up the freevibration analysis on the basis of the known static displacement field. The mathematical formulation of the static problem is based on the principle of minimum potential energy, whereas Hamilton's principle has been applied for the dynamic analysis. The results are validated with the published results of other researchers. The dynamic behavior is presented in the form of backbone curves in a dimensionless frequency-amplitude plane. Three-dimensional mode shape plots are also presented along with contour plots in a few specific cases.A list of symbols can be found on page 911.