Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method

Bhat, Rama

doi:10.1016/s0022-460x(85)80109-7

Cited by 484 publications

(236 citation statements)

References 10 publications

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“…Also the results for frequency are compare with [2,17] for aspect ratio a/b = 1.0 and b/a = 0.5 for Poisson ratio v = 0.3 and found in very good agreement. Further it is interesting to note that effect of taper in x-direction is more dominate in comparison to y-direction.…”

Section: Resultsmentioning

confidence: 60%

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Thermal Effect on Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variation in Both Directions

Gupta¹,

Kaur

Kumar³

2010

Shock and Vibration

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Abstract. The analysis presented here is to study the effect of thermal gradient on the vibration of visco-elastic rectangular plate (having clamped boundary condition on all the four edges) of variable thickness whose thickness varies parabolically in both directions. The effect of linear temperature variation has been considered. A frequency equation of plate has been obtained by Rayleigh-Ritz technique with two terms of deflection function. The assumption of small deflection and linear viscoelastic properties of 'Kelvin' type are taken. Deflection and time period corresponding to the first two modes of vibrations for clamped plate have been computed for various combinations of aspect ratio, thermal constants, and taper constants. Numerical computations have been performed for an alloy 'Duralium' and the results obtained are depicted graphically.

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Section: Resultsmentioning

confidence: 60%

“…Singh and Chakarverty [17] solved the problem for vibration of skew plates using characteristic orthogonal polynomials. Bhat [2] analyses the natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayliegh-Ritz method.…”

Section: Introductionmentioning

confidence: 99%

Thermal Effect on Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variation in Both Directions

Gupta¹,

Kaur

Kumar³

2010

Shock and Vibration

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“…A comparison of frequency parameter Ω for homogeneous (α 1 = α 2 = β 1 = β 2 = 0) square (a/b = 1) plate of uniform (γ 1 = γ 2 = 0) thickness obtained by Rayleigh-Ritz method [7,34,37], exact and approximate results using Ritz method [33], Differential quadrature method [11,36], Optimized Kantorovich method [35] and non-uniform thickness obtained by finite element method [6], Rayleigh-Ritz method [7,9], differential quadrature method [11], optimized Kantorovich method [35] has been presented in Table 2. A close agreement of results is obtained.…”

Section: Resultsmentioning

confidence: 99%

Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation

Lal

Kumar

2012

Shock and Vibration

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Abstract. The free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickness variation is bidirectional and is the cartesian product of linear variations along two concurrent edges of the plate. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of the nonhomogeneity and thickness variation with varying values of aspect ratio on the natural frequencies of vibration is illustrated for the first three modes of vibration. Three dimensional mode shapes for all the four boundary conditions have been presented. A comparison of results with those available in the literature has been made.

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“…To this end, Φ x (x, y), Φ y (x, y), and w 0 (x, y) have been projected on an orthonormal polynomial basis of order Q satisfying the free-free boundary conditions [10]:…”

Section: Rayleigh-ritz Proceduresmentioning

confidence: 99%

Identiﬁcation of honeycomb sandwich properties by high-resolution modal analysis

Rébillat

Boutillon²

2010

EPJ Web of Conferences

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Abstract.A method is proposed to identify the mechanical properties of the skin and core materials of honeycomb sandwich. All the elastic coefficients and loss-factors that matter in the dynamics of a panel in the thick-plate approximation are identified. To this end, experimental natural modes (i.e. eigenmodes of the damped system) are compared to the numerical modes of a large sandwich panel (l x,y /h ≃ 80). The chosen generic model for the visco-elastic behaviour of the materials is E(1 + jη). The numerical modes are computed by means of a Rayleigh-Ritz procedure and their dampings are predicted according to the visco-elastic model. The frequencies and dampings of the natural modes of the panel are estimated experimentally by means of a high-resolution modal analysis technique. An optimisation procedure yields the desired coefficients. A sensitivity analysis assess the reliability of the method.

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Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method

Cited by 484 publications

References 10 publications

Thermal Effect on Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variation in Both Directions

Thermal Effect on Vibration of Clamped Visco-Elastic Rectangular Plate with Parabolic Thickness Variation in Both Directions

Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation

Identiﬁcation of honeycomb sandwich properties by high-resolution modal analysis

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