“…2(a,c,e and g) . Figure 2 Comparison of mode shapes between irregular-shaped plate and the equivalent rectangular plate for the lowest 4 modes 11 . ( a ) Mode 1:T(1,1), ( b ) Mode 1: m = 1 , n = 1, ( c ) Mode 2: T(1,2), ( d ) Mode 2: m = 2, n = 1, ( e ) Mode 3: T(2,1), ( f ) Mode 3: m = 1 , n = 2, ( g ) Mode 4: T(1,3), ( h ) Mode 4: m = 3, n = 1.…”
Section: Resultsmentioning
confidence: 99%
“…It is therefore proposed to adopt some criteria to determine the dimensions of an equivalent rectangular plate of constant thickness. The criteria for determining its dimensions 11 are as follows: The rectangular plate vibrates transversely under dynamic compression in the direction of its longitudinal grain. The longitudinal Young’s modulus is identical to that of the guitar soundboard material as its longitudinal grain is always aligned parallel to the strings and the guitar soundboard is constantly under dynamic compression under playing conditions.…”
Section: Resultsmentioning
confidence: 99%
“…Equation ( 5 ) is a 4 th -order parabolic partial differential equation with variable coefficients. The analytical solution of Equation ( 5 ) using the homotopy perturbation method 11 for the thin plate which is simply supported on all sides is given by: and …”
Section: Resultsmentioning
confidence: 99%
“…This type of irregular-shaped plate can be structurally designed to withstand the cumulative string tension of the first, second and third nylon strings and the fourth, fifth and sixth wire-wound nylon strings under playing conditions. Since a guitar soundboard can be considered as a modified form of a rectangular plate 10 , this paper will use the complete analytical solution of an equivalent rectangular plate 11 to compute the sound power of an unbraced irregular-shaped plate which is identical in shape to that of the guitar soundboard.…”
An irregular-shaped plate with dimensions identical to a guitar soundboard is chosen for this study. It is well known that the classical guitar soundboard is a major contributor to acoustic radiation at high frequencies when compared to the bridge and sound hole. This paper focuses on using an analytical model to compute the sound power of an unbraced irregular-shaped plate of variable thickness up to frequencies of 5 kHz. The analytical model is an equivalent thin rectangular plate of variable thickness. Sound power of an irregular-shaped plate of variable thickness and with dimensions of an unbraced Torres’ soundboard is determined from computer analysis using ANSYS. The number of acoustic elements used in ANSYS for accurate simulation is six elements per wavelength. Here we show that the analytical model can be used to compute sound power of an unbraced irregular-shaped plate of variable thickness.
“…2(a,c,e and g) . Figure 2 Comparison of mode shapes between irregular-shaped plate and the equivalent rectangular plate for the lowest 4 modes 11 . ( a ) Mode 1:T(1,1), ( b ) Mode 1: m = 1 , n = 1, ( c ) Mode 2: T(1,2), ( d ) Mode 2: m = 2, n = 1, ( e ) Mode 3: T(2,1), ( f ) Mode 3: m = 1 , n = 2, ( g ) Mode 4: T(1,3), ( h ) Mode 4: m = 3, n = 1.…”
Section: Resultsmentioning
confidence: 99%
“…It is therefore proposed to adopt some criteria to determine the dimensions of an equivalent rectangular plate of constant thickness. The criteria for determining its dimensions 11 are as follows: The rectangular plate vibrates transversely under dynamic compression in the direction of its longitudinal grain. The longitudinal Young’s modulus is identical to that of the guitar soundboard material as its longitudinal grain is always aligned parallel to the strings and the guitar soundboard is constantly under dynamic compression under playing conditions.…”
Section: Resultsmentioning
confidence: 99%
“…Equation ( 5 ) is a 4 th -order parabolic partial differential equation with variable coefficients. The analytical solution of Equation ( 5 ) using the homotopy perturbation method 11 for the thin plate which is simply supported on all sides is given by: and …”
Section: Resultsmentioning
confidence: 99%
“…This type of irregular-shaped plate can be structurally designed to withstand the cumulative string tension of the first, second and third nylon strings and the fourth, fifth and sixth wire-wound nylon strings under playing conditions. Since a guitar soundboard can be considered as a modified form of a rectangular plate 10 , this paper will use the complete analytical solution of an equivalent rectangular plate 11 to compute the sound power of an unbraced irregular-shaped plate which is identical in shape to that of the guitar soundboard.…”
An irregular-shaped plate with dimensions identical to a guitar soundboard is chosen for this study. It is well known that the classical guitar soundboard is a major contributor to acoustic radiation at high frequencies when compared to the bridge and sound hole. This paper focuses on using an analytical model to compute the sound power of an unbraced irregular-shaped plate of variable thickness up to frequencies of 5 kHz. The analytical model is an equivalent thin rectangular plate of variable thickness. Sound power of an irregular-shaped plate of variable thickness and with dimensions of an unbraced Torres’ soundboard is determined from computer analysis using ANSYS. The number of acoustic elements used in ANSYS for accurate simulation is six elements per wavelength. Here we show that the analytical model can be used to compute sound power of an unbraced irregular-shaped plate of variable thickness.
“…e nonlinear governing equations were solved by the incremental harmonic balance method. Lee et al [31] adopted the homotopy perturbation method to solve parabolic partial differential equations with constant coefficients for the nonlinear plate problem. Gao et al [32] adopted the multiple scales method to analyze the nonlinear primary resonance of functionally graded porous cylindrical shells.…”
This paper addresses the vibration and sound radiation of a nonlinear duct. Many related works assume that the boundaries are linearly vibrating (i.e., their vibration amplitudes are small), or that the duct panels are rigid, and their vibrations can thus be neglected. A classic method combined with Vieta’s substitution technique is adopted to develop an analytic formula for computing the nonlinear structural and acoustic responses. The development of the analytic formula is based on the classical nonlinear thin plate theory and the three-dimensional wave equation. The main advantage of the analytic formula is that no nonlinear equation solver is required during the solution procedure. The results obtained from the proposed classic method show reasonable agreement with those from the total harmonic balance method. The effects of excitation magnitude, panel length, damping, and number of flexible panels on the sound and vibration responses are investigated.
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