Patent ID: 6845671

Claim:
A method of determining structural properties of a flexural beam comprising the steps of: securing at least seven accelerometers spaced approximately equidistant from each other along a length of said beam; providing a transverse vibrational input to said beam at a base; measuring seven frequency domain transfer functions of displacement from said secured accelerometers; and estimating a flexural wavenumber from said seven frequency domain transfer functions; wherein said seven frequency domain transfer functions comprise: T - 3 = ⁢ U - 3 ⁡ ( - 3 ⁢ ⁢ δ , ω ) V 0 ⁡ ( ω ) = A ⁢ ⁢ cos ⁢ ( 3 ⁢ α ⁢ ⁢ δ ) - ⁢ B ⁢ ⁢ sin ⁢ ( 3 ⁢ αδ ) + C ⁢ ⁢ cosh ⁢ ( 3 ⁢ α ⁢ ⁢ δ ) - D ⁢ ⁢ sinh ⁢ ( 3 ⁢ α ⁢ ⁢ δ ) , T - 2 = ⁢ U - 2 ⁡ ( - 2 ⁢ ⁢ δ , ω ) V 0 ⁡ ( ω ) = A ⁢ ⁢ cos ⁢ ( 2 ⁢ α ⁢ ⁢ δ ) - ⁢ B ⁢ ⁢ sin ⁢ ( 2 ⁢ αδ ) + C ⁢ ⁢ cosh ⁡ ( 2 ⁢ α ⁢ ⁢ δ ) - D ⁢ ⁢ sinh ⁡ ( 2 ⁢ α ⁢ ⁢ δ ) , T - 1 = ⁢ U - 1 ⁡ ( - δ , ω ) V 0 ⁡ ( ω ) = A ⁢ ⁢ cos ⁢ ( α ⁢ ⁢ δ ) - ⁢ B ⁢ ⁢ sin ⁢ ( αδ ) + C ⁢ ⁢ cosh ⁡ ( α ⁢ ⁢ δ ) - D ⁢ ⁢ sinh ⁡ ( α ⁢ ⁢ δ ) , T 0 = ⁢ U 0 ⁡ ( 0 , ω ) V 0 ⁡ ( ω ) = A + C , T 1 = ⁢ U 1 ⁡ ( δ , ω ) V 0 ⁡ ( ω ) = A ⁢ ⁢ cos ⁡ ( α ⁢ ⁢ δ ) + B ⁢ ⁢ sin ⁡ ( αδ ) + C ⁢ ⁢ cosh ⁡ ( α ⁢ ⁢ δ ) + D ⁢ ⁢ sinh ⁡ ( α ⁢ ⁢ δ ) , T 2 = ⁢ U 2 ⁡ ( 2 ⁢ ⁢ δ , ω ) V 0 ⁡ ( ω ) = A ⁢ ⁢ cos ⁢ ( 2 ⁢ α ⁢ ⁢ δ ) + ⁢ B ⁢ ⁢ sin ⁢ ( 2 ⁢ αδ ) + C ⁢ ⁢ cosh ⁡ ( 2 ⁢ α ⁢ ⁢ δ ) + D ⁢ ⁢ sinh ⁡ ( 2 ⁢ α ⁢ ⁢ δ ) , and T 3 = ⁢ U 3 ⁡ ( 3 ⁢ ⁢ δ , ω ) V 0 ⁡ ( ω ) = A ⁢ ⁢ cos ⁢ ( 3 ⁢ α ⁢ ⁢ δ ) + ⁢ B ⁢ ⁢ sin ⁢ ( 3 ⁢ αδ ) + C ⁢ ⁢ cosh ⁡ ( 3 ⁢ α ⁢ ⁢ δ ) + D ⁢ ⁢ sinh ⁡ ( 3 ⁢ α ⁢ ⁢ δ ) .