Natural Frequencies Calculators

Vibration Frequency of a Rectangular Plate with Simply Supported Edges

In this calculation, a rectangular plate with the dimensions a × b, thickness s, and own mass m is considered. The plate edges are simply supported. For the calculation, the elastic modulus E and Poisson's ratio ν of the plate should be specified. As a result of calculations, the natural vibration frequency of the plate f is determined for the first vibration mode.

Natural frequency of rectangular plate with simply supported edges

Calculation of Natural frequency of rectangular plate with simply supported edges

INITIAL DATA

a - Length of the plate;

b - Width of the plate;

s - Plate thickness;

m - Plate weight;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

f - First mode frequency.

Metric Imperial

Length (a)

Width (b)

Thickness (s)

Plate mass (m)

Young's modulus (E)

Poisson's ratio (ν)

Natural frequency (f)

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BASIC FORMULAS

Natural frequency of the first mode:

f = [π²*[1 + (b/a)²]]*[[Es³ / 12(1 - ν²)]*[a/(m*b³)]]^0.5

INITIAL DATA

a - Length of the plate;

b - Width of the plate;

s - Plate thickness;

m - Plate weight;

E - Young's modulus;

ν - Poisson's ratio.

RESULTS DATA

f - First mode frequency.

MATERIALS PROPERTIES

Material	Young’s modulus Pa (psi)	Poisson’s ratio
Steel	1.86÷2.1×10¹¹ (2.7÷3.05×10⁷)	0.25÷0.33
Cast iron	0.78÷1.47×10¹¹ (1.1÷2.1×10⁷)	0.23÷0.27
Copper	1.0÷1.3×10¹¹ (1.45÷1.9×10⁷)	0.34
Tin bronze	0.74÷1.22×10¹¹ (1.1÷1.8×10⁷)	0.32÷0.35
Brass	0.98÷1.08×10¹¹ (1.4÷1.6×10⁷)	0.32÷0.34
Aluminum alloy	0.7×10¹¹ (1.0×10⁷)	0.33
Magnesium alloy	0.4÷0.44×10¹¹ (5.8÷6.4×10⁶)	0.34
Nickel	2.5×10¹¹ (3.6×10⁷)	0.33
Titanium	1.16×10¹¹ (1.7×10⁷)	0.32
Lead	0.15÷0.2×10¹¹ (2.2÷2.9×10⁶)	0.42
Zinc	0.78×10¹¹ (1.1×10⁷)	0.27
Glass	4.9÷5.9×10¹⁰ (7.1÷8.5×10⁶)	0.24÷0.27
Concrete	1.48÷2.25×10¹⁰ (2.1÷3.3×10⁶)	0.16÷0.18
Wood (along the grain)	8.8÷15.7×10¹⁰ (12.8÷22.8×10⁶)	-
Wood (across the grain)	3.9÷9.8×10¹⁰ (5.7÷14.2×10⁶)	-
Nylon	1.03×10¹⁰ (1.5×10⁶)	-

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