Modal Analysis Visualizer
See how structures vibrate. This visualizer animates the idealised 2D mode shapes (eigenmodes) of a beam, a rectangular plate, a circular membrane (drumhead) and a cylindrical shell — with selectable boundary conditions, nodal lines (zero-motion regions) highlighted in pink, and a plot of relative natural frequency vs. mode number. It is a teaching tool for understanding modal analysis, resonance and nodes.
ℹ This is an educational visualizer of idealised, undamped, geometrically-perfect mode shapes — the classic textbook eigenmodes. It is not a measurement and not a simulation of your part. Real structures have damping, material imperfections, joints, welds and added mass, so their true mode shapes and frequencies differ. The frequency plot shows relative spacing only (a dimensionless eigenvalue), not absolute hertz — getting real Hz needs the actual material, dimensions and a proper calculator or FEA / experimental modal analysis. No microphone, no sensor, no data leaves your browser.
Choose a structure & mode
On the plate, membrane and shell surface maps, green = positive displacement and cyan = negative; the beam shows a single green deflection curve about the dashed rest line. Pink marks the nodal lines / points (zero motion). The shape oscillates about the rest position; the whole pattern is one standing wave.
Relative frequency vs. mode index
Bars show the dimensionless frequency parameter (relative spacing), highest bar = highest mode. The active mode is the bright bar. These are ratios, not hertz.
How It Works
Every flexible structure has a set of preferred patterns of motion called mode shapes, each with its own natural frequency. Drive the structure at a mode’s natural frequency and it resonates in that exact shape — a phenomenon engineers call resonance amplification or, in structural dynamics, a resonant response. A node is a point, line or circle that stays still while the rest of the structure moves — the displacement passes through zero there. The number and position of nodes is what distinguishes one mode from the next, and it rises with mode number. This tool draws each mode’s shape and marks the nodes in pink. The set of all a structure’s natural frequencies and mode shapes together is called its modal model or eigenspectrum, and characterising it is the central goal of both experimental modal analysis (EMA) and finite-element analysis (FEA).
The four structures use their standard textbook shape functions. A beam follows Euler–Bernoulli theory: beam vibration in a simply-supported case produces a shape of sin(nπx/L), while clamped ends use cosh − cos − σ(sinh − sin) and free ends use cosh + cos − σ(sinh + sin), both with the published eigenvalues βL (1.875, 4.694, 7.855… for a cantilever; 4.730, 7.853, 10.996… for fixed–fixed and free–free); the natural frequency is proportional to (βL)². A rectangular plate with simply-supported edges produces plate modes of the form sin(mπx/a)·sin(nπy/b), with frequency proportional to (m/a)² + (n/b)². A circular membrane (an ideal drumhead with a fixed rim) vibrates as a Bessel function Jm(αmn·r/R)·cos(mθ), where α is a zero of Jm; the integer m sets the number of nodal diameters and n sets the nodal circles. Cylindrical shell modes with simply-supported ends are shown unrolled (developed) as sin(mπx/L)·cos(nθ), with m axial half-waves and n waves around the circumference.
Two honest cautions. First, these are idealised, undamped, perfectly uniform eigenmodes — they are exactly right for the model, but a real beam or plate has viscous or structural damping, non-ideal supports, thickness variation, joints and added mass that shift the frequencies and blur the shapes; shell frequencies in particular depend strongly on radius, thickness and material in a way this relative view does not capture. Second, the frequency plot is the dimensionless eigenvalue — it shows how the modes are spaced, not their value in hertz. To get real frequencies, feed actual material properties and dimensions into a calculator (try the natural frequency calculator or the structural resonance calculator) or run finite-element or experimental modal analysis on the real part.